加拿大安大略省十年级数学试卷 英文

GRADE 10 PRINCIPLES OF MATHEMATICS (ACADEMIC)

MPM 2D

Total Marks:

INSTRUCTIONS:

1. Calculators may be used.

2. Read all instructions carefully in order to maximize your mark.

A/C [K] 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) 2=x b) 4=y c) 2=y d) 4=x

5. The equation of a line with a slope of 5=m and a y intercept of 8 is:

a) 85+=x y b) 85+-=x y c) 85--=x y d) 58+=x y

6. The slopes of 2 lines are -7 and

7

1

. These lines are said to be:

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 28922=+y x 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) 1022=+y x b) 10022=+y x c) 1422=+y x d) 4822=-y x

11. The y-intercept of the line 01052=+-y x is:

a) 2 b) -2 c) 10 d) 5

12. The slope of the line 0124=-+y x is:

a) 2 b) -2 c) 1 d) 0

13. If (-3, y) is a solution to the equation 132=+y x , what is the value of y ?

a) 3 b) 6 c) 5 d) 8

14. The product ()()z y x z y x 323243-- is equal to:

a) 2612z xy b) 26412z y x c) 2612z xy - d) 00412z y x

15. A simplified expression for ()()n m n m ----52 is:

a) m 7 b) n m 27+ c) m 3- d) n m 27-

16. A simplified expression for 2

4

2927abc

bc a -- is:

a) ac 3 b) abc 3 c) 23ac d) 223c a

17. The slope of the line, which is perpendicula r to the line, 084=+-y x is:

a) -4 b) 4 c) 1 d) -1

18. The shortest distance from the point (2, -3) to the line 4-=x is:

a) 5 b) 3 c) 2 d) 6

19. The value of the polynomial 8542+-a a when 3-=a is:

a) 59 b) 44 c) 13 d) 29

20. Which of the following is not a function :

a) ()()(){}7,6,5,4,3,2 b) 22x y = c) 22y x = d) ()()(){}3,8,3,7,2,6

21. The range of the relation whose equation is 52--=x y is:

a) 5-≤y b) 5≤y c) 5-≥y d) 5≥y

22. The vertex of the parabola ()642

--=x y is:

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

23. The equation of the axis of symmetry of the parabola ()5242

+--=x y is:

a) 5=x b) 5-=x c) 2=x d) 2-=x

24. A parabola with a vertex of ()3,2 and a stretch factor of 4

1

- (relative to 2x y =) would

have an equation of:

a) ()32412+--=x y b) ()32412++-=x y c)()23412-+-=x y d) ()234

12

++-=x y

25 The parabola k x y +-=24 passes through the point ()3,2-. T he 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] 2. The x-intercepts of the parabola 2892-=x y are: __________ and __________. (Show your work) (2 Marks)

[A] 3. The roots of the quadratic equation 0101732=+-x x are: __________ and __________. (Show your work) (3 Marks)

[A]

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)

____________________ [T] 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 0

=

+

+C

By

Ax. (Show your work) (4 Marks)

____________________ ____________________

Slope Equation

[K] 6. The Tangent of

45 is: __________ (1 Mark)

[A] 7. a) In the accompanying diagram, the two triangles are similar. What is the value of x?

(Show your work) (2 Marks)

=

x__________

[T] 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 = __________

[K] 8 Given that sin A =

2

1

, find A

∠ (to the nearest degree) __________ (1 Mark)

[A] 9. In the accompanying right triangle, find the value of x to one decimal place.

(Show your work) (2 Marks)

=x ________

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

x = ________

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

x = ________

[T] 12. Factor each of the following to the fullest extent possible: (4 Questions * 2 marks each)

a) y x my mx 22--+

________________________

b) 31142--x x

________________________

c) 2416916y x -

________________________

30

28?

x

56?

42?

x

30

56?

20

30

x

d) 2225309s rs r +- ________________________

A/C

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.

[A] 1. Solve the linear system using the elimination method . Remember to find values for both x and y. (5 Marks) 225=+y x

2132-=-y x

[C]

Explain what the solution above represents geometrically. How do you know that the solution you arrived at is the correct answer? (2 Marks)

[A] 2. Expand and simplify the polynomial ()()()2

1432+-+-x x x . (4 Marks)

[T] 3. Find the equation of the line perpendicular to the line 088=-+y x and passing through the point (-4, 1). (4 Marks)

[T] 4. From the window of one building, a man finds that the angle of elevation to the top of

a second building is 47? and the angle of depression to the bottom of the same

building is 58?. The buildings are 60 m apart. Find the height of the 2nd building to

the nearest metre. A diagram is required. (6 Marks)

[T] 5. ?ABC has vertices A(1, 7), B(-5, 3) and C(3, -1). Determine the equation for AE, the altitude from vertex A to the opposite side BC. (5 Marks)

6. The hypotenuse of a right triangle is 26 cm. The sum of the other two sides is 34 cm.

(9 Marks)

[T] a) Find the length of the other two sides of the triangle. (3 Marks)

[T] b) Find the measure of the other two angles. Round to the nearest degree. (3 Marks) [C] c) Describe a situation where you would be able to use knowledge of the

Pythagorean theorem in a practical, real life situation. (3 Marks)

[T] 7. A rectangular skating rink measures 20m by 20m. It has been decided to increase the area of the rink by a factor of 4. Determine how much each side should be

extended. Assume that each side is extended by the same amount. (6 Marks)

[C] What is the significance of keeping the skating rink in the shape of a square?

Justify your answer. (3 Marks)

[A] 8. a) Solve3

d using th

e quadratic formula. (2 Marks)

=d

5

122+

[A] b)Solve 0

x by factoring. Check your solutions. (2 Marks)

-

3

122=