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MPM 1D Practice Exam

Page 1 of 9

June 2016

Waterloo Collegiate Institute MATHEMATICS DEPARTMENT MPM1D (Grade 9 Academic) PRACTICE EXAM June 2016

STUDENT’S NAME: ________________________________________

Instructions to Students: This exam contains 10 pages altogether, including an additional formula sheet. Check to make sure you have all pages immediately. 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.

Part A

Part B

Communication

TOTAL

27

45

5

77

MPM 1D Practice Exam Page 2 of 9 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.

June 2016

1. Evaluate each of the following: a) (3) 3

__________________

b) [( 3 1) 2 ]4

__________________ 2. Simplify each of following a) x2 x4 x 3x 2 y 3 b) 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 5

slope:

4

_____________

3

y-intercept:

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 ?

__________________

MPM 1D Practice Exam Page 3 of 9 June 2016 7. What is the missing value, k, such that the relation is linear? x y __________________ 3 0 6 k 9 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 ABCD 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.

__________________

MPM 1D Practice Exam Page 4 of 9 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?

June 2016 __________________

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 ofABE.

__________________

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]

__________________

MPM 1D Practice Exam Please show ALL calculations.

Page 5 of 9

June 2016

1. Simplify: ( 1x 2 y )(2 xy ) [2] 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) 3 +

3− 2𝑥 6

=

𝑥+8 3

− 4𝑥

[2] [4]

4. The graph below shows the amount of money in a bank account. y

a) Identify the dependent variable.

1400 1300 1200

Account Balance ($)

1100 1000 900

b) Describe (in words) the relationship between the variables.

800 700 600 500 400 300 200

c) Estimate the bank balance after 6.5 weeks.

100 1

2

3

4

5

Week [3]

6

7

8

9

x

MPM 1D Practice Exam

Page 6 of 9

June 2016

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]

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]

MPM 1D Practice Exam

Page 7 of 9

June 2016

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

1

2

3

4

5

x

–2 –3 –4 –5

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]

MPM 1D Practice Exam

Page 8 of 9

June 2016

12. A farmer wants to make a rectangular pen that will enclose an area of 275 m2. The farmer would like to use the minimum amount of fencing necessary. Determine: a) the dimensions of the pen if it is built in what is currently an open field [2]

b) if the farmer used the same amount of fencing as calculated in a) above but built the pen against the side of the barn, how much more area could he enclose? [4]

MPM 1D Practice Exam

Page 9 of 9

June 2016

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. [3]

Page 1 of 9

June 2016

Waterloo Collegiate Institute MATHEMATICS DEPARTMENT MPM1D (Grade 9 Academic) PRACTICE EXAM June 2016

STUDENT’S NAME: ________________________________________

Instructions to Students: This exam contains 10 pages altogether, including an additional formula sheet. Check to make sure you have all pages immediately. 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.

Part A

Part B

Communication

TOTAL

27

45

5

77

MPM 1D Practice Exam Page 2 of 9 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.

June 2016

1. Evaluate each of the following: a) (3) 3

__________________

b) [( 3 1) 2 ]4

__________________ 2. Simplify each of following a) x2 x4 x 3x 2 y 3 b) 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 5

slope:

4

_____________

3

y-intercept:

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 ?

__________________

MPM 1D Practice Exam Page 3 of 9 June 2016 7. What is the missing value, k, such that the relation is linear? x y __________________ 3 0 6 k 9 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 ABCD 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.

__________________

MPM 1D Practice Exam Page 4 of 9 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?

June 2016 __________________

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 ofABE.

__________________

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]

__________________

MPM 1D Practice Exam Please show ALL calculations.

Page 5 of 9

June 2016

1. Simplify: ( 1x 2 y )(2 xy ) [2] 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) 3 +

3− 2𝑥 6

=

𝑥+8 3

− 4𝑥

[2] [4]

4. The graph below shows the amount of money in a bank account. y

a) Identify the dependent variable.

1400 1300 1200

Account Balance ($)

1100 1000 900

b) Describe (in words) the relationship between the variables.

800 700 600 500 400 300 200

c) Estimate the bank balance after 6.5 weeks.

100 1

2

3

4

5

Week [3]

6

7

8

9

x

MPM 1D Practice Exam

Page 6 of 9

June 2016

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]

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]

MPM 1D Practice Exam

Page 7 of 9

June 2016

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

1

2

3

4

5

x

–2 –3 –4 –5

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]

MPM 1D Practice Exam

Page 8 of 9

June 2016

12. A farmer wants to make a rectangular pen that will enclose an area of 275 m2. The farmer would like to use the minimum amount of fencing necessary. Determine: a) the dimensions of the pen if it is built in what is currently an open field [2]

b) if the farmer used the same amount of fencing as calculated in a) above but built the pen against the side of the barn, how much more area could he enclose? [4]

MPM 1D Practice Exam

Page 9 of 9

June 2016

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. [3]

*When life gives you a hundred reasons to cry, show life that you have a thousand reasons to smile*

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