美国高中数学测试题 MathPlacement

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美国数学题——精选推荐

美国数学题Math IA1/IA2/IA3/IAB1/IAB2 Placement TestSpring 2013 – March 2 & 3, 2013Please check & correct your grade and the school name on the Admit Card. Make sure that you are taking the test indicated on the Admit Card. Indicate any schedule preferences on the Admit Card. The placement test will be posted on the web as Week #1 homework on March 13th. Math IAB students requesting advancement to Math IB must also take the Math IB test as a second test. You must score at least 15 (50%) to take the Math IB test. Please staple the placement test along with your answers and the Admit Card.1.Different figures represent the different digits. Find the digit corresponding to the square.2.In a trunk there are 5 chests, in each chest there are 3 boxes, and in each box there are 10gold coins. The trunk, the chests, and the boxes are locked. How many locks must beopened in order to get 50 coins?3. A caterpillar starts from his home and move directly on a ground, turning after each hourat 90° to the left or to the right. In the first hour he moved 1 m, in the second hour 2 m,and so on. At what minimum distance from his home the caterpillar would be after sixhours traveling?4.The sum of ten distinct positive numbers is 100. The largest of these numbers is?5. A rod of length 15 dm was divided into the greatest possible number of pieces ofdifferent integer lengths in dm. The number of cuts is:6. A river goes through a city and there are two islands. There are also six bridges as shownin the figure. How many paths there are going out of a shore of the river (point A) andcome back (to point B) after having spent one and only one time for each bridge?7.In which of triples the central number is strictly in the middle between two others.A) 1/2, 1/3, 1/4 B) 12, 21, 32 C) 3, 7, 13 D) 1/3, 1/2, 2/38.What is the smallest number of dots that need to be removed from the pattern shown, sothat no three of the remaining dots are at the vertices of an equilateral triangle?9.Iqra is 10 years old. Her mother Asma is 4 times as old. How old will Asma be when Iqrais twice as old as she is now?10.To the right side of a given 2-digit number we write the same number obtaining 4-digitnumber. How many times the 4-digit number is greater than the 2-digit number?11.Ahmed thought of an integer. Umar multiplied it either by 5 or by 6. Ali added to theUmar’s result either 5 or 6. Tahir subtracted from Ali’s result either 5 or 6. The obtained result was 73. What number did Ahmed think of?12.The multiplication uses each of the digits 1 to 9 exactly once. What is digit Y?13.One of the cube faces is cut along its diagonals (see the fig.). Which of the following netsare impossible?14.Seven cards lie in a box. Numbers from 1 to 7 are written on these cards (exactly onenumber on the card). Two persons take the cards as follows: The first person takes, atrandom, 3 cards from the box and the second person takes 2 cards (2 cards are left in the box). Then the first person tells the second one: “I know that the sum of the numbers of your cards is even”. The sum of card’s numbers of the first person is equal to15.For each 2-digit number from 30 to 50, the digit of units was subtracted from the digit oftens. What is the sum of all the results?16.How many digits can be at most erased from the 1000-digit number 20082008…2008,such that the sum of the remaining digits is 2008?17.Basil wants to paint the slogan VIVAT KANGAROO on a wall. He wants differentletters to be colored differently, and the same letters to be colored identically. How many colors will he need?18.When it is 4 o'clock in the afternoon in London, it is 5 o'clock in the afternoon in Madridand it is 8 o'clock in the morning on the same day in San Francisco. Ann went to bed in San Francisco at 9 o'clock yesterday evening. What was the time in Madrid at thatmoment?19.The picture shows a pattern of hexagons. We draw a new pattern by connecting all themidpoints of any neighboring hexagons. What pattern do we get?20.The upper coin is rotated without slipping around the fixed lower coin to a positionshown on the picture. Which is the resulting relative position of kangaroos?21.Vivien and Mike were given some apples and pears by their grandmother. They had 25pieces of fruit in their basket altogether. On the way home Vivien ate 1 apple and 3 pears, and Mike ate 3 apples and 2 pears. At home they found out that they brought home thesame number of pears as apples. How many pears were they given by their grandmother?22.Which three of the numbered puzzle pieces should you add to the picture to complete thesquare?23.There are 4 gearwheels on fixed axles next to each other, as shown. The first one has 30gears, the second one 15, the third one 60 and the last one 10. How many revolutionsdoes the last gearwheel make, when the first one turns through one revolution?24. A regular octagon is folded in half exactly three times until a triangle is obtained, asshown. Then the apex is cut off at right angles, as shown in the picture. If the paper isunfolded what will it look like?25.Winnie's vinegar-wine-water marinade contains vinegar and wine in the ratio 1 to 2, andwine and water in the ratio 3 to 1. Which of the following statements is true?A.There is more vinegar than wine.B.There is more wine than vinegar and water together.C.There is more vinegar than wine and water together.D.There is more water than vinegar and wine together.E.There is less vinegar than either water or wine.26.Kangaroos Hip and Hop play jumping by hopping over a stone, then landing across sothat the stone is in the middle of the segment traveled during each jump. Picture 1 shows how Hop jumped three times hopping over stones marked 1, 2 and 3. Hip has theconfiguration of stones marked 1, 2 and 3 (to jump over in this order), but starts in adifferent place as shown on Picture 2. Which of the points A, B, C, D or E is his landing point?27.There were twelve children at a birthday party. Each child was either 6, 7, 8, 9 or 10years old, with at least one child of each age. Four of them were 6 years old. In the group the most common age was 8 years old. What was the average age of the twelve children?28.Rectangle ABCD is cut into four smaller rectangles, as shown in the figure. The foursmaller rectangles have the properties: (a) the perimeters of three of them are 11, 16 and19, (b) the perimeter of the fourth is neither the biggest nor the smallest of the four. What is the perimeter of the original rectangle ABCD?29.Peter wants to cut a rectangle of size 6 × 7 into squares with integer sides. What is theminimal number of squares he can get?30.Abid's house number has 3 digits. Removing the first digit of Abid's house number, youobtain the house number of Ben. Removing the first digit of Ben's house number, you get the house number of Chiara. Adding the house numbers of Abid, Ben and Chiara gives912. What is the second digit of Abid's house number?。

美国高中中考数学试卷

一、选择题（每题3分，共30分）1. 下列哪个数是负数？A. -2B. 0C. 3D. -3.52. 下列哪个方程的解是x=2？A. 2x - 4 = 0B. 2x + 4 = 0C. 3x - 6 = 0D. 4x - 8 = 03. 如果一个三角形的两个内角分别是40度和60度，那么第三个内角的度数是多少？A. 40度B. 60度C. 80度D. 100度4. 下列哪个图形是圆？A. 正方形B. 矩形C. 三角形D. 圆形5. 一个长方形的长是10厘米，宽是5厘米，那么它的周长是多少？A. 20厘米B. 25厘米C. 30厘米D. 35厘米6. 下列哪个数是分数？A. 3.5B. 0.25C. 100D. 1.27. 一个等腰三角形的底边长是8厘米，腰长是10厘米，那么这个三角形的面积是多少？A. 32平方厘米B. 40平方厘米C. 48平方厘米D. 56平方厘米8. 下列哪个数是整数？A. 2.5B. 0.75C. 1/4D. -39. 如果一个圆的半径是5厘米，那么它的直径是多少？A. 10厘米B. 15厘米C. 20厘米D. 25厘米10. 下列哪个方程的解是y=4？A. 2y + 6 = 14B. 3y - 12 = 0C. 4y + 2 = 18D. 5y - 10 = 0二、填空题（每题5分，共20分）11. 下列数中，最小的负数是__________。

12. 如果一个数比另一个数大5，那么这两个数的差是__________。

13. 一个三角形的两边长分别是6厘米和8厘米，那么第三边的可能长度是__________。

14. 一个长方体的长、宽、高分别是4厘米、3厘米和2厘米，那么它的体积是__________立方厘米。

15. 下列数中，最接近1的数是__________。

三、解答题（每题10分，共30分）16. 解下列方程：2x - 5 = 9。

17. 一个等边三角形的边长是7厘米，求这个三角形的面积。

美国高考数学试卷高清版

一、选择题1. 已知函数f(x) = 2x - 3，若f(2) = 1，则x的值为：A. 2B. 1C. 0D. -12. 在直角坐标系中，点A(2,3)，点B(-1,1)，则线段AB的中点坐标为：A. (1,2)B. (1,3)C. (0,2)D. (0,3)3. 已知等差数列{an}的公差为d，若a1 = 2，a4 = 10，则d的值为：A. 2B. 3C. 4D. 54. 已知圆的方程为x^2 + y^2 - 4x - 6y + 9 = 0，则圆心坐标为：A. (2,3)B. (2,-3)C. (-2,3)D. (-2,-3)5. 已知三角形ABC的三边长分别为a、b、c，且a+b+c=12，a^2+b^2-c^2=4，则三角形ABC的面积为：A. 6B. 8C. 10D. 12二、填空题6. 已知函数f(x) = x^2 - 4x + 3，若f(x) = 0，则x的值为______。

7. 已知等比数列{an}的首项a1 = 3，公比q = 2，则第n项an =______。

8. 在直角坐标系中，点P(1,2)，点Q(3,4)，则线段PQ的长度为______。

9. 已知圆的方程为x^2 + y^2 - 6x - 4y + 5 = 0，则圆的半径为______。

10. 已知三角形ABC的边长分别为a、b、c，且a^2 + b^2 = c^2，则三角形ABC 为______三角形。

三、解答题11. 已知函数f(x) = x^3 - 3x^2 + 4x - 6，求f(x)的零点。

12. 已知等差数列{an}的首项a1 = 1，公差d = 2，求前10项的和。

13. 已知三角形ABC的三边长分别为a、b、c，且a+b+c=10，a^2+b^2=c^2，求三角形ABC的面积。

14. 已知圆的方程为x^2 + y^2 - 4x - 6y + 9 = 0，求圆内与x轴、y轴距离相等的点的坐标。

15. 已知三角形ABC的边长分别为a、b、c，且a^2 + b^2 = c^2，求三角形ABC 的内角A、B、C的正弦值。

美国高考数学试卷中文版

1. 如果4(tu)^3 = 19，那么tu的值是多少？A. 3B. 4C. 5D. 6E. 72. 如下图，三条直线相交于一点。

如果f(85°)，e(25°)，那么a的值是多少？A. 60°B. 65°C. 70°D. 75°E. 85°3. 如果玛丽开车行驶n英里用了t小时，那么下列哪个可以表示她行驶的平均速度，英里/小时？A. n/tB. t/nC. 1/ntD. ntE. n^2t4. 如果a是一个奇数，b是一个偶数，那么选项中哪一个是奇数？A. 3bB. a^3C. 2(ab)D. a^2bE. 2ab5. 在平面坐标内，点F(-2,1)，G(1,4)，H(4,1)在以P为圆心的圆上，那么点P 的坐标是什么？A. （0,0）B. （1,1）C. （1,2）D. （1，-2）E. （2.5,2.5）6. 如下图，如果-3 < x < 6，那么x有几个值，使得f(x) ≥ 2？A. 零B. 一个C. 两个D. 三个E. 三个以上7. 在直角坐标系中，点A(2,3)，B(5,6)，C(-1,2)构成的三角形ABC是等腰三角形，那么AB与AC的长度比是多少？A. 1:2B. 2:1C. 1:1D. 3:2E. 2:38. 已知函数f(x) = x^2 - 4x + 3，那么f(2)的值是多少？A. 1B. 2C. 3D. 4E. 59. 在等差数列中，第一项为a，公差为d，那么第n项an的值是多少？A. a + (n-1)dB. a - (n-1)dC. a + ndD. a - ndE. a + (n+1)d10. 已知圆的方程为x^2 + y^2 = 16，那么圆的半径是多少？A. 2B. 4C. 6D. 8E. 101. 已知等比数列的第一项为2，公比为3，那么第5项的值是多少？2. 已知函数f(x) = 2x + 3，那么f(-1)的值是多少？3. 在直角坐标系中，点A(1,2)，B(4,5)，C(7,8)构成的三角形ABC是等边三角形，那么AB的长度是多少？4. 已知函数f(x) = x^2 - 5x + 6，那么f(3)的值是多少？5. 在直角坐标系中，点A(2,3)，B(5,6)，C(-1,2)构成的三角形ABC是等腰三角形，那么BC的长度是多少？6. 已知函数f(x) = 3x - 2，那么f(4)的值是多少？7. 在等差数列中，第一项为3，公差为2，那么第10项的值是多少？8. 已知圆的方程为x^2 + y^2 = 9，那么圆的半径是多少？9. 在直角坐标系中，点A(1,2)，B(4,5)，C(7,8)构成的三角形ABC是等边三角形，那么AC的长度是多少？10. 已知函数f(x) = 2x^2 + 3x - 5，那么f(1)的值是多少？三、解答题（每题10分，共30分）1. 已知函数f(x) = x^2 - 4x + 3，求f(x)的值域。

美国高中生数学试题及答案

美国高中生数学试题及答案一、选择题（每题2分，共20分）1. 下列哪个数是无理数？A. 3.14159B. πC. 0.33333...D. √22. 如果一个函数f(x) = 2x^2 + 3x - 5，那么f(-2)的值是多少？A. -1B. 1C. 3D. 53. 一个直角三角形的两条直角边分别为3和4，斜边的长度是多少？A. 5B. 6C. 7D. 84. 以下哪个方程没有实数解？A. x^2 + 4x + 4 = 0B. x^2 - 4x + 4 = 0C. x^2 + 4x - 5 = 0D. x^2 - 9 = 05. 一个圆的半径是5，那么它的面积是多少？A. 25πC. 75πD. 100π6. 以下哪个是二次方程的根？A. x = 2B. x = -2C. x = 3D. x = -37. 如果一个数列是等差数列，且前三项为2, 5, 8，那么第10项是多少？A. 23B. 24C. 25D. 268. 一个函数g(x) = 3x - 2，当x = 4时，g(x)的值是多少？A. 10B. 12C. 14D. 169. 以下哪个是线性方程的解？A. x = 0B. x = 1C. x = 2D. x = 310. 一个正方体的体积是27立方单位，它的边长是多少？A. 3C. 9D. 12二、填空题（每题3分，共15分）11. 一个圆的周长是2πr，其中r是______。

12. 一个二次方程ax^2 + bx + c = 0的判别式是______。

13. 一个数的平方根是4，那么这个数是______。

14. 如果一个数列是等比数列，且首项为2，公比为3，那么第5项是______。

15. 一个函数h(x) = kx + b，当k不等于0时，这个函数是______函数。

三、解答题（每题5分，共25分）16. 解方程：3x + 5 = 14。

17. 证明：如果一个三角形的两边长分别为a和b，且a + b > c，那么这个三角形是存在的。

美国高考数学试卷及答案

一、选择题（每题2分，共40分）1. 已知函数f(x) = x^2 - 3x + 2，那么f(2)的值为：A. 0B. 1C. 2D. 3答案：A2. 如果一个等差数列的首项为a，公差为d，那么第n项an的表达式为：A. an = a + (n-1)dB. an = a - (n-1)dC. an = (n-1)d + aD. an = (n-1)d - a答案：A3. 已知三角形ABC的边长分别为a、b、c，那么以下哪个公式是三角形ABC的面积公式？A. S = (1/2)abB. S = (1/2)bcC. S = (1/2)caD. S = (1/2)ab + bc + ca答案：A4. 已知直线l的方程为y = 2x + 1，那么直线l与y轴的交点坐标为：A. (0,1)B. (1,0)C. (1,1)D. (0,-1)答案：A5. 已知圆的方程为x^2 + y^2 = 16，那么圆心坐标为：A. (0,0)B. (2,0)C. (0,2)D. (2,2)答案：A6. 已知函数f(x) = log2(x+1)，那么f(3)的值为：A. 1B. 2C. 3D. 4答案：B7. 已知数列{an}的通项公式为an = 2n - 1，那么数列{an}的前10项之和为：A. 90B. 100C. 110D. 120答案：A8. 已知三角形ABC的角A、B、C的对边分别为a、b、c，那么余弦定理的公式为：A. c^2 = a^2 + b^2 - 2abcosCB. a^2 = b^2 + c^2 - 2bccosAC. b^2 = a^2 + c^2 - 2accosBD. a^2 = b^2 + c^2 - 2abcscC答案：A9. 已知函数f(x) = e^x，那么f(0)的值为：A. 1B. 2C. eD. e^2答案：A10. 已知数列{an}的通项公式为an = 3^n，那么数列{an}的第4项与第5项之比为：A. 1/3B. 1/9C. 3/9D. 9/27答案：B二、填空题（每题2分，共20分）11. 已知函数f(x) = x^2 - 4x + 3，那么f(2)的值为______。

美国高三数学试卷及答案

一、选择题（每题5分，共50分）1. 已知函数f(x) = 2x - 3，则f(-1)的值为：A. -5B. -2C. 0D. 12. 若a > 0，b < 0，则下列不等式中正确的是：A. a + b > 0B. a - b > 0C. a - b < 0D. a + b < 03. 已知等差数列{an}的公差为2，首项为3，则第10项an的值为：A. 21B. 19C. 17D. 154. 已知等比数列{bn}的公比为2，首项为3，则第5项bn的值为：A. 48B. 24C. 12D. 65. 若a、b为实数，且a^2 + b^2 = 1，则下列结论正确的是：A. a + b = 0B. a - b = 0C. ab = 0D. a^2 - b^2 = 06. 已知直线l的方程为2x - 3y + 1 = 0，则直线l与x轴的交点坐标为：A. (1/2, 0)B. (1/3, 0)C. (0, 1/2)D. (0, 1/3)7. 已知圆C的方程为(x - 2)^2 + (y + 3)^2 = 9，则圆C的半径为：A. 2B. 3C. 4D. 58. 已知函数f(x) = x^2 - 4x + 3，则f(x)的图像与x轴的交点坐标为：A. (1, 0)B. (2, 0)C. (3, 0)D. (1, 3)9. 已知函数f(x) = log2(x - 1)，则f(x)的定义域为：A. (1, +∞)B. (2, +∞)C. (0, 2)D. (1, 2)10. 已知函数f(x) = (x - 1)/(x + 2)，则f(x)的图像在x轴上的渐近线方程为：A. x = 1B. x = -2C. y = 1D. y = -1二、填空题（每题5分，共50分）1. 已知等差数列{an}的首项为3，公差为2，则第10项an的值为______。

2. 已知等比数列{bn}的首项为3，公比为2，则第5项bn的值为______。

高考数学试卷美国版答案

Part A：选择题（每题2分，共40分）1. 答案：B解析：题目要求选择一个关于函数单调性的正确说法。

选项A和C错误，因为函数在某区间内单调递增或递减，不代表在所有区间内都如此。

选项D错误，因为题目没有给出函数的具体形式，无法判断其在整个定义域内的单调性。

2. 答案：C解析：这是一个关于复数的题目。

复数a+bi的模长是√(a²+b²)，所以|2+i|=√(2²+1²)=√5。

3. 答案：A解析：这是一个关于数列的题目。

等比数列的通项公式是an=a1r^(n-1)，所以a5=a1r^(5-1)=a1r^4。

4. 答案：D解析：这是一个关于平面几何的题目。

在直角三角形ABC中，∠A=90°，所以根据勾股定理，AB²+BC²=AC²。

5. 答案：B解析：这是一个关于极限的题目。

根据极限的定义，当x趋近于0时，(sinx)/x的极限是1。

6. 答案：C解析：这是一个关于导数的题目。

函数f(x)=x³在x=0处的导数是f'(0)=30²=0。

7. 答案：A解析：这是一个关于概率的题目。

从一副52张的扑克牌中随机抽取4张，抽取到红桃的概率是13/5212/5111/5010/49。

8. 答案：D解析：这是一个关于对数的题目。

log2(16)=4，因为2的4次方等于16。

9. 答案：B解析：这是一个关于三角函数的题目。

sin(π/6)=1/2，所以选项B正确。

10. 答案：A解析：这是一个关于立体几何的题目。

在正方体ABCD-A1B1C1D1中，对角线AC1的长度是√(3²+3²+3²)=3√3。

Part B：解答题（每题10分，共30分）11. 答案：解析：首先，我们需要找到函数的极值点。

函数f(x)=x³-6x²+9x在x=0、x=1和x=3时取得极值。

美国高中考试题及答案

美国高中考试题及答案【注意：本文仅提供虚构的考试题目及答案，旨在演示如何按照题目要求进行格式写作，请勿将其作为真实的参考资料】美国高中的考试是学生评估学术水平的重要方式之一。

本文将为大家介绍一些典型的美国高中考试题目及答案，以帮助读者更好地了解这些考试的类型和内容。

1. SAT数学部分题目：题目1：在坐标系中，给定两个点A(3, 5)和B(8, -2)，求线段AB的长度。

答案：使用勾股定理求解。

首先计算AB的横向距离为8-3=5，纵向距离为-2-5=-7。

然后利用勾股定理计算AB的长度，即√(5^2+(-7)^2)=√74。

题目2：已知三角形ABC中，角A=45°，边AC=10，边BC=8，求边AB的长度。

答案：利用正弦定理求解。

根据正弦定理，sinA/AB=sinB/BC=sinC/AC。

由于角A=45°，则sinA=sin(90°-A)=sin45°=1/√2。

代入已知数据得到1/√2/AB=sinB/8，解方程可得AB≈11.31。

2. AP语言考试作文题目：题目：请根据以下引述，写一篇关于幸福的短文。

"I believe that the purpose of life is to be happy. From the moment of birth, every human being wants happiness and does not want suffering." - Dalai Lama答案：幸福是人生的终极目标。

从出生开始，每个人都渴望幸福，不想经历苦难。

然而，幸福是一个多元化的概念，因为每个人对幸福的定义都有所不同。

对于一些人来说，物质财富和成功是实现幸福的关键，他们认为只有拥有足够的财富和荣誉才能感到满足。

然而，我认为真正的幸福来自于内心的满足和与他人的关系。

幸福不是通过追求无止境的物质财富来获得的。

相反，幸福源于对自己的接纳和自我实现的感觉。

北美数学高中试题

北美数学高中试题### 北美数学高中试题题目一：几何问题在直角三角形ABC中，角C为直角。

已知AB=c，BC=a，AC=b。

如果a和c的值已知，求b的值。

解答：利用勾股定理，我们有：\[ b^2 = a^2 + c^2 \]因此，b的值为：\[ b = \sqrt{a^2 + c^2} \]题目二：代数问题给定一个二次方程 $ ax^2 + bx + c = 0 $，其中 $ a \neq 0 $。

求方程的根。

解答：二次方程的根可以通过公式求得：\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]两个根分别为：\[ x_1 = \frac{-b + \sqrt{b^2 - 4ac}}{2a} \]\[ x_2 = \frac{-b - \sqrt{b^2 - 4ac}}{2a} \]题目三：概率问题一个袋子里有5个红球和3个蓝球。

随机从袋子中取出一个球，观察颜色后放回，重复这个过程两次。

求两次都取出红球的概率。

解答：第一次取出红球的概率为 $ P_1 = \frac{5}{8} $，第二次取出红球的概率为 $ P_2 = \frac{5}{8} $。

因为每次取球都是独立事件，所以两次都取出红球的概率为：\[ P_{\text{两次红球}} = P_1 \times P_2 =\left(\frac{5}{8}\right)^2 \]题目四：数列问题给定一个等差数列，首项为a，公差为d。

求第n项的值。

解答：等差数列的第n项可以通过以下公式求得：\[ a_n = a + (n-1)d \]题目五：函数问题考虑函数 $ f(x) = 2x^3 - 3x^2 + x - 5 $。

求导数 $ f'(x) $。

解答：对函数 $ f(x) $ 求导，我们得到：\[ f'(x) = 6x^2 - 6x + 1 \]。

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Emma Willard SchoolTroy, New York 12180MATHEMATICS PLACEMENT TESTPurpose: The tests in this booklet are to help determine proper mathematics placement and minimize the need for course changes after the start of the academic year. It is important that the student work independently so that the test will give us a fair representation of her current knowledge and skills. The tests are for placement purposes only. They do not affect admissions decisions in any way. However, it is important to answer questions to the best of your ability in order for the mathematics department to place you properly.Date student received test:_________________Name: (please print)_______________________________ Date test taken:___________ Circle grade you are entering at Emma Willard School: 9 10 11 12 PG Phone number (with area code): _________________________________________________ E-mail address: _____________________________________________ (print legibly please) Name of most recent school attended and the city and state/country where it is located.______________________________________________________________________________ What math course did you take this year, and what is your average grade at the time you are taking this test?______________________________________________________________________________ Have you taken a full-year course called Geometry? Circle your answer. YES NOIf you were remaining in your current school district or at your current school, what would be the name of the course you would take next year?______________________________________________________________________________ How do you view yourself as a mathematics student?Please read the following carefully:Directions to Parents: Please see that your daughter has a quiet place to complete the test in one sitting. The test has four levels. Each level is designed to be completed in less than an hour. Calculators may be used (EXCEPT on the Level One test), but texts and notes should not be used. We do not recommend extensive review prior to taking the test. It is meant to reflect your daughter’s accessible knowledge of her retained mathematics knowledge. It is not to your daughter’s advantage to obtain help on this test since proper placement is contingent on accurate assessment of her current knowledge of mathematics.Directions to the Student: This booklet contains four tests, Level One, Level Two, Level Three, and Level Four. Do as much of all four parts of the tests as you can. The sooner you complete the tests and return them to the school, the sooner we can properly place you and start the process of creating your schedule for the fall. Print out the levels you wish to complete. Be sure to check that all diagrams and problems have printed correctly. Please mail in all parts that you have completed as soon as possible after you complete them. You may use a calculator except on Level One. It is important that you give these tests your serious consideration as they will be the main factor in determining the math course in which you are enrolled.Please show your work neatly next to the problem (including scratch work) as it is useful in our evaluation of your methods and skills. Do not use extra paper, and simplify all answers. Showing your work helps us see where your mistakes were and adds to proper assessment of your understanding and hence proper placement.Calculator Use: It is important to note that all Emma Willard mathematics students will use the Texas Instruments TI-84 PLUS Graphing Calculator in all of our courses. These may be purchased at cost in our school store. While we teach students to use their calculators proficiently, we also stress the need to recognize problems that do not need a calculator and may require students to solve those problems without one. For this reason, on these placement tests we ask that you do as many problems as possible without the use of a calculator. On the Level One test, NO calculators are allowed.Please complete as many questions as you can on all levels of the four tests. For example, if you are an entering freshman and have only completed an eighth grade math course, and are only capable of completing a few problems on the Level One part, THIS IS FINE. If you are an entering junior, and hope to have proper placement, complete as much as you can of all four tests.The purpose of these tests is not to make a judgment about your mathematical ability. It is to assess how well you have been prepared for the sequence of coursesat Emma Willard. We strive to place new students in the course in which they will find the most appropriate challenge.4/12RevisedLevel One Test(total points = 108)In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. Do NOT use a calculator on this test. 1. A suit that is regularly sold for $120 is now advertised on sale at 30% off. What is the sale price of the suit?1. __________________(3 pts) 2. A school’s ratio of boys to girls is 4:5. If there are 360 students, how many girls attend the school?2. __________________(3 pts) 3. Evaluate 2492x x −− when x = -1.3. __________________ (3 pts)In 4-8, simplify the expression.4. 3678x x −+−−4. __________________ (3 pts)5. 325()()x x x −−−5. __________________ (3 pts)6. 343762c c c +−6. __________________(3 pts)7. a a a 462⋅7. __________________(3 pts)8. (3x )38. __________________(3 pts)In 9-12 solve the equation.9. −+=−369d9. _________________(3 pts)10. 25652x x +=−10. _________________(3 pts)11. The formula 9532F C =+ converts Celsius temperature (C) to Fahrenheit (F). What is the Fahrenheit equivalent of 20o C?11. _________________(3 pts)12. Solve for C in the formula 9325F C =+.12. _________________(3 pts)13. Multiple Choice. To rent a truck for a day, a driver pays a $15 fee. She pays an additional 18 cents for each mile she drives. If the total cost in dollars is c and she drives d miles, thenA) d c =+15018. B) d c =+01815. C) c d =+15018. D) c d =+01815.13. _________________(3 pts)14. Solve the equation for y . 236x y −=14. _________________(3 pts)15. Is (1, 3) a solution of y x =−25? (Support your answer with work below.)15. _________________(3 pts)16. Graph the line y x =−253 using slope & y-intercept. Do notuse a table of values. (1 square = 1 unit)16. (3 pts)xa. Find its numerical slope.17. a. __________________ (3 pts)b. __________________ (3 pts)18. A line passes through the points (4, -2) and (-9, 8). a. Find the slope of the line. Show work. b. Write an equation for this line.18. a. __________________(3 pts)b. __________________ (3 pts)19. Given the slope of a line is 53 and the point (-8, 2) is on the line. Write an equation for the line.20. Solve the system:6222=−=+y x y x19. _________________ (3 pts)20. _________________ (3 pts)21. Multiply: ()()2135x x +−21. _________________(3 pts)22. Simplify: ()x +8222. _________________(3 pts)In 23-26, factor (using integers) the polynomial expression.23. Factor: 51532ab a b −23. _________________(3 pts)24. Factor: x 225−24. _________________(3 pts)25. Factor: x x 2412+−26. Factor: 12x 2−5x −225. _________________(3 pts)26. _________________(3 pts)27. Solve for x: ()()x x −+=53027. _________________(3 pts)28. Solve the equation: 3524t =+28. _________________(3 pts)in simplified radical form.29. _________________(3 pts)30. Solve for x : 270x −=30. _________________(3 pts)31. Solve for x : 24137x +=31. _________________(3 pts)32. Simplify: 23()46()32. _________________(3 pts)+33. _________________(3 pts)34. Use the quadratic formula, x b b aca=−±−242 to solve the equation: 2602x x −−=.34. _________________(3 pts)Level Two Test(total points = 100)In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. You may use a scientific or graphing calculator.1. Measure of angle x = ?1. __________________(2 pts) 2. In the figure, ||m n and 50.m x ∠=°Find m y ∠.2. _________________ (2 pts)3. ?m y ∠=3. _________________ (2 pts)4. In the figure, 90m Q ∠=°and 40m SRT ∠=°. ?m P ∠=4. _________________ (2 pts)5. If is parallel to AB CD , then ?m x ∠=5. _________________ (2 pts)15°x55°65°nm x y 70°55°y40°T S R Q PDC B A 35°80°x6. In the plane figure, MN=NT=TV. Find the measure of TMN ∠.6. _________________(2 pts) 7. Which of the following reasons can always be used to prove two triangles congruent? Circle all that apply. No partial credit. (2 pts)SSS AAA SAS SSA AAS ASA8. Given the figure with DE BC , which of the followingproportions is not true? No partial credit.8. _________________ (2 pts) A. 456x = B. 4512y = C. 456x = D. 496x x =+9. Which one of the following sets of points is not collinear?A. B & DB. D, A & HC. D, B & GD. G, C &B9. __________________(2 pts) 10. Refer to the diagram in #9. The intersection of plane P and plane Q is:10. _________________(2 pts) A. line KC B. line AC C. line GC D. line PQ E. point CN35°V TM11. Given ABC Δ such that 50m A ∠=°and 64m B ∠=°. The longest side of the triangle isA. ABB. ACC. BCD. all sides are equalE. not enough information is given11. _________________(2 pts)12. Two similar triangles have areas in the ratio 4:9. The ratio of a pair of corresponding sides is12. _________________(2 pts) A. 4:9 B. 16:81 C. 9:4 D. 2:313. ABCD is a parallelogram. Solve for x.13. _________________(2 pts)14. If the side of an equilateral triangle measures 6, then what is the measure of an altitude of the triangle?14. _________________(3 pts)15. What is the radius of circle O if PQ=12.15. _________________(3 pts)16. Find the sum of the interior angles in a hexagon.16. _________________(3 pts)17. A 6 foot ladder leans against a wall. Its top touches a point on the wall 4 feet above the floor. How many feet is the bottom of the ladder from the base of the wall? Draw a diagram and put your answer in simplest radical form. 17. _________________(3 pts)18. A rhombus has diagonals of 20 and 16. What is the perimeter of the rhombus? Draw a diagram and put your answer in simplest radical form. 18. _________________(3 pts)19. In right triangle ABC, AC=12. What is the perimeter of the triangle? 19. _________________(3 pts)20. Find the area and perimeter of the rectangle below.20.Area = ______________(2pts) Perimeter = __________(2 pts)B21. Write the following proof either in a two-column format or written in paragraph form. (6 pts)Given: DA bisects BDC ∠BD=DC Prove: AB=AC22. What is the area of ADB Δin square units?22. _________________ (3 pts) 23. What is the area of parallelogram ABCD in square units?23. _________________(3 pts)BC24. What is the area of a circle whose circumference is 12π.24. _________________(2 pts)25. Square ABCD is inscribed in circle O. OA=4. What is area of the shaded region in square units?25. _________________(3 pts)26. In the circle below, what is the degree measure of arc AB?26. _________________(3 pts)27. The edge of a cube is 2 cm. Find the total surface area of the cube. Include units of measurements in your answer.27. _________________(3 pts)28. The diameter and height of a cone both measures 4 cm. What is the volume of the cone?28. _________________(3 pts)A29. Find the distance between the points (-2, 3) and (1, -4). 29. _________________(3 pts)30. Write an equation of the line perpendicular to152y x=+goingthrough the point (3, 4). 30. _________________(3 pts)31. Given the line segment with endpoints (1, -4) and (3, 2), determine the coordinates (x, y) of the midpoint. 31. _________________(3 pts)32. List the letters of the answer(s) that give (s) you enough information to determine that the quadrilateral is a parallelogram. No partial credit.A. Both pairs of opposite sides are parallel.B. Two pairs of consecutive sides are congruent.C. Diagonals are congruent.D. Consecutive angles supplementary. 32. _________________(3 pts)33. Name the vector from A(3, 5) to B(7, 0). 33. _________________(2 pts)In 34-39, define the geometric term in your own words, a diagram alone is NOT sufficient.(2 pts each)34. Complementary Angles35. Isosceles Right Triangle36. Alternate Interior Angles37. Altitude of a Triangle38. Rhombus39. Median of a TriangleLevel Three Test(total points = 101)In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. You may use a scientific or graphing calculator.1. Write an equation of a line perpendicular to 523x y +=andcontaining the point (4, -1).1. __________________ (3 pts)2. State the radius and center of the circle with the equation: 22(3)16x y +−=2.Radius:______________(1 pts)Center:______________(2 pts)3. State the domain & range of the relation graphed below.3.Domain:_____________(1 pts)Range:_______________(1 pts)4. Is the relation in #3 a function? Explain why or why not?4. __________________(3 pts)5. Identify whether the function 2()3g x x =− is an even function, odd function or neither. 5. __________________(3 pts)(2, -1) x y6. Given the point (1, -3) is on the graph ()y f x =, what point is on the graph of.a. 3()y f x =b. (3)3y f x =++c. 2()3y f x =−+6.a. __________________(3 pts)b. __________________(3 pts)c. __________________(3 pts)7. Let 2()1f x x =+and ()23g x x =−. Find (())g f x and simplify.7. __________________(3 pts)8. If ()32f x x =−, then 1()f x −=_?_8. __________________(3 pts)9. Find the EXACT (no decimals) x -intercept(s), y -intercept, and vertex of the parabola 22810y x x =−−algebraically. Show your work below. 9.x -int:________________(2 pts)y -int:________________(1 pts)vertex:_______________(3 pts)10. Simplify over the set of complex numbers.b. 2(12)i −10.a. __________________(3 pts)b. __________________(3 pts)11. Simplify: 023543()x y z x yz−−. Write your answer with positive exponents.11. _________________(3 pts)12. Simplify: 236427−⎛⎞⎜⎟⎝⎠. Write your answer as a simplifiedfraction.12. _________________(3 pts)13. Graph the function 1()f x x=. Be certain to plot at least three points and include any asymptotes as dashed lines.(3 pts) (1 square =1 unit)14. Write 239=in logarithmic form.14. _________________(3 pts)x15. Evaluate 2log 8.15. _________________(3 pts)16. Solve 450x =. Round to the nearest thousandth.16. _________________(3 pts)17. Write as a single logarithm with base 6:1662log 9log 5+.17. _________________(3 pts)18. Graph. 2()log f x x =. Be certain to plot at least three points and include any asymptotes as dashed lines.(3 pts)(1 square =1 unit)19. Write an equation for a polynomial function that has the roots 0, -5 and 1/3. There is no need to simplify your answer.19. _________________(3 pts)20. What is the quotient when 321110x x x +−+is divided by 2x −? 20. _________________(3 pts)x21. Calculate θto the nearest tenth of a degree.21. _________________(3 pts)22. Give the exact value (no decimal) of sin 240°.22. _________________(3 pts)23. Solve 1cos 2x =− for x in degrees where 0360x °≤<°.23. _________________(3 pts)22. State the amplitude and period of the graph of 3cos(2)y x =.22.Amp. =______________(1 pts)Period=______________(2 pts)23. Graph at least one full period of ()2tan f x x =. Be certain to lines.23. (3 pts)125θ24. Graph at least one full period of ()sin f x x =−. Be certain to plot at least three points and include any asymptotes as dashed lines.24. (3 pts)25. Give the exact solution (no decimals) of sin 0x =for x in radians 02x π≤<.25. _________________(3 pts)26. Find the exact radian value for 1sin (−.26. _________________(3 pts)27. Give the exact solution (no decimals) of cos x =for x in radians 02x π≤<.27. _________________(3 pts)28. Give the exact solution(s) (in radians) of 1tan (1)x −−=.28. _________________(3 pts)Level Four Test(total points = 75)In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. You may use a scientific or graphing calculator.1. Solve for x (no decimals):ln 4x =.1. __________________ (2 pts)2. To the nearest tenth, solve for x in the triangle shown below.2. __________________(3 pts) 3. Use the Law of Cosines to solve for the missing side. x5860°3. __________________(3 pts)4. Find the sum of the infinite geometric series: 111......2832+++4. __________________(2 pts)5.Calculate the 145th term in the arithmetic sequence: 6, 10, 14,…5. __________________(2 pts)12x 30°100°6. Find 4353lim 7n n n→∞−6. __________________ ( 3 pts)7. Find 54354326871lim 39106n n n n n n n n→∞−+−+−−+7.__________________ (3pts)8. A nearby ice cream shop has 31 flavors of ice cream to choose from. In how many ways can you choose a bowl of three flavors?8. __________________(3 pts)9. Write an equation for the ellipse graphed below. (1 square =1 unit)9. __________________(3 pts)10. Solve showing steps: 5557log log 2log 80x +=. Express answer as a decimal rounded to the hundredths. 10.__________________ (3 pts)x11. Women’s heights are normally distributed with a mean of 64 inches and a standard deviation of 2.5 inches. Please use the standard normal distribution table on pages 7 and 8 to answer the following questions.a. Find the women’s height at the 80th percentile.b. What is the standard value (z-score) of a women’s height of 61 inches?c. What is the probability that a women has a height of 67 inches or more? 11.a.__________________(3 pts)b.__________________(3 pts)c.__________________(3 pts)12. If the junior class has 80 members, then how many different ways can the class choose four members to be president, vice president, secretary, and treasurer? 12.__________________(3 pts)13. The weather forecaster says that there is a 10% chance of rain for each day.a.What is the probability that it rains at least one of the nextthree days?b.What is the probability that it will rain exactly 2 days ofthe next 14 days? Round to thousandths. 13.a.___________________(3 pts)b.___________________(3pts)14. Given vectors [1,3]u =−and [5,2]v =−, make an accurate sketch on the grid of 2u v −. Include the resultant vector in your sketch. (1 square = 1 unit)(3 pts)15. Prove this trigonometric identity. Show all steps.cos cos 2tan 1sin 1sin θθθθθ−=−+−(3 pts)16. Given the identity:2222cos 2cos sin 12sin 2cos 1x x x x x =−=−=−.Find the EXACT radian solutions for cos 23sin 2x x =−+ where 02x π≤<. 16. _________________(3 pts)17. A box with a square base and no top has volume 8 cubic meters. The material for the base cost $8 per square meter, and the material for the sides cost $6 per square meter. Express the cost, C, of the materials to make the box as a function of the width, w, of the bases. 17. _________________(3 pts)18a. Write an equation for a hyperbola with these points: Center at(0,2)One vertex at (0,3)−One focus at (0,9)b. Write the asymptote equations for the hyperbola. 18a._________________(3 pts)b. __________________(3 pts)19. 9 students are chosen at random for the prom committee from a group that includes 5 sophomores, 12 juniors, and 10 seniors. What is the probability that the committee will have 1 sophomore, 5 juniors, and 3 seniors on it? 19._________________(3 pts)20. Does the graph of 25y xy −= have y axis − symmetry?Justify your answer algebraically showing work.20.__________________ (3 pts)21. An airplane flying northeast with a speed of 500 miles perhour encounters a 100 mile per hour wind blowing to the west.a. What is the new speed of the plane rounded to thehundredths place?b. To the nearest whole degree, How many degrees will the wind blow the plane off its northeast course?21. a.___________________ (3 pts)b.___________________ (3pts)。