加拿大安大略省十年级数学试卷英文.doc

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Feel free to use any of the material in this document. Marks are only guidelines.
We have categorized each question into one of the 4 achievement chart (A/C)
categories: Knowledge/Understanding (K), Thinking and Inquiry (T), Application

(A) and Communication (C). You can change or modify the categories as you GRADE 10 PRINCIPLES OF MATHEMATICS (ACADEMIC)
see fit. MPM 2D
Total Marks:
INSTRUCTIONS:
1. Calculators may be used.

A/C [K]
2. Read all instructions carefully in order to maximize your mark.

Part A - Multiple Choice 25 Marks (25 questions * 1 mark each)
For each of the following questions in this section, circle the letter representing the
correct answer.
1. A linear system of two equations that has one solution represents two lines that are:

a) parallel b) coincident c) intersecting d) none of these
2. The midpoint of RS is M(8, -1). If point S has coordinates (11, 4) what are the coordinates
of point R?
a) (3, -6) b) (15, -6) c) (5, -6) d) (3, 9)
3. The midpoint of the line segment with end points A(-8, 8) and B(6, 4) is:
a) (0, 10) b) (1, 2) c) (7, 2) d) (-1, 6)
4. The equation of a horizontal line passing through the point (4, 2) is:
a) x = 2 b) y = 4 c) y = 2 d) x = 4
5. The equation of a line with a slope of m = 5 and a y intercept of 8 is:
a) y = 5x + 8 b) y = -5x + 8 c) y = -5x - 8 d) y = 8x + 5
6. The slopes of 2 lines are -7 and 1 . These lines are said to be:

7
a) parallel b) perpendicular c) coincident d) none of these
7. The slope of a line segment passing through 2 points (10,- 4) and (-2, -16) is:
a) 1 b) 2 c) -1 d) -2
8. The length of a line segment with end points (-6, 7) and (-1, -5) is:
a) 12 b) 5 c) 13 d) 169
9. The diameter of a circle whose equation is x 2 + y 2 = 289 is:
a) 15 b) 16 c)17 d) none of these
10. The equation of a circle with a centre of (0, 0) that also passes through the point (-8, -6) is:
a) x 2 + y 2 = 10 b) x 2 + y 2 = 100 c) x 2 + y 2 = 14 d) x 2 - y 2 = 48
11. The y-intercept of the line 2x - 5y + 10 = 0 is:
a) 2 b) -2 c) 10 d) 5
12. The slope of the line 4x + 2 y -1 = 0 is:
a) 2 b) -2 c) 1 d) 0
13. If (-3, y) is a solution to the equation x + 2 y = 13 , what is the value of y?

a) 3
14. The product
a) 12 xy 6 z 2
b) 6
(- 3x2 y3z)(- 4x2 y3z)isequalto:
b) 12 x4 y 6 z 2
c) 5

c) - 12 xy 6 z 2
d) 8

d) 12 x 4 y 0 z 0

15. A simplified expression for (2m - n)- (- 5m - n) is:
a) 7m b) 7m + 2n c) - 3m d) 7m - 2n

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16. A simplified expression for - 27a bc is:

a) 3ac


b) 3abc
2
- 9abc2
4


c) 3ac2


d) 3a 2c2

17. The slope of the line, which is perpendicular to the line, x - 4 y + 8 = 0 is:
a) -4 b) 4 c) 1 d) -1
18. The shortest distance from the point (2, -3) to the line x = -4 is:
a) 5 b) 3 c) 2 d) 6
19. The value of the polynomial 4a 2 - 5a + 8 when a = -3 is:
a) 59 b) 44 c) 13 d) 29
20. Which of the following is not a function:
a) {(2,3), (4,5), (6,7)} b) y = 2x2 c) x = 2 y2 d) {(6,2), (7,3), (8,3)}
21. The range of the relation whose equation is y = -x 2 - 5 is:
a) y £ -5 b) y £ 5 c) y ³ -5 d) y ³ 5
22. The vertex of the parabola y = (x - 4)2 - 6 is:

a) (- 4,6)
b) (4,-6)
c) (- 6,4)
d)
(6,-4)

23. The equation of the axis of symmetry of the parabola y = -4(x - 2)2 + 5 is:
a) x = 5 b) x = -5 c) x = 2 d) x = -2
24. A parabola with a vertex of (2,3) and a stretch factor of - 1 (relative to y = x2 ) would
4
have an equation of:
a) y = - 1 (x - 2)2 + 3 b) y = - 1 (x + 2)2 + 3 c) y = - 1 (x + 3)2 - 2 d) y = - 1 (x + 3)2 + 2
4 4 4 4
25 The parabola y = -4x2 + k passes through the point (- 2,3). The value of k is:
a) -19 b) 11 c) 13 d) 19

A/C
Part B - Short Answers
For each of the questions in this section, write your answers in the spaces provided .
Use the foolscap provided for any rough work. Show details of calculations wherever
requested.
1. In the accompanying diagram, state each of the following: (4 Marks)

[K] a) domain: __________ (1 Mark) [K] b) range: __________ (1 Mark) [C] c) Is the relation a function? Justify
your answer. (2 marks)

[A]

[A]

[A]

[T]
2. The x-intercepts of the parabola y = x2 - 289 are: __________ and __________.
(Show your work) (2 Marks)
3. The roots of the quadratic equation 3x2 -17x + 10 = 0 are: __________ and __________.
(Show your work) (3 Marks)
4. Write the equation of the parabola with a vertex of (4, 23) if it passes through the
point (-1, -2): (Show your work) (3 Marks)
____________________
5. A line passes through 2 points (1, 4) and (2,-4). Calculate the slope of the line. Also show
the equation of the line in the form Ax + By + C = 0 . (Show your work)(4 Marks)

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____________________ ____________________
Slope Equation

[K]
[A]
6. The Tangent of 45o is: __________ (1 Mark)
7. a) In the accompanying diagram, the two triangles are similar. What is the value of x ?
(Show your work) (2 Marks)
18
x
12

27
x = __________

[T]

[K]

[A]
b) If the area of the smaller triangle is 8 cm2, what is the area of the larger triangle?
(Show your work) ( 2 Marks)
Area = __________
8 Given that sin A = 1 , find ÐA (to the nearest degree) __________ (1 Mark)
2
9. In the accompanying right triangle, find the value of x to one decimal place.
(Show your work) (2 Marks)
x = ________

30
28°

[A]
10. Use the SINE LAW to find the value of side x to one decimal place. x
(Show your work) (2 Marks)

x = ________
56°

[A]
11. Use the COSINE LAW to find the value of side x to one decimal place.
30
(Show your work) (2 Marks)

56° x = ________

[T]
12. Factor
each of 42°
30
the following to

x
a) mx + my - 2x - 2 y
b) 4x2 -11x - 3
c) 16 x4 -169 y 2
d) 9r 2 - 30rs + 25sx2
20
the fullest extent possible: (4 Questions * 2 marks each)
________________________
________________________
________________________
________________________

A/C

[A]

[C]

[A] [T]
Part C - Full Solutions Required
For each of the questions in this section, full solutions are required. Record your
answers in the spaces provided. Use the foolscap provided for any rough work.
1. Solve the linear system using the elimination method. Remember to find values for
both x and y. (5 Marks)
Explain what the solution above represents geometrically. How do you know that the
solution you arrived at is the correct answer? (2 Marks)
2. Expand and simplify the polynomial 2(x - 3)(x + 4)- (x + 1)2 . (4 Marks)
3. Find the equation of the line perpendicular to the line 8x + y - 8 = 0 and passing
through the point (-4, 1). (4 Marks)