Math 1D Practice Exam
Page 1 of 8
January 2015
WATERLOO COLLEGIATE INSTITUTE
MATHEMATICS DEPARTMENT
MPM1D (Grade 9 Academic)
PRACTICE EXAM
STUDENT’S NAME: ________________________________________
Instructions to Students:
 This exam contains 8 pages including this cover page. Check to make sure your exam is complete.
 Students may have foolscap paper for rough work.
 Please write clearly. Show all formulas and work where requested.
 Scientific, non-programmable calculators may be used for this examination (which means that TI-83
graphing calculators are NOT allowed). Calculators may NOT be shared between students.
THIS PRACTICE EXAM IS NOT A REPRESENTATIVE OVERVIEW OF THE COURSE.
IT IS NOT THE ONLY PREPARATION YOU SHOULD BE DOING FOR THE EXAM.
Math 1D Practice Exam
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January 2015
Part A – Short Answer [27 marks]
It is not necessary to show your calculations.
Please answer each of the following questions in the space provided.
1. Evaluate each of the following:
a) (3) 3
__________________
b) [( 3  1) 2 ]4
__________________
2. Simplify each of following
a) x2  x4  x
b)
__________________
 3x 2 y 3
__________________
6x 2 y 2
c) 3 y ( y  1)
__________________
3. Identify each of the following as linear or non-linear:
a) x  y  1
__________________
b) y  x 2  1
__________________
4. What is the slope of the line below?
__________________
y
5
4
3
2
1
–5
–4 –3 –2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
5. State the slope and y-intercept for the line below:
y
slope:
5
_____________
4
y-intercept:
3
_________
2
1
–5
–4 –3 –2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
6. What is the slope of a line perpendicular to y  3x  2 ?
__________________
Math 1D Practice Exam
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January 2015
7. What is the missing value, k, such that the relation is linear?
x
3
6
9
__________________
y
0
k
10
8. If the points (2, 3) and (1, y) have a slope of 2 between them, then the value
of y is:
y
__________________
5
4
3
2
1
–5
–4 –3 –2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
9. What is the point of intersection of these two lines?
y
5
__________________
4
3
2
1
–5
–4 –3 –2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
10. State the slope for the following equation of a line: y  2
__________________
11. Simplify: 2x + 3x2 – 3x + x 2
__________________
12. Solve: 5  2 y  1
__________________
13. Solve for r: A  r 2
__________________
14. The OTHS student council is running a dance to raise money for the local
food bank. They will charge each student $5 per ticket, but the cost for the
DJ is $250.
a) Identify the fixed cost.
__________________
b) Write an equation to model the revenue for the dance.
__________________
Math 1D Practice Exam
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January 2015
15. A school is planning on planting a garden. A member of the community
donated 60 feet of fence. What are the optimal dimensions of the garden?
__________________
16. Which of the following quadrilaterals has perpendicular diagonals of equal
lengths: rectangle, rhombus, parallelogram or square?
__________________
17. A cone has a radius of 3 cm and a slant height of 5 cm.
What is the height of the cone?
__________________
18. Examine the figure below. Determine the measure of FEG.
__________________
19. In the diagram below, line segment EB bisects ABD. Determine the
measure ofABE.
__________________
20. What is the measure of each exterior angle of a regular polygon with 5 sides?
__________________
21. Determine whether the following conjecture is true or false (write T or F):
If a triangle has two acute angles, then the third angle must be acute.
Part B – Answer each of the following in the space provided. [45 marks]
Please show ALL calculations.
1. Simplify: ( 1x 2 y )(2 xy)
[2]
__________________
Math 1D Practice Exam
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January 2015
2. Express the equation x  2 y  3  0 in the form y  mx  b
[2]
3. Solve each equation. No check is necessary.
a) 3(1  x )  2( x  1)
b)
y
42
3
[2]
[2]
4. The graph below shows the amount of money in a bank account.
y
a) Identify the dependent variable.
1400
1300
Account Balance ($)
1200
1100
1000
b) Describe (in words) the relationship between the variables.
900
800
700
600
500
c) Estimate the bank balance after 6.5 weeks.
400
300
200
100
1
2
3
4
5
6
7
8
9
x
Week
[3]
5. The graph below represents four segments of Selena’s morning walk. Describe the four segments of
Selena’s walk including information about direction, distance, time and speed, in m/min.
[4]
Math 1D Practice Exam
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January 2015
6. A gym charges a $80 membership fee, plus a fee of $20 per month.
a) How much does it cost to use to belong to the gym for a year?
[1]
b) If you made a payment of $220, how many months would this cover?
[2]
7. A submarine starts at sea level and descends 40 m every 5 min. How long would it take the submarine
to reach a depth of 380 m?
[2]
8. Determine the equation of the line that passes through P(, 3) and the origin.
[2]
9. Graph the line y  
2
x on the grid below.
3
[2]
y
5
4
3
2
1
–5
–4 –3 –2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
Math 1D Practice Exam
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January 2015
10. Calculate the value of x.
[3]
11. A laundry detergent company plans to sell a “bargain box” that contains 10 L of detergent. Find the
dimensions of the rectangular box that uses the smallest amount of cardboard.
[Recall: 1 L = 1000 mL; 1 mL = 1 cm3]
[4]
12. A farmer wants to make a cylindrical water tank using metal. Suppose she has 75 m2 of metal
available. Determine:
a) the dimensions of the tank that will hold the largerst volume of water.
[2]
b) the volume of water, to one decimal place, this tank could hold.
[2]
Math 1D Practice Exam
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January 2015
13. Patrick works 35 hours per week in retail selling shoes. He earns a base salary of $9.50/h and receives
a commission of 4% on the sales that he makes.
a) Determine Patrick’s earnings for a week when he sells $3000 worth of shoes.
[2]
b) Graph Patrick’s total salary, T, versus his weekly sales, S. Clearly label the axes on the graph below.
[2]
T
s
c) What is the equation of the relation?
[1]
d) What is the slope of the relation? What does this slope represent?
[1]
e) What is the T-intercept of the relation? What does it represent?
[1]
f) Patrick’s friends, Grace and Malcolm, also work at shoe stores. They also work 35 h per week. Grace
earns $8/h with 6% commission. Malcolm earns $15/h with no commission. Each of the three friends
sells about $2500 worth of shoes each week. Which person seems to have the best-paid job? Justify
your answer mathematically. Use the back of this page if you need more space.
[3]