2013届汇佳初中毕业生IB入学考试数学试题
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2013届汇佳初中毕业生IB入学考试数学试题
IB Entrance Exams for 2013 Huijia Middle School students
Exams Length:90 minutes
1 Basic Operations. Simplify
a) 75232735 b)2324
c)34348yzx d) )2332)(2332(
2 Solving Equations and/or inequality. Solve for x and/or y.
a) )336(325)32(25xx b) 51682xx
c)321112xxx d)5451423yxyx
Solve and graph the solution set on the number line.
e) Graph 3|12x
3 Basic Trigonometry
Given:62,6;450YZXYX
Find the measurement or length of:
a)0________XYZ
b)0________XZY
c) XZ=___________.
4 Mathematical Term and Comprehension.
a) Find the area of parallelogram with an angle 1350 and length of sides
8cm&12cm.
b) The sum of two positive numbers is 16 and their product is seven
more than three times the sum. Find the the numbers.
c) The sum of a number and its reciprocal is .1225 Find the number.
X
Y
Z
d) The circle with radius 6 is inscribed in an equilateral triangle.
Find the area of the shaded region.
e) A parabolic curve passes through the points (-1,4),(1,-2),(3,-4).
Determine the equation of this curve in the form of
.2cbxaxy
5 Analytical Geometry.
Prove the lines that contain the altitudes of a triangle intersect in
a point(called the orthocenter).
Given triangle ROM,with lines l,j,k containing the altitudes, associates
with chosen axes and coordinates as shown.
a) The equation of line k is _____________________.
b) The slope of MR is_________________________.
c) Therefore , the slope of line l is________________.
d) Show that an equation of line l is xcbay)(
e) The coordinate of the intersection of lines l and k is (_____,________)
f) The slope of MR is ___________________.
g) The slope of line j is___________________.
h) Show that an equation of line j is cabxcby.
y
O
x
M (b, c)
R (a, 0)
l
k
j
i) The coordinate of the intersection of lines j and k is (_____,______).
j) The lines contain the altitudes of triangle are concurrent (intersect in
one point). This point is called the ______________ of the triangle.
6 Quadratic Function and Graph
Let 8)2(21)(2xxf
(a) Show that 6221)(2xxxf.
(b) For the graph of f
(ⅰ) write down the coordinates of the vertex;
(ⅱ)write down the equation of the axis of symmetry;
(ⅲ)write down the y-intercept;
(ⅳ)find both x-intercepts.
(c) Hence sketch the graph of f
(d) Let 2)(xxg.The graph of f may be obtained from the graph
Of g by a reflection in regarding to x-axis and the following
transformations:
(ⅰ) a stretch of scale factor t in the y-direction;
(ⅱ) a horizontal translation of p units;
and (ⅲ) a vertical translation of q units.
Find the value of t, of p , and of q .
7 Inverse Function, Composite Function, Domain & Range
a) The function f is given by forxxf,158x)(2 x4.
(ⅰ) Write f(x) in the form bax2)(
(ⅱ) Find the inverse function f 1.
(ⅲ) State the domain of f 1.
b) The functions f(x) and g(x) are given by 12)(xxf and
g(x)xx32. The function ))((xgfis defined for all real x
except for the interval a
(ⅱ) Find the range of gf
