加拿大安大略省十级数学试卷 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) Solve 35122+=d d using the quadratic formula. (2 Marks)
[A]
b) Solve 03122=-x by factoring. Check your solutions. (2 Marks)。