Practice Test 1

Technology Math Skills Assessment

1. Which of the following is the best description of 35

x2?

a. Monomialb. Binomialc. Polynomiald. Both a and c

2. Create a table of values for the equation y = –2x + 8x y

–2–1012

3. Choose the answer that represents each number in exponential form:5 × 5 × 5 × 5 × 8 × 8 × 8 × 11 × 11

a. 54 × 83 × 112

b. 44024

c. (5 × 8 × 11)4

d. None of the above

4. Simplify: 2(7 – 62 ÷ 3) + √25

5. Write 1945% as a decimal.

6. Write the equation of a line given by 3y = x in standard form (i.e., in the form Ax + By + C = 0)

7. If it takes 150 minutes to fill up a pool of 20 cubic meters, what is the filling rate in cubic meter per hour?

8. Solve: 3x5

– 2 = x5

9. Which ratio is equivalent to 36 : 27?

a. 18 : 14b. 72 : 81c. 4 : 3d. All of the above

10. 25 is what percent of 45? Express your answer rounded to the nearest percent.

11. Arthur is paid $25,000 for completing his novel and will receive an additional $7 for every book sold. Choose the equation that best represents this situation.

a. y = 7x + 25000b. y = 25000 – 7xc. y = 7 + 25000xd. y = 25000(7x)

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12. True or False: The line y = 4 has a y-intercept of (4, 0).

13. Identify whether the following situation can be modelled by a linear relationship:The distance travelled by Laura walking at a constant rate of 1 km per 10 minutes.

14. Identify the greatest common factor: 32a3, 20a2, 40a.

a. 4ab. 40a3

c. 20ad. 4

15. In the following situation, identify the independent and dependent variables. Over the past few years, the local weather station has kept track of the average temperature every month.Months = Average temperature =

16. Which of the following represents the volume of a cone?

a. V = l × h × w

b. V = 13πr2

c. V = 13πr2 h

d. V = 13πrh

17. At the end of the school year, a math teacher calculated his students’ attendance frequency as a percent and created a scatterplot of attendance frequency versus final mark. On this scatterplot, the point (75, 80) would represent a student who attended class 75% of the time and who received 80% as a final mark. Which is the dependent and independent variable?

a. Both variables are dependent.

b. Final grade is independent, and attendance is dependent.

c. Final grade is dependent, and attendance is independent.

d. The teacher and the students are both independent.

18. John rents a car at a car rental. The payment plan requires a $50 upfront charge and an additional $0.50 per mile travelled. Which equation represents John’s cost (y) if he travels x miles?

a. y = 0.5 + 50x

b. y = 50 + 0.5x

c. y = 0.5 – 50x

d. y = 50 – 0.5x

19. There are 24 red cars and 9 black cars in the airport parking lot. What is the ratio of black cars to the total number of cars in the parking lot? Express your answer reduced to the lowest terms.

20. What is the value of the first differences of y = –3x + 2?

2

21. Given the following graph, determine the equation which fits the graph.

X

Y

1

1

2

3

4

0–1–2–3 2

a. y = 2x + 72

b. y = –2x + 72

c. y = 12

x + 2

d. y = –12

x + 2

22. Fill in the missing cells in the following table of values, based on the given scatterplot.

X

Y

8

1

2

4

6

8

10

12

14

16

6420 10 12 14 16

x y0 16123 144 164 125 12

1110

7 77 68 98 89 12

12 1312 1212 613 8

23. Solve: 2(x + 1) – (x2 + 3x + 6) + x2 = 0

3

24. Divide, simplify, and choose the most correct answer: (8p6 q3 ) ÷ (2p2 q)

a. 4p3 q3b. 16p8 q4

c. 4p4 q2

d. p4 q2

25. Write the equation of a line given by 6x – 3y + 9 = 0 in slope-intercept form (i.e., in the form y = mx + b).

26. Find the volume of a triangular prism with a base area of 485.3 cm2 and a height of 8.5 cm. Express your answer rounded to one decimal place.

27. To teach Mandy the value of money, her parents help her start a business of making and delivering cupcakes in the neighborhood. They have discussed three different pricing models, which each include a standard delivery cost and a cost per cupcake, as shown on the graph below. Which of the following statements is false? Select all that apply.

X

Y

8

5

10

15

20

25

30

35

40

6

Model A

Model B

Model C

420 10

a. The standard delivery cost for Model C is smaller than the standard delivery cost of Model A.

b. The cost per cupcake for Model A is half the cost per cupcake for Model B.

c. The cost per cupcake for Models B and C are the same.d. The delivery charge for Model B is greater after three cupcakes.

28. The volume of a cube can be modelled with an algebraic equation of degreea. One

b. Two

c. Threed. It cannot be modelled with an algebraic equation

29. Young is moving from Toronto to Ottawa and needs to hire a moving company. The first company he calls offers him the truck rental and two movers for $1000, plus $60 per hour. The second company charges a rate of $100 per hour. Determine the number of hours of use for which both companies would charge the same amount.

30. Letisha’s website had 485 visitors today, which is 3% less than yesterday. How many visitors did she have yesterday?

4

31. Calculate the area of the shape below and express your answer rounded to the nearest integer.

16 m

4 m

32. What is the sum of the interior angles of a hexagon (6 sides)?

33. Which of the following equations will result in a line perpendicular to the line displayed in the graph?

X

Y

3

1

2

3

210–1 4

a. y = 2x + 1

b. y = –2x + 1

c. y = 12

x – 3

d. y = –12

x – 3

34. Two painters place a bid to paint the exterior of a building that has a surface area of 5,000 square feet. The first painter charges $25,000 plus $2 per square foot, while the second painter charges $6 per square foot. Which painter will you choose for a greater financial benefit?

35. The supports on a treehouse intersect in the following triangular pattern. At what angle do the supports join at point A?

115°

55°

A

5

36. Which of the following equations represents the line of best fit for the following scatterplot?

X

Y

8

2

4

6

8

10

12

14

16

6420 10 12 14 16

a. y = 12

x + 8

b. y =–23

x + 9

c. y = x + 1

d. y = 134

x + 4

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Answer Key

1. a2. x y

–2 12–1 100 81 62 4

3. a4. –55. 0.1986. x – 3y = 07. 8 cubic meters per hour8. x = 59. c10. 56%11. a12. False13. Yes14. a15. Months = Independent variable

Average temperature = Dependent variable16. c17. c18. b19. 3 : 1120. –321. d

22. x y0 161 122 133 144 164 125 126 116 107 77 68 98 89 12

10 1112 1312 1212 613 815 4

23. x = –424. c25. y = 2x + 326. 4125.1 cm3

27. c, d28. c29. 25 hours30. 500 visitors31. 45 m2

32. 720˚33. a34. Second painter35. 60˚36. c

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