MPM 2D1: PRACTICE EXAM
1. Solve each of the following by the method specified:
a) Solve by Graphing. Check your answer.
y  4 x  6
2
y  x 8
3

b) Solve by Substitution:
c) Solve by Elimination:
5y  3x  1
4 x  3y  6
y  2x  7
12y  5x  8


2. State the equation of a circle with centre (0,0) that passes through the point (5,2). Include a sketch.
3. Given the points A(2,-4) and B(-3,8) find:
a) The length of the line segment AB.
c) The equation of the line through A and B
b) The midpoint of the line segment AB.
d) The slope of a line perpendicular to AB.
4. Complete the following table and then sketch y=x2 in pencil and each of the following parabolas in colour:
Equation
Vertex

Axis of
Symmetry
Domain
Range
y  (x  2) 2  6

y  3x 2 1
5. Expand and simplify each of the following.
a) (4 x  2)(2x  5)
b) (12x  5)(12x  5)


c)
(7x  4) 2

6. Factor fully:
a)
24 x 2 y 3 z  6xz
2
b) x  9x  20


d) 100x  49y
2
2
c) 5x 12x  9

2

7. Solve each of the following quadratic equations using the method specified.
a) Solve by Factoring:
b) Solve by the Quadratic Formula:
x 2 11x  24  0

2x 2  5x  9  0

8. Using trigonometry, find the missing value in each of the following diagrams. Round to 1 decimal place.
a)
b)
c)
15
x
20
x
9
80o
7

35o
d)
e)
75o
x
13
x
62o
55o
10 cm
16 m
9. The sum of two numbers is 31. The sum of the second number less 10 and twice the first number is 33.
What are the two numbers?
10. Flora invests a total of $10 000 in two different bonds. One bond earns 1.5% interest per annum and the
other earns 2.0% per annum. At the end of the year she received 198.40 in interest from the two bonds
together. How much did she invest in each bond?
11. Expand and simplify the following:
a) 10( x  3y)(2 y  5x)

b) (x  2)(x  5)  2(x  4)(3x  5)

12. Factor fully:
2
a) 12x 12 x  9

2
2
b) 50a  32b

13. The vertices of a triangle ABC are A(1,1), B(6,5) and C(12,-7). Find the equation of the perpendicular
bisector of BC.
14. What type of triangle is formed by the vertices A(0,10), B(9,-9), and C(14,5)?
15. Complete the square and state the vertex of the parabola y  3x  30x 10 .
2

h  0.5(x  3) 2  4.5
16. Solomon kicks a soccer ball in the arc
, where h is the height of the ball in metres
and
t is the time in seconds.
 the ball reaches?
a) What is the maximum height that
b) How long does it take for the ball to hit the
ground.
c) How high is the ball 2 seconds after Solomon kicked it?
17.
The neighbours decided to re-carpet their rectangular living room, which is 6 m longer than it is wide. The
wall to wall carpeting that they purchases covers 55 m2. What are the dimensions of the room?
18. Solve the following quadratic equation. State both the exact roots and the approximate roots rounded to 2
decimal places. x2 = 90 – 6x
19. Hal looks out of his apartment window at the building across the street. He looks up at a 35 o angle and sees
a bird on a ledge 5m above his apartment. How far apart are the building? Round your answer to 2 decimal
places.
20. A golf ball is hit from a raised platform in the arc
d is the horizontal distance.
a) How high is the platform?

h  0.5d 2  2d  6
, where h is the height in metres and
b) How far away does the ball land on the ground.