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MPM2D – Final Exam Review
Exam Date: Tuesday January 24, 2017 – 9:00am – 12:00pm
Exam Format
Part A – Fill in the blank (Knowledge & Understanding)
Part B – Choose 5 terms and define with example (Communication)
Part C – Short Answer Problem Solving (Thinking & Inquiry)
Part D – Long Answer Problem Solving (Application)
TOTAL
/20 marks
/10 marks
/35 marks
/35 marks
/100 marks
Unit 1 - Linear Systems:
1.
Solve the following linear systems of equations using the method given.
a) 2x + 4y = 14 (Graphically)
b) 3m + n = 5 (Substitution)
c) 4x – 3y = –9 (Elimination)
3x – y = 14
m – 2n = 11
5x – 2y = 1
2.
Luke’s age is two less than twice Peter's age. The sum of their ages is 37. How old are they?
3.
a)
b)
Tony has a total of $580 in $5 and $10 bills. How many of each type does he have if he has 76
bills in total?
The school hockey team travelled 150 km to a tournament by bus. The bus drove at 90 km/h
most of the way, but was delayed by a storm, when its speed was only 30 km/h. If the trip took
3 h, how far did the bus travel in the storm?
Unit 2 – Analytical Geometry:
4.
Given the points A(4, 5) and B(-2, 17), find:
a) The slope of AB.
c) The length of AB.
b) The midpoint of AB.
d) The equation of the line through AB.
5.
A see-saw has its pivot at P(1, -1) and one end at A(-3, 5). Find the coordinates of the other end.
6.
Describe the steps needed to: (Do not solve!!)
a) Find the equations of the median lines of the triangle with vertices A(1, 5), B(5, 7) and C(3, -3).
b) Determine whether the triangle with vertices X(-1, 3), Y(3, 5) and Z(2, 4) is a right triangle or not.
c) Determine whether the quadrilateral with vertices P, Q, R and S is a parallelogram.
7.
Determine whether the triangle with vertices X(5,6), Y(-1,2) and Z(1,-3) is scalene, isosceles or
equilateral.
8.
Find the equation of the perpendicular bisector of the line segment with endpoints A(-1, 4) and B(3, 2).
9.
Show that the quadrilateral with vertices E(-2,3), F(2,1), G(0,-3) and H(-4,-1) is a square.
10. Find the equation of the circle centred at the origin that goes through the point (5, 3).
MPM2D – Final Exam Review
Unit 3 – Algebra:
11. Expand and simplify the following:
b)  2 x  1
a)  x  2 x  5
2
c)  3x  4 2 x  1
d) 2 2 x  3 3x  5
d) 49m2 – 100n2
12. Factor the following:
a) 15x 2  35xy
b) x 2  8x  15
c) 3x 2  24 x  21
e) 4a 2  36a  81
f) 2 x 2  x  15
g) 6t 2  7t  2
Units 4 & 5 – Quadratic Functions and Equations:
13. a) Find the vertex form of y = 2x2 + 28x + 90.
b) Describe the transformations and sketch the graph of the function
14. State the equation of the axis of symmetry if the zeros of a quadratic are 10 and -2.
15. If the second differences of a parabola are positive, determine whether the optimum value would be
a maximum or minimum.
16. Determine the zeroes of y = 2x2 + 8x – 24.
17. Solve the following quadratic equations.
a) x 2  5x  14  0
b) x  12  20x 2
c) 4t 2  196  0
e) x 2  8 x  1  0
d) 2(x - 1)2 - 4= 52
18. A ride at Canada’s wonderland can be modeled by the equation h = -5t2 + 20t + 14, where h is in
metres, and t is in seconds.
a) What is the ride’s initial height?
b) What is the maximum height of the ride?
c) After how many seconds is the height of the 25m?
d) When does the ride touch the ground?
19. A commuter train carries 2000 passengers daily from a suburb into a large city. The cost to ride is $4
per person. Market research shows that 40 fewer people will ride the train for each $0.10 increase.
a) Determine the revenue equation.
b) What should the cost be to maximize revenue?
Unit 6 – Similar Triangles and Trigonometry:
20. Determine whether the following triangles are similar, congruent or neither. Explain your reasoning.
a) J
b)
D
A
N
x
K
x
C
M
L
B
E
21. Find the unknown side.
a) h
15
35
m
m
10
42
x
8
5
6
50
c)
b)
x
d)
x
8
58
MPM2D – Final Exam Review
22. Find the missing angles:
a)
b)
x 23 m
15 m
10 m
D
c)
A
d)
8.1 m
6
12 m
4
x
E
3
10.6 m
44
F
23. A tunnel goes through a mountain. From the two ends of the tunnel, the angles of elevation to the
peak are 37o and 49o. Find the length of the tunnel if the peak is 2750 m above the tunnel.
24. Jessie and Matt went out in separate boats to place markers for a boat race. From the dock, their
paths formed an angle of 85o. Jessie rowed 85 m and Matt rowed 102 m to place their markers. How
far apart are the markers?
25. At an amusement park, the straight water slide is 42 m long and drops 20 m. What angle does the
slide make with the horizontal?
26. An isosceles triangle has a base of 10m. Find the lengths of each side of the triangle if the base
angles are 35o.
Answers:
1. a) (5,1)
b) (3, -4)
c) (3, 7)
2. 24, 13
3. a) 36 $5s, 40 $10s
b) 60km
4. a) -2
b) (1, 11)
c) 13.42u
d)y = -2x + 13
11. a) x 2  3x  10
b) 4 x 2  4 x  1
c) 6x 2  11x  4
d) 12 x 2  2 x  30
12. a) 5x3x  7 y
b)  x  3 x  5
c) 3 x  1 x  7
d) (7m + 10)(7m – 10)
e) 2a  9
f) 2 x  5 x  3
g) 3t  22t  1
5. (5, -7)
7. Scalene
8. y  23 x  13
10. x2 + y2 = 34
2
13. a) y=2(x+7)2 - 8
b) VT by a factor of 2, VT 9 units down, HT 7 units left
14. x = 4
15. Minimum
16. 2, -6
MPM2D – Final Exam Review
17. a) x  7, x   2
b) x 
18. a) 14m
b) 34m
3
4
,x  
4
5
19. a) R=(2000-40x)(4 +.1x).
20. a) Similar
b) Similar
21. a) 21.4
b) 1.67
22. a) 58.6°
23. 6039.9m
24. 127m
25. 28.44o
26. 6.10m
b) 33.7°
c)7, -7
d) 1 2 7
c) 0.66s and 3.34s
d) 4.6s
e)  4  15
b) $4.50.
c) 11.1
d) 7.0
o
O
c) D=65.37 , E = 70.63
d) A=26.4°