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一年级下册第12页的数学作文的答案Mathematics is an important subject for young students to learn. 数学是一个对年轻学生来说很重要的学科，它不仅可以帮助他们提高逻辑思维能力，还可以培养他们的数学素养和解决问题的能力。
First of all, learning mathematics can help children develop problem-solving skills. 首先，学习数学可以帮助孩子们培养解决问题的能力。
Through solving math problems, students learn to analyze and break down complex issues into manageable parts, which is a valuable skill in many areas of life. 通过解决数学问题，学生们学会分析和拆解复杂问题，这是生活中许多领域中都非常有价值的技能。
Secondly, mathematics plays a crucial role in developing logical thinking in young children. 其次，数学在培养年幼儿童的逻辑思维能力方面起着至关重要的作用。
By working through mathematical equations and concepts, students are able to enhance their critical thinking and reasoning abilities. 通过解决数学方程式和概念，学生们可以增强他们的批判性思维和推理能力。
Furthermore, mastering the basics of mathematics early in life can have long-term benefits, both academically and professionally. 此外，在生活早期掌握数学的基础知识可以在学业和职业方面带来长远的好处。
math kangaroo level1 题库Math Kangaroo Level 1是一个专为小学生设计的数学竞赛项目，旨在激发学生对数学的兴趣和热爱。
Level 1的题目涵盖了加减乘除、几何、逻辑推理等多个领域，考察学生的数学运算能力和解决问题的能力。
以下是一些Math Kangaroo Level 1题库中常见的题目类型及解题方法：一、加减乘除题目：1. 题目：有一只小狗，它有3个小骨头，如果再给它5个小骨头，它一共有多少个小骨头？解题方法：将已有的小骨头数目3个和新增的小骨头数目5个相加，即3+5=8，小狗一共有8个小骨头。
2. 题目：小明有12颗糖果，他分给小红2颗，小蓝3颗，小绿4颗，他自己还剩下多少颗糖果？解题方法：将小明拿到的糖果数目12颗减去分给小红、小蓝和小绿的糖果数目2颗、3颗和4颗，即12-2-3-4=3，小明自己还剩下3颗糖果。
二、几何题目：1. 题目：如图，正方形的一条边长为5厘米，求正方形的周长和面积。
解题方法：正方形的周长等于4倍边长，即4*5=20厘米；正方形的面积等于边长的平方，即5*5=25平方厘米。
2. 题目：如图，一个长方形的长为8厘米，宽为3厘米，求长方形的周长和面积。
解题方法：长方形的周长等于长和宽的两倍之和，即2*(8+3)=22厘米；长方形的面积等于长乘以宽，即8*3=24平方厘米。
三、逻辑推理题目：1. 题目：小明说：“我有3个好朋友，他们的名字是小红、小蓝和小绿。
”，小红说：“小蓝是我最好的朋友。
”，小蓝说：“小绿是小明的好朋友。
”，小绿说：“小明的好朋友不是小蓝。
”，请问小红的最好的朋友是谁？解题方法：根据小红的话，小蓝是小红的最好的朋友；根据小蓝的话，小绿是小红的最好的朋友；因此，小绿是小红的最好的朋友。
2. 题目：小狗、小猫和小兔子一起玩，小狗说：“小猫的颜色和小猫的耳朵一样。
”，小猫说：“小狗的颜色和小猫的颜色不一样。
”，小兔子说：“小猫的颜色和小狗的耳朵一样。
指定每天学习计划的英文6:00am-7:00am: Morning Routine- Wake up- Do some stretching exercises- Meditate for 10 minutes- Take a shower and get dressed7:00am-8:00am: Breakfast and Planning- Eat a healthy breakfast- Review the day's schedule and plan out study sessions 8:00am-10:00am: Language Study- Read a chapter of a English textbook and take notes- Watch a documentary or listen to a podcast in English- Write a short essay or journal entry in English10:00am-12:00pm: Science and Math- Work on math problems and exercises- Watch educational videos on science topics- Research and write a summary of a scientific article 12:00pm-1:00pm: Lunch Break- Eat a nutritious lunch- Take a short walk or do some light exercise1:00pm-3:00pm: History and Social Studies- Read a chapter from a history book- Watch a historical documentary- Research and write a report on a historical event or figure 3:00pm-5:00pm: Break and Relaxation- Take a nap or rest- Go for a walk outside- Listen to music or do a creative activity5:00pm-7:00pm: Foreign Language Practice- Review vocabulary and grammar in a foreign language- Practice speaking and listening exercises- Watch a foreign film or TV show with subtitles7:00pm-8:00pm: Dinner and Recreation- Have a balanced dinner- Spend time with family or friends- Engage in a recreational activity or hobby8:00pm-10:00pm: Review and Revision- Review the day's lessons and notes- Complete any unfinished assignments or exercises- Plan out the next day's study schedule10:00pm: Bedtime Routine- Wind down and relax- Reflect on the day's progress and achievements- Read a book or listen to calming music before going to sleepThis daily study plan is designed to help you stay organized, focused, and productive. By following this schedule, you can effectively manage your time and make the most out of your study sessions. Remember to take breaks, stay active, and nourish both your body and mind throughout the day. With dedication and perseverance, you can achieve your learning goals and excel in your academic pursuits.。
My Days of the week1The Rhythm of My Weekly LifeLife is like a beautiful symphony, composed of various notes and rhythms. Each week is a unique movement in this grand composition, filled with different experiences, emotions, and learnings. Let me take you on a journey through my past week, a week that was both ordinary and extraordinary.1. MondayMonday dawned with a burst of energy. I woke up early, feeling the anticipation in the air. It was the day of the much-awaited basketball game. The sun was shining bright, and the court was calling my name. As I stepped onto the court, the adrenaline rush was palpable. The sounds of sneakers screeching, the cheers of the crowd, and the thumping of the ball against the floor created a symphony of its own. We played with passion and determination, giving it our all. Every pass, every shot, and every defense was a moment of excitement. At the end of the game, regardless of the outcome, I felt a sense of achievement. It wasn't just about winning; it was about the teamwork, the effort, and the joy of playing the game Ilove.2. TuesdayTuesday was a day of tranquility. I found myself lost in the world of books at the library. The smell of old pages and the silence that surrounded me provided a haven for my thoughts. I picked up a classic novel and let myself be transported to different times and places. The words on the pages became my companions, and I felt a connection with the characters and their stories. It was a day of reflection and learning, asI absorbed the wisdom and creativity of the authors.3. WednesdayWednesday brought a change of pace as I joined my friends for a volunteer activity. We spent the day helping at a local shelter, providing food and comfort to those in need. Seeing the smiles on the faces of the people we assisted filled my heart with warmth. It made me realize the power of giving and the impact even a small act of kindness can have on someone's life.4. ThursdayThursday was a day of challenges at school. The pile of assignments and the pressure of upcoming exams loomed over me. But I faced them head-on, determined to overcome the obstacles. Late into the night, I satat my desk, poring over textbooks and notes, knowing that hard work would pay off in the end.5. FridayFriday was a relief. The week's stress started to melt away as I spent the evening with my family, sharing stories and laughter over a delicious dinner. It was a reminder of the importance of these precious moments and the love that binds us together.6. SaturdaySaturday was a day for adventure. I went hiking with a group of friends, breathing in the fresh air and taking in the beauty of nature. The climb was tough, but the view from the top was worth every step. It was a day of pushing my limits and discovering my resilience.7. SundayAs the week came to an end on Sunday, I took a moment to reflect. It had been a week filled with ups and downs, joys and challenges. I had learned new things, made memories, and grown as a person. I realized that each day is a gift, and it's up to us to make the most of it.This past week has been a chapter in the story of my life, and I look forward to the many more to come, ready to embrace whatever they may bring.21. The Colorful Canvas of My Weekly DaysLife is like a colorful canvas, and each week is a unique stroke of paint that adds to the masterpiece. Let me take you on a journey through my eventful week, filled with various experiences and emotions.2. MondayMonday was a vibrant start to the week. I joined the school's art club and had the most wonderful time. We were given a task to create a mural for the school hallway. The theme was "Dreams and Aspirations." Working together with my fellow club members, sharing ideas, and bringing our imagination to life on that blank wall was truly amazing. The sense of teamwork and the joy of creating something beautiful made my Monday a memorable one.3. TuesdayTuesday was a day filled with warmth and love. I spent the entire day with my family. We went on a picnic to a nearby park. The sun was shining, and the grass was green. We played games, laughed, and shared stories. It was a simple yet precious time that reminded me of the importance of family bonds.4. WednesdayWednesday brought challenges in my studies. I had a difficult math test that seemed almost impossible to crack. But I refused to give up. I spent hours poring over textbooks, seeking help from my teachers and classmates. Eventually, with determination and hard work, I managed to overcome the hurdles. That day taught me the value of perseverance and the satisfaction that comes with it.5. ThursdayThursday was a bit tumultuous. I had a fierce argument with my best friend over a trivial matter. We both said hurtful things and were left feeling angry and sad. However, by the end of the day, we realized the importance of our friendship and decided to put aside our egos and make up. It was a lesson in forgiveness and understanding.6. FridayFriday was a day of excitement and competition. I participated in a sports event at school - the 100-meter dash. The adrenaline rush as I stood at the starting line, the cheers of the crowd, and the feeling of crossing the finish line with all my might was an experience I'll never forget. It was a moment of victory and pride.7. SaturdaySaturday was a day of giving back. I joined a volunteer activity at a local orphanage. Seeing the smiles on the children's faces as we played with them and distributed gifts filled my heart with a sense of purpose. It made me realize how fortunate I am and the need to spread kindness.8. SundaySunday was a peaceful day of solitude. I spent the entire day at home, curled up with a good book. The quietness of the house allowed me to immerse myself in the world of words, reflecting on the week that had passed.Looking back at this week, it was a mixture of joy, challenges, learning, and growth. Each day was a unique lesson, shaping me into a better person. I have learned to appreciate the good times, face the difficulties head-on, cherish relationships, and find meaning in giving. This colorful canvas of my weekly days is a reminder of the beauty and complexity of life, and I look forward to painting many more such wonderful weeks in the future.3The Rhythm of My Weekly LifeLife is a beautiful symphony, composed of various notes andrhythms. Each week is like a unique movement in this grand symphony, filled with different experiences and emotions. Let me take you through the rhythm of my weekly life.1. Monday is always a fresh start.I joined the school's literature club, where passionate discussions and exchanges of ideas filled the air. We shared our favorite books and poems, and the enthusiasm of my fellow club members inspired me to explore more profound literary works. The day was filled with the excitement of intellectual exploration.2. Tuesday brought challenges.I encountered a difficult math problem during class that seemed insurmountable at first. But I refused to give up. I spent hours poring over textbooks and seeking help from teachers and classmates. Finally, with perseverance and the support of others, I found the solution. This experience taught me the value of persistence and the power of teamwork.3. Wednesday was a day of joy and friendship.I had a wonderful gathering with my friends. We laughed, shared stories, and enjoyed each other's company. It was a time to forget about the stress of school and simply enjoy the moment. The bonds offriendship grew stronger, and I felt truly grateful for having such amazing friends in my life.4. Thursday witnessed my shining moment in the classroom.I actively participated in the discussion, presenting my thoughts and insights clearly. The praise from the teacher and the nods of approval from my classmates filled me with confidence and a sense of achievement. It was a day that made me believe in my abilities and the importance of seizing opportunities to express myself.5. On Friday, I attended an art class after school.I immersed myself in the world of colors and creativity, expressing my emotions and imagination through brushstrokes. The art class was not only a form of relaxation but also a way to develop my artistic skills and appreciation for beauty.6. Saturday was dedicated to outdoor activities.I went hiking with my family, breathing in the fresh air and enjoying the beauty of nature. The mountains, the rivers, and the vast blue sky made me feel small yet connected to the vast world. It was a day of rejuvenation and a reminder of the importance of disconnecting from the digital world and reconnecting with nature.7. Sunday was a day of family time.We cooked together, played games, and shared stories. The warmth and love within the family made me feel safe and cherished. It was a day to recharge and reflect on the week that had passed.Looking back on this week, I have experienced a range of emotions and learned many valuable lessons. I have faced challenges and overcome them, enjoyed the company of friends and family, and pursued my interests and passions. Each day has been a step forward in my journey of growth and self-discovery. I look forward to the new rhythms and melodies that the coming weeks will bring.。
作业一、 汉译英1．唯一性：若数列{n x }收敛，则它只有一个极限.证明. 设lim ,n n x A →∞= 对于给定的正数ε，存在正整数1,N 对于一切 1,n N >有||.2n x A ε-< （1） 又设lim ,n n x B →∞= 对于上述的正数ε，存在正整数2,N 对于一切2,n N >有||.2n x B ε-< （2） 取12max{,},N N N =当,n N >（1）与（2）式都成立，此时有|||()()|||||,22n n n n A B x B x A x A x B εεε-=---≤-+-<+=即||,A B ε-<由于A ，B 均为常数，而ε是任意正数，故只能.A B =2．作业一、 汉译英1．唯一性：若数列{n x }收敛，则它只有一个极限. 证明. 设lim ,n n x A →∞= 对于给定的正数ε，存在正整数1,N 对于一切 1,n N >有||.2n x A ε-< （1） 又设lim ,n n x B →∞= 对于上述的正数ε，存在正整数2,N 对于一切2,n N >有||.2n x B ε-< （2） 取12max{,},N N N =当,n N >（1）与（2）式都成立，此时有|||()()|||||,22n n n n A B x B x A x A x B εεε-=---≤-+-<+=即||,A B ε-<由于A ，B 均为常数，而ε是任意正数，故只能.A B =2． 基于学生数学能力结构的分析提出的培养建议摘要 公民数学素养的提高无论对于社会发展还是其个人发展都具有重要意义。
为了提高中小学数学教育质量，必须明确中小学数学能力结构。
中小学生的数学能力可以分为两个层次，运算能力、空间想象能力、信息处理能力是第一个层次，逻辑思维能力和问题解决能力是第二个层次；模式能力在这两个层次之间起着非常重要的桥梁作用。
Math Section------------------------------------------------------------------------------------------------------------ Q1: If 615.0 = x 1, what is the value of x ?A. 30B. 3C. 56D. 31E. 301Answer:------------------------------------------------------------------------------------------------------------ Q2:If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?A. 144B. 132C. 66D. 33E. 23Answer:------------------------------------------------------------------------------------------------------------ Q3:What is the remainder when the two-digit, positive integer x is divided by 3 ?(1) The sum of the digits of x is 5.(2) The remainder when x is divided by 9 is 5.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q4:If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?(1) n is odd.(2) n is greater than 20.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q5:In 1993 Mr. Jacobs paid 4.8 percent of his taxable income in state taxes. In 1994 what percent of Mr. Jacobs’ tax able income did he pay in state taxes?(1) In 1993 Mr. Jacobs’s taxable income was $42,500.(2) In 1994 Mr. Jacobs paid $232 more in state taxes than he did in 1993.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q6:What is the greatest prime factor of 2100– 296 ?A.2B. 3C. 5D.7E.11Answer:------------------------------------------------------------------------------------------------------------ Q7:A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?(1) It is possible to assign each of 3n students to one of m classrooms so that eachclassroom has the same number of students assigned to it.(2) It is possible to assign each of 13n students to one of m classrooms so that eachclassroom has the same number of students assigned to it.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q8:wlw―The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?A.15B.20C.25D.30E.40Answer:------------------------------------------------------------------------------------------------------------ Q9:If xyz > 0, is xy2z3 < 0 ?(1) y < 0(2) x > 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------Q10:If the average (arithmetic mean) of positive integers x , y , and z is 10, what is the greatest possible value of z ?A. 8B. 10C. 20D. 28E. 30Answer:------------------------------------------------------------------------------------------------------------ Q11:If n is positive, which of the following is equal to nn -+11?A. 1B. 12+nC. nn 1+D. 1+n – nE.1+n + nAnswer:------------------------------------------------------------------------------------------------------------ Q12:What was the percent increase in the average (arithmetic mean) contribution per member of a certain public radio station from 1985 to 1995 ?(1) Total contributions by members increased from $505,210 in 1985 to $1,225,890in 1995.(2) The number of members exactly doubled from 1985 to 1995.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q13:43 + 43 + 43 + 43 =A. 44B. 46C. 48D. 49E.412Answer:------------------------------------------------------------------------------------------------------------ Q14:In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?A.$1,326B.$1,352C.$1,378D.$2,652E.$2,756Answer:------------------------------------------------------------------------------------------------------------ Q15:x- > 0 ?Is xy + z = z, is y(1) x≠ 0(2) y = 0A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q16:Is k = 2 ?(1) k2 = 4-(2) k = 2A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q17:If n is the greatest positive integer for which 2n is a factor of 10!, then n =A.2B. 4C. 6D.8E.10Answer:------------------------------------------------------------------------------------------------------------ Q18:Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat’s investment plus interest at the end of 5 years?A.5(0.08x)B.5(1.08x)C.[1 + 5(0.08)]xD.(1.08)5xE.(1.08x)5Answer:------------------------------------------------------------------------------------------------------------ Q19:How many 4-digit positive integers are there in which all 4 digits are even?A.625B.600C.500D.400E.256Answer:------------------------------------------------------------------------------------------------------------ Q20:In the figure shown, triangle ABC is inscribed in the circle. What is the circumference of the circle?(1) AB is a diameter of the circle.(2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q21:Color X ink is created by blending red, blue, green, and yellow inks in the ratio 6 : 5 : 2 : 2. What is the number of liters of green ink that was used to create a certain batch of color X ink?(1) The amount of red ink used to create the batch is 2 liters more than the amountof blue ink used to create the batch.(2) The batch consists of 30 liters of color X ink.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q22:Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?A.56B.57C.58D.61E.63Answer:------------------------------------------------------------------------------------------------------------ Q23:The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?A.2x - 8B.x - 4C.8 - 2xD.16 - xxE.8 -2Answer:------------------------------------------------------------------------------------------------------------ Q24:lThe graph of which of the following equations is a straight line that is parallel to line l in the figure above?A.3y– 2x = 0B.3y + 2x = 0C.3y + 2x = 6D.2y– 3x = 6E.2y + 3x = -6Answer:------------------------------------------------------------------------------------------------------------ Q25:If each of the 8 employees working on a certain project received an award, was the amount of each award the same?(1) The standard deviation of the amounts of the 8 awards was 0.(2) The total amount of the 8 awards was $10,000.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q26:What is the value of x2 ?(1) 5 < x2 < 10(2) x is an integer.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q27:A box contains exactly 24 balls, of which 12 are red and 12 are blue. If two balls are to be picked from this box at random and without replacement, what is the probability that both balls will be red?11A.461B.45C.1217D.4019E.40Answer:------------------------------------------------------------------------------------------------------------ Q28:If x2– 2 < 0, which of the following specifies all the possible values of x ?A.0 < x < 2B.0 < x < 2C.-2 < x < 2D.-2 < x < 0E.-2 < x < 2Answer:------------------------------------------------------------------------------------------------------------ Q29:Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?(1) She bought $4.40 worth of stamps.(2) She bought an equal number of $0.15 stamps and $0.29 stamps.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q30:Machine A , operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B , operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C , operating alone at its constant rate, produces 500 feet of the same fiber in 5 hours. How many hours will it take machines A , B , and C , operating together at their respective constant rates, to produce 1,000 feet of the fiber?A. 3160B. 715C. 1125D. 310E. 320Answer:------------------------------------------------------------------------------------------------------------ Q31:A certain right triangle has sides of length x , y , and z , where x < y < z . If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?A. y > 2B. 23 < y < 2C. 32 < y < 23D. 43 < y < 32E. y < 43Answer:------------------------------------------------------------------------------------------------------------ Q32:What is the value of p r ?(1) p = 1 (2) r = 1A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q33:During a spring season, a certain glacier surged at the rate of 1 mile per 100 days. What was its rate in feet per hour? (1 mile = 5,280 feet)5A.1111B.5C.55D.110E.22,000Answer:------------------------------------------------------------------------------------------------------------ Q34:If 2x2–y2 = 2xy, then (x + y)2 =A.x2B.3x2C.4xyD.2y2E.–y2Answer:------------------------------------------------------------------------------------------------------------ Q35:The total charge to rent a car for one day from Company J consists of a fixed charge of $15.00 plus a charge of $0.20 per mile driven. The total charge to rent a car for one day from Company K consists of a fixed charge of $20.00 plus a charge of $0.10 per mile driven. Is the total charge to rent a car from Company J for one day and drive it x miles less than $25.00 ?(1) The total charge to rent a car from Company K for one day and drive it x miles isless than $25.00.(2) x < 50A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q36:If x, y, and z are positive integers, is xz even?(1) xy is even.(2) yz is even.A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.Answer:------------------------------------------------------------------------------------------------------------ Q37:In a large investment firm, 25 percent of the male employees and 30 percent of the female employees are stockbrokers. If 60 percent of the firm’s employees are males, what is the ratio of the number of male stockbrokers to the number of female stockbrokers?A.6 to 5B. 5 to 4C. 3 to 2D.4 to 3E. 5 to 2Answer:------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ Answers:。
Mathematica入门教程第1篇第1章MATHEMATICA概述 (3)1.1 M ATHEMATICA的启动与运行 (3)1.2 表达式的输入 (4)1.3 M ATHEMATICA的联机帮助系统 (6)第2章MATHEMATICA的基本量 (8)2.1 数据类型和常数 (8)2.2 变量 (10)2.3 函数 (11)2.4 表 (14)2.5 表达式 (17)2.6 常用的符号 (19)2.7 练习题 (19)第2篇第3章微积分的基本操作 (20)3.1 极限 (20)3.2 微分 (20)3.3 计算积分 (22)3.4 无穷级数 (24)3.5 练习题 (24)第4章微分方程的求解 (26)4.1 微分方程解 (26)4.2 微分方程的数值解 (26)4.3 练习题 (27)第3篇第5章MATHEMATICA的基本运算 (28)5.1 多项式的表示形式 (28)5.2 方程及其根的表示 (29)5.3 求和与求积 (32)5.4 练习题 (33)第6章函数作图 (35)6.1 基本的二维图形 (35)6.2 二维图形元素 (40)6.3 基本三维图形 (42)6.4 练习题 (46)第4篇第7章MATHEMATICA函数大全 (48)7.1 运算符和一些特殊符号，系统常数 (48)7.2 代数计算 (49)7.3 解方程 (50)7.4 微积分 (50)7.5 多项式函数 (51)7.6 随机函数 (52)7.7 数值函数 (52)7.8 表相关函数 (53)7.9 绘图函数 (54)7.10 流程控制 (57)第8章MATHEMATICA程序设计 (59)8.1 模块和块中的变量 (59)8.2 条件结构 (61)8.3 循环结构 (63)8.4 流程控制 (65)8.5 练习题 (67)--------------习题与答案在68页-------------------第1章Mathematica概述1.1 Mathematica的启动与运行Mathematica是美国Wolfram研究公司生产的一种数学分析型的软件，以符号计算见长，也具有高精度的数值计算功能和强大的图形功能。
amc12考试知识点The AMC 12 exam covers a wide range of topics in high school mathematics. Here are some of the key knowledge points that you should be familiar with:1. Algebra: concepts such as linear equations, inequalities, systems of equations, quadratic equations, functions, polynomial operations, and logarithmic and exponential functions.2. Geometry: Euclidean geometry, including properties of lines, angles, triangles, quadrilaterals, circles, transformations, congruence and similarity, and relations between area and perimeter/volume.3. Number Theory: divisibility, prime factorization, modular arithmetic, sequences, series, and basic properties of integers.4. Probability and Statistics: basic probability concepts, counting methods, permutations and combinations, expected value, and basic statistical measures.5. Trigonometry: basic trigonometric functions, trigonometric identities, equations and graphs, and solving trigonometric equations.6. Pre-Calculus: properties and graphs of elementary functions (polynomial, exponential, logarithmic, and trigonometric), solving equations involving these functions, and basic properties of vectors and matrices.7. Discrete Mathematics: logical reasoning, combinatorics, sets, relations, and mathematical induction.It is important to note that the AMC 12 exam is designed to test problem-solving skills and mathematical reasoning rather than pure memorization of formulas and facts. So, it is alsorecommended to practice with past exam questions and develop problem-solving strategies.。
Principles of Mathematics 12: Explained! 273Permutations & CombinationsLesson 1, Part One: The Fundamental Counting PrincipleThe Fundamental Counting Principle: This is an easy way to determine howmany ways you can arrange items. The following examples illustrate how to use it:Example 1: How many ways can you arrange the letters in the word MICRO?The basic idea is we have 5 objects, and 5 possible positions they can occupy.Example 2: How many ways can 8 different albums be arranged?We could approach this question in the same way as the last one by using the spaces and multiplying all the numbers, but there is a shorter way. The factorial function on your calculator will perform this calculation for you!8! = 8 • 7 • 6 …. 2 •1 8! = 40320Questions:1) How many ways can the letters in the word PENCIL be arranged?TI-83 Info You can get the factorial function using: Math Prb !2) If there are four different types of cookies, how many ways can you eat all of them? 3) If three albums are placed in a multi-disc stereo, how many ways can the albums be played? 4) How many ways can you arrange all the letters in the alphabet? 5) How many ways can you arrange the numbers 24 through 28 (inclusive)?Answers:1) 6! = 720 2) 4! = 24 3) 3! = 6 4) 26! = 4.03 • 1026 5) 5! = 120Principles of Mathematics 12: Explained! 274Permutations & CombinationsLesson 1, Part Two: Repetitions Not AllowedRepetitions Not Allowed: In many cases, some of the items we want toarrange are identical. For example, in the word TOOTH, if we exchange the places of the two O’s, we still get TOOTH. Because of this, we have to get rid of extraneous cases by dividing out repetitions.Example 1: How many ways can you arrange the letters in the word THESE?Do this as a fraction. Factorial the total number of letters and put this on top. Factorial the repeated letters and put them on the bottom.5! 120 = = 60 2! 2Example 2: How many ways can you arrange the letters in the word REFERENCE?9! 362880 = = 7560 2!•4! 2•24Questions:1) How many ways can the letters in the word SASKATOON be arranged? 2) How many ways can the letters in the word MISSISSIPPI be arranged? 3) How many ways can the letters in the word MATHEMATICS be arranged? 4) If there are eight cookies (4 chocolate chip, 2 oatmeal, and 2 chocolate) in how many different orders can you eat all of them?TI-83 Info Make sure you put the denominator in brackets or you’ll get the wrong answer!Answers:5) If a multiple choice test has 10 questions, of which one is answered A, 4 are answered B, 3 are answered C, and 2 are answered D, how many answer sheets are possible?1) 2) 3) 4) 5)9! = 45360 2!• 2!• 2! 11! = 34650 4!• 4!• 2! 11! = 4989600 2!• 2!• 2! 8! = 420 4!• 2!• 2! 10! = 12600 4!•3!• 2!Principles of Mathematics 12: Explained! 275Permutations & CombinationsLesson 1, Part Three: Repetitions Are AllowedRepetitions Are Allowed: Sometimes we are interested in arrangementsallowing the use of items more than once.Example 1: There are 9 switches on a fuse box. How many different arrangements are there?Each switch has two possible positions, on or off. Placing a 2 in each of the 9 positions, we have 29 = 512.Example 2: How many 3 letter words can be created, if repetitions are allowed?There are 26 letters to choose from, and we are allowed to have repetitions. There are 263 = 17576 possible three letter words.Questions:1) If there are 4 light switches on an electrical panel, how many different orders of on/off are there?2) How many 5 letter words can be formed, if repetitions are allowed?3) How many three digit numbers can be formed? (Zero can’t be the first digit)There are ten digits in total, from zero to nine.4) A coat hanger has four knobs. If you have 6 different colors of paint available, how many different ways can you paint the knobs?Answers:1) 24 = 16 2) 265 = 11881376 3) 9 • 10 • 10 = 900 4) 64 = 1296Principles of Mathematics 12: Explained! 276Permutations & CombinationsLesson 1, Part Four: Arranging A SubsetArranging a subset of items: Sometimes you will be given a bunch ofobjects, and you want to arrange only a few of them: Example 1: There are 10 people in a competition. How many ways can the top three be ordered?A fast way to do questions like this is to use the nPr feature on your calculator. n is the total number of items. r is the number of items you want to order. For Example 1, you would type:10 Math PRBn rSince only 3 positions can be filled, we have 3 spaces. Multiplying, we get 720.Penter3Example 2: There are 12 movies playing at a theater, in how many ways can you see two of them consecutively?You could use the spaces, but let’s try this question with the permutation feature. There are 12 movies, and you want to see 2, so type 12P2 into your calculator, and you’ll get 132.ORExample 3: How many 4 letter words can be created if repetitions are not allowerd?The answer is: 26P4 = 358800ORQuestions:1) How many three letter words can be made from the letters of the word KEYBOARD 2) If there are 35 songs and you want to make a mix CD with 17 songs, how many different ways could you arrange them? 3) There are six different colored balls in a box, and you pull them out one at a time. How many different ways can you pull out four balls? 4) A committee is to be formed with a president, a vice-president, and a treasurer. There are 10 people to be selected from. How many different committees are possible? 5) A baseball league has 13 teams, and each team plays each other twice; once at home, and once away. How many games are scheduled?Answers:1) 8P3 =336 2) 35P17 = 1.6 • 1024 3) 6P4 = 360 4) 10P3 = 720 5) 13P2 = 156Principles of Mathematics 12: Explained! 277Permutations & CombinationsLesson 1, Part Five: Specific PositionsSpecific Positions: Frequently when arranging items, a particular positionmust be occupied by a particular item. The easiest way to approach these questions is by analyzing how many possible ways each space can be filled. Example 1: How many ways can Adam, Beth, Charlie, and Doug be seated in a row if Charlie must be in the second chair?The answer is 6.Example 2: How many ways can you order the letters of KITCHEN if it must start with a consonant and end with a vowel?The answer is 1200.Example 3: How many ways can you order the letters of TORONTO if it begins with exactly two O’s?Exactly Two O’s means the first 2 letters must be O, and the third must NOT be an O. If the question simply stated two O’s, then the third letter could also be an O, since that case wasn’t excluded.Don’t forget repetitions! The answer from the left will be the numerator with repetitions divided out. 5763!•2!= 48Principles of Mathematics 12: Explained! 278Permutations & CombinationsLesson 1, Part Five: Specific PositionsQuestions:1) Six Pure Math 30 students (Brittany, Geoffrey, Jonathan, Kyle, Laura, and Stephanie) are going to stand in a line: How many ways can they stand if:a) Stephanie must be in the third position?b) Geoffrey must be second and Laura third?c) Kyle can’t be on either end of the line?d) Boys and girls alternate, with a boy starting the line?e) The first three positions are boys, the last three are girls?f) A girl must be on both ends?g) The row starts with two boys?h) The row starts with exactly two boys?i) Brittany must be in the second position, and a boy must be in the third?2) How many ways can you order the letters from the word TREES if:a) A vowel must be at the beginning?b) It must start with a consonant and end with a vowel?c) The R must be in the middle?d) It begins with an E?e) It begins with exactly one E?f) Consonants & vowels alternate?Principles of Mathematics 12: Explained! 279Permutations & CombinationsLesson 1, Part Five: Specific Positions1) a) If Stephanie must be in the third position, place a one there to reserve her spot. You can then place the remaining 5 students in any position.Answers:b) Place a 1 in the second position to reserve Geoffrey’s spot, and place a 1 in the third position to reserve Laura’s spot. Place the remaining students in the other positions. c) Since Kyle can’t be on either end, 5 students could be placed on one end, then 4 at the other end. Now that 2 students are used up, there are 4 that can fill out the middle. d) Three boys can go first, then three girls second. Two boys remain, then two girls. Then one boy and one girl remain. e) Three boys can go first, then place the girls in the next three spots. f) Three girls could be placed on one end, then 2 girls at the other end. There are four students left to fill out the middle. g) Three boys could go first, then 2 boys second. Once those positions are filled, four people remain for the rest of the line. h) Three boys could go first, then two boys second. The third position can’t be a boy, so there are three girls that could go here. Then, three people remain to fill out the line. i) Place a 1 in the second position to reserve Brittany’s spot, then 3 boys could go in the third position. Now fill out the rest of the line with the four remaining people. a) There are two vowels that can go first, then four letters remain to (Answer = 48 / 2! = 24) fill out the other positions.2) Note that since there are 2 E’s, all answers MUST be divided by 2! to eliminate repetitions.b) Three consonants could go first, and two vowels could go last. There are three letters to fill out the remaining positions. (Answer = 36 / 2! = 18) c) Place a 1 in the middle spot to reserve the R’s spot. Then fill out the rest of the spaces with the remaining 4 letters. (Answer = 24 / 2! = 12) d) Two E’s could go in the first spot, then fill the remaining spaces (Answer = 48 / 2! = 24) with the 4 remaining letters. e) Two E’s could go in the first spot, but the next letter must NOT be an E, so there are 3 letters that can go here. Fill out the three last spaces with the 3 remaining letters.(Answer = 36 / 2! = 18)f) Three consonants could go first, then 2 vowels, and so on.(Answer = 12 / 2! = 6)Principles of Mathematics 12: Explained! 280Permutations & CombinationsLesson 1, Part Six: Adding PermutationsMore than one case (Adding): Given a set of items, it is possible toform multiple groups by ordering any 1 item from the set, any 2 items from the set, and so on. If you want the total arrangements from multiple groups, you have to ADD the results of each case.Example 1: How many words (of any number of letters) can be formed from CANSSince we are allowed to have any number of letters in a word, we can have a 1 letter word, a 2 letter word, a 3 letter word, and a 4 letter word. We can’t have more than 4 letters in a word, since there aren’t enough letters for that!We could also write this using permutations: 4P1 + 4P2 + 4P3 + 4P4 = 64The answer is 64Example 2: How many four digit positive numbers less than 4670 can be formed using thedigits 1, 3, 4, 5, 8, 9 if repetitions are not allowed?We must separate this question into different cases. Numbers in the 4000’s have extra restrictions.Case 1 - Numbers in the 4000’s: There is only one possibility for the first digit {4}. The next digit hasthree possibilities. {1, 3, 5}. There are 4 possibilities for the next digit since any remaining number can be used, and 3 possibilities for the last digit.Case 2 - Numbers in the 1000’s and 3000’s: There are two possibilities for the first digit {1, 3}. Anything goes for the remaining digits, so there are 5, then 4, then 3 possibilities.Add the results together: 36 + 120 = 156Questions:Answers:3) 1) 6P1 + 6P2 + 6P3 = 156 2) 8P3 + 8P4 + 8P5 = 8736There are two cases: The first case has five1) How many one-letter, two-letter, or three-letter words can be formed from the word PENCIL? 2) How many 3-digit, 4-digit, or 5-digit numbers can be made using the digits of 46723819? 3) How many numbers between 999 and 9999 are divisible by 5 and have no repeated digits?as the last digit, the second case has zero as the last digit. Remember the first digit can’t be zero!Add the results to get the total: 952Principles of Mathematics 12: Explained! 281Permutations & CombinationsLesson 1, Part Seven: Items Always TogetherAlways Together: Frequently, certain items must always be kept together. To dothese questions, you must treat the joined items as if they were only one object.Example 1: How many arrangements of the word ACTIVE are there if C & E must always be together?There are 5 groups in total, and they can be arranged in 5! ways. The letters EC can be arranged in 2! ways. The total arrangements are 5! x 2! = 240Example 2: How many ways can 3 math books, 5 chemistry books, and 7 physics books be arranged on a shelf if the books of each subject must be kept together?There are three groups, which can be arranged in 3! ways. The physics books can be arranged in 7! ways. The math books can be arranged in 3! ways. The chemistry books can be arranged in 5! ways. The total arrangements are 3! x 7! x 3! x 5! = 21772800Questions:1) How many ways can you order the letters in KEYBOARD if K and Y must always be kept together?2) How many ways can the letters in OBTUSE be ordered if all the vowels must be kept together?3) How many ways can 4 rock, 5 pop, & 6 classical albums be ordered if all albums of the same genre must be kept together?Answers:1) 2) 3).7! • 2! = 10080 4! • 3! = 1443! • 4! • 5! • 6! = 12441600Principles of Mathematics 12: Explained! 282Permutations & CombinationsLesson 1, Part Eight: Items Never TogetherNever Together: If certain items must be kept apart, you will need to figureout how many possible positions the separate items can occupy. Example 1: How many arrangements of the word ACTIVE are there if C & E must never be together?Method 1:First fill in the possible positions for the letters ATIV Next draw empty circles representing the positions C & E can go.You can place C & E in these spaces 5P2 ways. Get the answer by multiplying: 4! x 5P2 = 480Method 2:First determine the number of ways ACTIVE can be arranged if C & E are ALWAYS together. (5! • 2!) Then subtract that from the total number of possible arrangements without restrictions (6!) The answer is 6! – (5! • 2!) = 480 ***This method does not work if there are more then two items you want to keep separate.Example 2: How many arrangements of the word DAUGHTER are there if none the vowels can ever be together?First fill in the possible positions for the consonants Next draw empty circles representing the positions the vowels can go.You can place the 3 vowels in the 6 spaces in 6P3 ways. 5! x 6P3 = 14400Example 3: In how many ways can the letters from the word EDITOR be arranged if vowels and consonants alternate positions?First determine the number of arrangements with consonants first in the arrangement: Then determine the number of arrangements with vowels coming first: Add the results to get 72 possible arrangements.Questions:1) How many ways can you order the letters in QUEST if the vowels must never be together? 2) If 8 boys and 2 girls must stand in line for a picture, how many line-up’s will have the girls separated from each other? 3) How many ways can you order the letters in FORTUNES if the vowels must never be together? 4) In how many ways can the letters AEFGOQSU be arranged if vowels and consonants alternate positions? Answers:1) 3! • 4P2 = 72 or 5! – (4! • 2!) = 72 2) 8! • 9P2 = 2903040 or 10! – (9! • 2!) = 2903040 3) 5! • 6P3 =14400 4) Consonants first: 4×4×3×3×2×2×1×1 = 576 Vowels first: 4×4×3×3×2×2×1×1 = 576 Add results: 576 + 576 = 1152Principles of Mathematics 12: Explained! 283。
英语一周学习计划怎么画Day 1: MondayMorning: 9:00am - 12:00pm- Review vocabulary and grammar from last week's lessons- Complete a listening comprehension exercise- Read a short story and answer comprehension questionsAfternoon: 1:00pm - 3:00pm- Watch a TED talk or other English-speaking video- Take notes on key points and new vocabulary- Practice summarizing the main ideas in EnglishEvening: 7:00pm - 9:00pm- Join a language exchange meetup or online chat- Engage in conversation with native English speakers- Take note of any new words or phrases and practice using them in conversation Day 2: TuesdayMorning: 9:00am - 12:00pm- Work on exercises from an English grammar workbook- Focus on a specific grammar point (e.g. past continuous tense)- Practice writing sentences and paragraphs using the grammar point Afternoon: 1:00pm - 3:00pm- Read a chapter from an English novel or non-fiction book- Highlight new vocabulary and look up definitions- Write a short summary of the chapter in EnglishEvening: 7:00pm - 9:00pm- Listen to an English podcast or audio book- Take notes on the content and vocabulary- Practice repeating or summarizing key points in EnglishDay 3: WednesdayMorning: 9:00am - 12:00pm- Practice speaking and pronunciation exercises- Record myself reading a passage or dialogue- Listen for mistakes in pronunciation and intonation Afternoon: 1:00pm - 3:00pm- Write a letter or email to a friend in English- Practice using informal language and idiomatic expressions- Review and edit the writing for grammar and vocabulary Evening: 7:00pm - 9:00pm- Watch an English movie or TV show with subtitles- Pay attention to colloquial language and slang- Take note of any new vocabulary and practice using it in context Day 4: ThursdayMorning: 9:00am - 12:00pm- Review and practice speaking on various topics- Record myself giving a short presentation or speech- Listen for fluency, coherence, and accuracyAfternoon: 1:00pm - 3:00pm- Work on a language learning app or website- Complete exercises for vocabulary, grammar, and pronunciation - Set and achieve a daily goal for points or progressEvening: 7:00pm - 9:00pm- Participate in an online language challenge or quiz- Test my knowledge of English idioms, vocabulary, and grammar- Review the results and learn from any mistakesDay 5: FridayMorning: 9:00am - 12:00pm- Explore English language resources on the internet- Find and save articles, videos, and exercises for future study- Organize and categorize the resources for easy accessAfternoon: 1:00pm - 3:00pm- Engage in a language learning game or activity- Play a word puzzle, memory game, or trivia quiz in English- Challenge myself to improve my score or timeEvening: 7:00pm - 9:00pm- Reflect on the week's progress and achievements- Write a journal entry in English about my language learning experience - Set specific goals and tasks for the upcoming weekDay 6: SaturdayMorning: 9:00am - 12:00pm- Work on a language project or creative activity- Write a short story, poem, or essay in English- Edit and revise the writing for structure, style, and accuracy Afternoon: 1:00pm - 3:00pm- Join an English language meetup or club meeting- Engage in group discussions and activities- Share and receive feedback on my language skillsEvening: 7:00pm - 9:00pm- Attend an English language event or performance- Watch a play, concert, or cultural presentation in English- Take note of new words and expressions used in the eventDay 7: SundayMorning: 9:00am - 12:00pm- Review the week's vocabulary and grammar- Organize flashcards or a vocabulary notebook- Practice recalling and using the new words and structuresAfternoon: 1:00pm - 3:00pm- Engage in a language immersion activity- Listen to English music, radio, or news broadcasts- Try to understand and interpret the content without translationEvening: 7:00pm - 9:00pm- Relax and enjoy an English language leisure activity- Read for pleasure, play a game, or watch a favorite show in English- Reflect on the overall progress and plan for the upcoming weekIn conclusion, this one-week learning plan is designed to enhance the English language skills of any learner who actively participates. By engaging in a variety of reading, writing, listening, and speaking activities, the learner can improve their vocabulary, grammar, pronunciation, and overall fluency in the language. Additionally, incorporating language exchange, cultural events, and creative projects can enhance the learner's cultural understanding and appreciation of the English language. This plan is intended to be adaptable and flexible to suit the individual needs and interests of the learner. With consistent effort and practice, the learner can make significant progress in their language learning journey within just one week.。
小学三年级下册英语模拟卷(答案和解释)(共50道题)下面有答案和解题分析一、综合题1.What animal is known as King of the Jungle?A. ElephantB. TigerC. LionD. Bear2.Every Sunday, my family _______ (cook) a big meal together. My father _______ (make) soup, and my mother _______ (prepare) the main dishes. My sister and I _______ (set) the table and _______ (serve) the food.3.What is the opposite of "full"?A. EmptyB. HeavyC. TallD. Slow4.Which of these is used to cut paper?A. KnifeB. ScissorsC. ForkD. Cup5.What do we wear to keep our feet warm in winter?A. HatB. GlovesC. SocksD. Scarf6.I _______ (see) a dog in the park.7.What is the opposite of "slow"?A. QuickB. TallC. HotD. Quiet8.She _______ (is / are / am) always kind to others.9.Anna and her friends are at the playground. They are playing a game of __________. Anna is the __________, and she tries to catch the other children. Her friend Lily is running really fast, but Anna manages to tag her. They all laugh and have a lot of__________ playing together.10.My friend, Lily, ________ (love) to sing. She ________ (sing) in the school choir. Last year, she ________ (perform) in a big concert. It ________ (be) amazing!11.This weekend, I _______ (help) my parents in the garden. We _______ (plant) some flowers and _______ (water) the plants. I _______ (be) very happy to see theflowers grow. In the afternoon, we _______ (sit) outside and _______ (enjoy) the fresh air. My little brother _______ (pick) some flowers and _______ (give) them to my mom. It _______ (be) a relaxing day, and we _______ (have) a lot of fun.12.What do we use to cut food?A. KnifeB. SpoonC. ForkD. Plate13.Which one is a vegetable?A. AppleB. BananaC. CarrotD. Orange14.You are at a restaurant with your family. A waiter brings you a menu and asks what you would like to eat. What are you doing?A. ShoppingB. Eating at a restaurantC. Playing a gameD. Watching TV15.I ______ (have) a pet hamster. His name ______ (be) Brownie. He ______ (live) ina small cage in my room. Every day, I ______ (feed) him seeds, and I ______ (give) him fresh water. He ______ (like) to run on his wheel.16.What is the opposite of “hot”?A. WarmB. CoolC. ColdD. Big17.Which one is the opposite of "short"?A. TallB. FastC. HeavyD. Light18.We _______ (take) a trip to the beach every summer.19.Which of these is the opposite of "big"?A. SmallB. TallC. LightD. Heavy20.She _______ her homework right now.21.I _______ (am / is / are) watching TV right now.22.Which of these is a fruit?A. TomatoB. OnionC. PotatoD. Carrot23.We _______ (be) at the museum last Saturday.24.Which of these is a body part?A. TableB. FootC. PlateD. BookA. ElephantB. DogC. BirdD. Cow26.This is my family. My father is a __________ and my mother is a __________. I have one __________ and two __________. We live in a __________ near a__________. Every weekend, we like to go to the __________ to play. My father likes to play __________, and my mother likes to walk. My brother likes to play with his__________, and my sister likes to play with her __________. After playing, we usually have __________ in the park and then go home in the afternoon. I love my family very much.27.Every Saturday, Lisa and her parents go to the __________ (1) to buy fresh__________ (2). Lisa loves to eat __________ (3) because they are very sweet. Her mother buys __________ (4) for dinner, and her father likes to buy __________ (5) for breakfast. They also stop by the __________ (6) to get some __________ (7) for the week. Lisa always enjoys these trips because they get to buy many __________ (8).28.We _______ (take / takes) the bus to school.29.Which of these is a fruit?A. PotatoB. OrangeC. OnionD. Carrot30.I _______ (was / were / is) playing with my friends yesterday.31.Which fruit is yellow and can be peeled?A. AppleB. BananaC. CherryD. Grapes32.In the morning, I wake up at __________. I get out of bed and go to the__________ to wash my __________ and brush my __________. Then, I get dressed in my __________. After breakfast, I take my __________ and go to __________. The school is very __________, and the __________ is full of students. I like school becauseI can learn new __________ and play with my __________.33.We __________ (visit) a museum yesterday. It __________ (be) a history museum, and we __________ (learn) about ancient Egypt. My favorite part __________ (be) the mummies. I __________ (take) lots of pictures. After the museum, we __________ (eat) lunch at a nearby cafe.34.Which of these is a shape?A. CircleB. AppleC. SpoonD. Book35.Which of the following is used for writing?A. SpoonB. PenC. ForkD. KnifeA. CowB. DogC. TigerD. Pig37.What color is grass?A. BlueB. GreenC. RedD. Yellow38.Jack is at school today. He has a lot of homework. First, he needs to finish his__________ homework. The teacher asked them to read a chapter from the __________. Jack writes down the answers to the questions and checks his __________. He also needs to study for his __________ test tomorrow. After finishing, Jack feels tired but proud of his work.39.Which of these is a cold drink?A. Hot waterB. LemonadeC. CoffeeD. Tea40.What do we use to eat pizza?A. SpoonB. KnifeC. ForkD. Hands41.Which one is a color?A. CakeB. TableC. RedD. Car42.Which of these is a season?A. JanuaryB. SummerC. MondayD. Marchst Saturday, my family went to the zoo. We saw many animals like lions, tigers, and elephants. My little brother liked the monkeys the most because they were very funny. My sister liked the pandas because they were very cute. My mother took many pictures of the animals, and my father bought some snacks. We also went to the playground and played on the swings. In the evening, we went to a restaurant to have dinner. It was a very fun day, and we all had a great time.44.I __________ (1) to the library every weekend. I __________ (2) read books there. Last weekend, I __________ (3) borrow a book about dinosaurs. I __________ (4) read it at home. My little sister __________ (5) borrow a book, too.45.How many days are there in a week?A. 6B. 7C. 8D. 546.Tom and his family are having a picnic in the park. They brought a big __________ with sandwiches, fruit, and drinks. Tom’s dad set up a __________ to keep them cool in the hot sun. Tom and his sister Emma are playing __________ with a frisbee on the grass.After eating, they will take a walk around the park and watch the __________ swimming in the pond.47.Which one is a school subject?A. BreadB. MathC. TableD. Chair48.Which of these animals is a mammal?A. FishB. BirdC. WhaleD. Lizard49.I __________ (study) English every day after school. My teacher __________ (teach) me new words and __________ (help) me with my pronunciation. I __________ (feel) that I __________ (improve) my skills.50.They _______ (live) in a big house.(答案及解释)。
Going home to do homework is a common part of a students daily routine.Heres a detailed look at the process in English:1.Understanding the Assignment:First,its important to understand what the homework entails.This could be reading a chapter,solving math problems,or writing an essay.In English,you might say,I need to finish reading Chapter5for my English class.2.Gathering Materials:Before starting,gather all the necessary materials.This could include textbooks,notebooks,pens,and any handouts provided by the teacher.You might say,Ive got all my books and notes ready to start my homework.3.Creating a Schedule:Organizing the homework by subject or due date can help manage time effectively.For example,Ill start with math because its due tomorrow,and then Ill move on to history.4.Finding a Quiet Place:A quiet and comfortable environment is conducive to focused work.You might say,Im going to my room where its quiet so I can concentrate on my homework.5.Starting the Work:Begin by tackling the most challenging or timeconsuming tasks first. For instance,Ill start with the math problems since they take me the longest.6.Taking Breaks:Its important to take short breaks to avoid burnout.You could say,Ill take a10minute break after finishing this chapter.7.Reviewing the Work:After completing the homework,review it to check for errors or areas that may need clarification.You might say,I need to go over my essay to make sure its wellstructured and free of mistakes.8.Asking for Help:If there are parts of the homework that are unclear,its okay to ask for help.You could say,Im not sure about this physics problem,I might ask my dad for some help.pleting Additional Tasks:Sometimes,there might be extra tasks like preparing fora test or project.You might say,After I finish my homework,I should start studying for my history test next week.anizing for the Next Day:Before finishing for the day,organize the backpack and prepare for the next days classes.You could say,Ill pack my bag and make sure I have everything I need for tomorrow.11.Reflecting on the Days Learning:Reflecting on what was learned can help reinforce the information.You might say,I learned a lot about the Civil War today,and I want to make sure I remember it for the test.12.Getting a Good Nights Sleep:Finally,after completing homework and preparing for the next day,its important to get a good nights sleep to be ready for the next days learning.You could say,Im going to bed early tonight so I can be wellrested for school tomorrow.Remember,the key to effective homework completion is organization,focus,and a positive attitude towards learning.。
用英语写一周的学习计划Week 1:Monday:- Start the day with a review of last week's study materials.- Spend 1 hour studying calculus, focusing on derivatives and integrals.- Work on a chemistry lab report for 2 hours.- Read and take notes on a chapter of the history textbook for 1 hour.- End the day with 30 minutes of physical exercise.Tuesday:- Review the previous day's calculus material for 30 minutes.- Spend 1 hour on physics, focusing on kinematics and dynamics.- Work on a research paper for biology for 2 hours.- Watch a documentary on a historical event for 1 hour and take notes.- Practice 30 minutes of relaxation techniques.Wednesday:- Review the physics material from Tuesday for 30 minutes.- Spend 1 hour on English literature, analyzing a poem and writing a short response.- Work on a group project for economics for 2 hours.- Practice 1 hour of Spanish vocabulary and grammar.- End the day with 30 minutes of yoga.Thursday:- Start the day with a review of the previous day's English literature material for 30 minutes. - Spend 1 hour on psychology, studying different theories and their applications.- Work on a math problem set for 2 hours.- Read a chapter from a sociology textbook for 1 hour and take notes.- Practice 30 minutes of mindfulness meditation.Friday:- Review the psychology material from Thursday for 30 minutes.- Spend 1 hour on geography, learning about different countries and their cultures.- Work on a coding assignment for computer science for 2 hours.- Watch a TED talk on a scientific topic for 1 hour and take notes.- End the day with 30 minutes of stretching and mobility exercises.Saturday:- Review the coding material from Friday for 30 minutes.- Spend 2 hours on a practice SAT exam, focusing on math and reading comprehension.- Work on a creative writing assignment for 2 hours.- Watch a documentary on a scientific discovery for 1 hour and take notes.- End the day with 30 minutes of light cardio exercise.Sunday:- Review the previous week's study materials for 1 hour.- Spend 2 hours on a practice ACT exam, focusing on science and English.- Work on a personal project for 2 hours, such as a hobby or self-study topic of interest.- Reflect on the week's progress and set new goals for the upcoming week.- End the day with 30 minutes of self-care activities, such as reading, drawing, or listening to music.This weekly study plan is designed to cover a wide range of subjects and skills, ensuring a well-rounded and comprehensive learning experience. It also includes time for relaxation, physical activity, and self-care, all of which are essential for maintaining a healthy and balanced lifestyle while pursuing academic goals. By following this plan consistently, students can make significant progress in their studies and personal development.。
Day 5Notes:Section 1.6Combining Transformations:Example:Given the original function ()x f y =state all transformations on the function as indicated by the new equation:
a)()[]1642++−−=x f y b) −−=321x f y
Answers:
a) ()[]1642++−−=x f y
Reflection in the x-axis Reflection in the y-axis Horizontal compression by a factor of 41 Vertical expansion by a factor of 2 Slide 6 units left Slide 1 unit up
b) −−=321x f y
−=∴f y
Example: Given x y =, write the new equation for the function given all of the following transformations:
• Reflect in the y-axis
• Compress horizontally by a factor of 3
1 • Translate 5 units left
• Translate 1 unit down
* * It is important to note that a function must first be written in standard form before stating any transformations. Specifically, the coefficient on “x” must be 1. If it is not 1, it must be factored out within the function. Reflection in the x-axis factor of 2
Answer: ()153−+−=x y or 1153−−−=x y
Graphing functions having more than one transformation:
• Be sure the equation is in standard form
• Draw a table of values with some basic points from the original curve • Expansions/Compressions are always calculated first (Remember that multiplying always comes before adding or subtracting in BEDMAS) • Translations/Slides are done last
• Plot the new coordinates and sketch in the new curve
• Check with your graphing calculator where appropriate
Example: Use a table of values to sketch the following: ()61212+ −−=x y Answer:
points from the most basic 2x y =
Example: Use a table of values to sketch the following: 463−−−=x y
Answer: Before any analysis can take place, the equation must be re-written in standard form, i.e. the -1 must be factored out within the function
Example: Given ()x f y =, graph ()512−−=x f y using a table of values:
Answer:
y
Basic points from
()x f y = =y。
