Gr. 10 Pre-Calc/Applied Math Exam Review 2013 Name: ______________________

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Which referent could you use for 1 cm?a. The depth of a kitchen sinkb. The length of a public swimming poolc. The width of your shortest fingerd. The length of a walking stick

____ 2. Which referent could you use for 1 km?a.

The distance equal to laps on an oval running trackb. The length of an iPodc. The length of a snowboardd. The length of your arm span

____ 3. A right cone has a height of 8 cm and a volume of 250 cm3. Determine the radius of the base of the cone to the nearest centimetre.a. 3 cm b. 11 cm c. 17 cm d. 5 cm

____ 4. The circumference of a medicine ball is 28 in. Determine its surface area to the nearest square inch.a. 998 square inches c. 111 square inchesb. 250 square inches d. 371 square inches

____ 5. Determine tan A and tan C.

A B

C

8

10

a. tan A = 1.25; tan C = 0.8 c. tan A = 0.8; tan C = 1.25b. tan A = 0.8; tan C = 0.7809... d. tan A = 0.6247...; tan C = 1.25

____ 6. Determine tan Q and tan R.

P

R

Q

16

12

a. tan Q = 0.428571; tan R = 0.75 c. tan Q = 1.3; tan R = 0.571428b. tan Q = 1.3; tan R = 0.75 d. tan Q = 0.75; tan R = 1.3

____ 7. Determine the measure of D to the nearest tenth of a degree.

D

F

E

821

a. 67.6° b. 69.1° c. 22.4° d. 20.9°

____ 8. Which of the following numbers is not both a perfect square and a perfect cube?a. 531 441 b. 12 544 c. 117 649 d. 15 625

____ 9. Factor the trinomial .a. c.b. d.

____ 10. Which of the following trinomials can be represented by a rectangle?a. c.b. d.

____ 11. Which of the following trinomials can be represented by a rectangle?a. c.b. d.

____ 12. Factor: a. c.b. d.

____ 13. Which of these roots lies between 3 and 4?

, , , a. b. c. d.

____ 14. Write in simplest form.a. b. c. d.

____ 15. A cube has a volume of 7290 cm . Determine the edge length of the cube as a radical in simplest form.a. cm b. cm c. cm d. cm

____ 16. Order these numbers from greatest to least: , , , , a. , , , , c. , , , , b. , , , , d. , , , ,

____ 17. Simplify by writing as a single power. a. b. c. d.

____ 18. Simplify .a. b. c. d.

____ 19. Joshua went on a bike ride. During the ride, he stopped to play at a park, as shown by line segment CD. How much time did Joshua spend at the park?

Time (min)

Dis

tanc

e fr

om h

ome

(km

)

Joshua's Bike Ride

O

A

B

C D

E

20 40 60 80 100 120

1

2

3

4

5

a. 65 min. b. 75 min. c. 70 min. d. 80 min.

____ 20. This graph shows the masses of people, m, as a function of age, a. Determine the range of the graph.

Age (years)

Mas

s (k

g)Ages and Masses of People

0 4 8 12 16 20 a

20

40

60

80

100m

a. c.b. d.

____ 21. This graph shows the cost of gas. The cost, C dollars, is a function of the volume, V litres, of gas purchased. What is the volume of gas purchased when the cost is $10.45?

Volume (L)

Cos

t ($)

The Cost of Gas

0 2 4 6 8 10 V

2

4

6

8

10

12

14 C

a. about 11.5 L c. about 9.5 Lb. about 10.5 L d. about 9 L

____ 22. This graph represents the time it takes to fill a 140-L hot-water tank. Determine the volume of water in the tank after 50 min.

Time (min)

Volu

me

(L)

Filling a Hot-Water Tank

0 10 20 30 40 50 60 70 t

40

80

120

160V

a. about 23 L c. about 119 Lb. about 97 L d. about 108 L

____ 23. A straight section of an Olympic downhill ski course is 34 m long. It drops 16 m in height. Determine the slope of this part of the course.a. c.

b. d.

____ 24. Determine the slope of the line that is perpendicular to this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a. 3 c. 13

b. –3 d.–

13

____ 25. Which graph represents the equation ?

a.

0 2 4–2–4 x

2

4

–2

–4

yc.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

yd.

0 2 4–2–4 x

2

4

–2

–4

y

____ 26. Which graph represents the equation ?a.

0 2 4–2–4 x

2

4

–2

–4

yc.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

yd.

0 2 4–2–4 x

2

4

–2

–4

y

____ 27. A line has x-intercept –9 and y-intercept 3. Determine the equation of the line in general form.a. c.b. d.

____ 28. Which linear system has the solution x = –2 and y = 6?a. x + 3y = 16

4x + 4y = 16c. x + 2y = –2

2x + 4y = –4b. x + 3y = 17

2x + y = 15d. 2x + y = –2

x + y = 16

____ 29. Which linear system has the solution x = 8 and y = 2.5?a. 2x + 2y = 21

2x – 2y = 11c. 2x + 2y = 8

x – y = 21b. x + 2y = 8

2x – 4y = 16d. x + 3y = 22

2x – y = 10

____ 30. At a skating rink, admission is $4.00 for a student and $8.00 for an adult. Tuesday evening, 20 people used the skating rink and a total of $132 in admission fees was collected. A linear system that models this situation is:4s + 8a = 132 s + a = 20where s represents the number of student admissions, and a represents the number of adult admissions purchased.Use the graph to solve this problem:How many students used the skating rink on Tuesday evening?

Num

ber o

f adu

lt ad

mis

sion

s

10

20

30

40

50

Number of student admissions0 10 20 30 40 50

s

a

a. 19 students b. 20 students c. 13 students d. 7 students

____ 31. Express each equation in slope-intercept form.–2x + 4y = 6813x + 4y = 284

a.y =

12x – 17

y = 13

4 x – 71

c.y =

12x + 17

y = 13

4 x + 71b.

y = 284

13 x + 17

y = 13

4 x + 413

d.y =

413x

28413

y = 12x

28413

____ 32. Determine the solution of this linear system:

a. (–2, 2) c. (2, 2)b. (2,–2) d. (–2, –2)

____ 33. Identify two like terms and state how they are related.

a.7x and –5y; by a factor of

57

c.8x and –4y; by a factor of

12

b. 8x and –96; by a factor of 12 d.8x and 7x; by a factor of

78

____ 34. The first equation of a linear system is 2x + 3y = 52. Choose a second equation to form a linear system with infinite solutions. i) 2x + 3y = –260 ii) –10x – 15y = –260 iii) –10x + 3y = –260 iv) –10x + 3y = 255

a. Equation iii b. Equation iv c. Equation i d. Equation ii

____ 35. The first equation of a linear system is 8x + 13y = 166. Choose a second equation to form a linear system with exactly one solution. i) 8x + 13y = –830 ii) –40x – 65y = –830 iii) –40x + 13y = –830 iv) –40x – 65y = 0

a. Equation iii b. Equation i c. Equation ii d. Equation iv

Short Answer – Show all of your work.

36. Determine the angle of inclination of the line to the nearest tenth of a degree.

6.3

4.4

37. A builder wants to cover a wall measuring 9 ft. by 15 ft. with square pieces of plywood.a) What is the side length of the largest square that could be used to cover the wall?

Assume the squares cannot be cut.

b) How many square pieces of plywood would be needed?

38. A cube has surface area 6900.0 cm2. What is the volume of the cube to the nearest tenth of a cubic centimetre?

39. Determine the edge length of a cube with volume 55 cm3.Write your answer to the nearest tenth of a centimetre.

40. A cube has a volume of 1280 cubic feet. Determine the edge length of the cube as a radical in simplest form.

41. Evaluate .

42. The graph shows the height of the tide in a harbour as a function of time in one day. About how high is the tide at 2 p.m., to the nearest metre?

Time (24-h clock)

Hei

ght (

m)

Height of the Tide in a Harbour

000:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00

2

4

6

8

10

43. How can you tell that this graph represents a function? C

ost (

$)

Number of people

Cost of Hosting a Dance

100 200 300 400

1000

2000

3000

4000

44. Suppose a student drew a graph of each function described below. For which graphs should the student connect the points?a) The mass of a stack of coins is a function of the number of coins.b) The temperature in Vancouver is a function of the time of day.c) The mass of an animal is a function of its age.d) The price of a carton of milk is a function of the size of the carton.

45. Describe the graph of the linear function whose equation is .

46. Write this equation in slope-intercept form:

47. Use graphing technology to solve this linear system.Where necessary, write the coordinates to the nearest tenth.–3x + 4y = –35x + 6y = –5

48. Create a linear system to model this situation. Then use substitution to solve the linear system to solve the problem.

At the local fair, the admission fee is $8.00 for an adult and $4.50 for a youth. One Saturday, 209 admissions were purchased, with total receipts of $1304.50. How many adult admissions and how many youth admissions were purchased?

49. Use an elimination strategy to solve this linear system.

50. Sheila plans to place crown moulding along the top of each wall in her family room. A total of 554 in. of moulding is required. The moulding costs $1.59/ft. and is sold in 8-ft. lengths. What is the cost of the crown moulding, before taxes?

51. A right square pyramid has a height of 7.5 m and a base perimeter of 36 m. Calculate the surface area of the pyramid to the nearest square metre.

52. Three squares with side length 9 mm are placed side-by-side as shown. Thomas says ACB is approximately 71.6. a) Is he correct? Justify your answer.

b) Describe what the value of tan C indicates.

A B

C

9

D

mm

E

G

53. A square has area 40.0 cm2. Determine the perimeter of the square to the nearest tenth of a centimetre.

54. Factor this trinomial. Verify that the factors are correct.

55. Factor . Explain your steps.

Time (h)

Flight from Beijing to Edmonton

0 2 4 6 8 10 12 t

1000

2000

3000

4000

5000

6000

7000

8000

9000d

Dis

tanc

e (k

m)

56. Identify any errors in each simplification. Write a correct solution.

a)

b)

57. This graph shows the distance, d kilometres, from Beijing, China, to Edmonton, Alberta, as a function of flying time, t hours.

a) Determine the vertical and horizontal intercepts. Write the coordinates of the points where the graph intersects the axes. Describe what the points of intersection represent.

b) Determine the rate of change. What does it represent?

c) Write the domain and range?

d) What is the distance to Edmonton when the plane has been flying for 5 h?

e) How many hours has the plane been flying when the distance to Edmonton is 6500 km?

58. Students at Tahayghen Secondary School sell punch during the school carnival. The number of cups sold, n, is a linear function of the temperature in degrees Celsius, t. The students sold 458 cups when the temperature was 25°C. They sold 534 cups when the temperature was 29°C. a) Write an equation in slope-point form to represent this function.

b) Use the equation in part a to determine the approximate temperature when the students sell 325 cups of punch.

59. a) Write a linear system to model this situation: The coin box of a vending machine contains $23.75 in quarters and loonies. There are 35 coins in all.

b) Use a graph to solve this problem:How many of each coin are there in the coin box?

Gr. 10 Pre-Calc/Applied Math Exam Review 2013Answer Section

MULTIPLE CHOICE

1. C2. A3. D4. B5. C6. B7. C8. B9. A

10. B11. A12. C13. C14. D15. B16. B17. A18. A19. C20. D21. C22. D23. B24. D25. B26. A27. C28. A29. A30. D31. C32. B33. D34. D35. A36. 55.1°37. a) 3 ft.

b) 1538. 38 998.4 cm3

39. 3.8 cm

40. ft.41. 1642. About 7.5 m43. The graph represents a function because there is only one cost for each number of people.44. a) The points on the graph should not be connected.

b) The points on the graph should be connected.c) The points on the graph should be connected.d) The points on the graph should not be connected.

45. The graph has a slope of and a y-intercept of 7.

46.

47. (–0.1, –0.8)

48. Let a represent the number of adult admissions, and y represent the number of youth admissions purchased.a + y = 209 8a + 4.5y = 1304.5104 adult admissions and 105 youth admissions were purchased.

DB

A

C

7.5 m

s s

4.5 m 4.5 m

49.

50. To convert inches to feet and inches, divide by 12.

554 in. =

554 in. = 554 in. =

Sheila requires approximately 47 ft. of moulding. To find the number of 8-ft. lengths Sheila needs, divide 47 by 8.

=

The number of 8-ft. lengths is greater than 5, so Sheila must buy 6 lengths.The total number of feet in 6 lengths is: 6(8 ft.) = 48 ft.

The cost, C, is:Before taxes, the crown moulding will cost $76.32.

51. Since the perimeter of the square base is 36 m, its side length is: 9 mVisualize cutting the pyramid vertically in half. Sketch a diagram.

Use the Pythagorean Theorem in right ACD.s2 = 7.52 + 4.52

s2 = 56.25 + 20.25s2 = 76.5

s =

Use the formula for the surface area of a right pyramid with a regular polygon base:

SA = s(perimeter of base) + (base area)

SA = ( )(36) + (81)SA = 238.4357...The surface area of the pyramid is approximately 238 m2.

52. a)AB = mm

In right ABC:

Thomas is correct.

b)

In ABC above, tan C indicates that the length of the side opposite C is 3 times the length of the side adjacent to C.53. To calculate the perimeter, first determine the side length of the square.

The side length, s, of a square is equal to the square root of its area.

...

The perimeter, P, of a square is 4 times its side length.

The perimeter of the square is approximately 25.3 cm.

54.

55. Sample answer:

To factor this trinomial, find factors of the form .

The coefficient of is 5, so the coefficients of the 1st terms in the binomial are factors of 5, which are 1 and 5.

So, the binomial has the form .The constant term in the trinomial is 6, so the 2nd terms in the binomial are factors of 6, which are 6 and 1, or 2 and 3.So, the binomials could be:

or or

or

Check which of the 4 binomial products above has its x-term equal to .

This is the correct trinomial.

So,

56. a) There is an error in the second line. When multiplying powers with the same base, the exponents should have been added, not multiplied.A correct solution:

b) There are two errors in the first line. The coefficient 2 was incorrectly multiplied by the exponent –4. And, the exponent of the variable n was added to –4 instead of being multiplied by –4.

A correct solution:

57. a) On the vertical axis, the point of intersection has coordinates (0, 9000). The vertical intercept is 9000. At the start of the trip, the distance from Beijing to Edmonton is 9000 km. On the horizontal axis, the point of intersection has coordinates (12, 0). The horizontal intercept is 12. It takes approximately 12 h to fly from Beijing to Edmonton.

b) Choose two points on the line. Calculate the change in each variable from one point to the other.

Change in distance:

Change in time:

Rate of change:

The rate of change is negative so the distance is decreasing with time.Every hour, the distance to Edmonton decreases by approximately 750 km.

c) The domain is the set of possible values of the time: The range is the set of possible values of the distance:

d) To estimate the distance to Edmonton, use the graph.

From 5 on the t-axis, draw a vertical line to the graph, then a horizontal line to the d-axis. From the graph, the distance to Edmonton is approximately 5250 km.

e) To estimate how many hours the plane has been flying, use the graph.

From 6500 on the d-axis, draw a horizontal line to the graph, then a vertical line to the t-axis. From the graph, the number of hours the plane has

been flying is approximately 3 h.

Num

ber o

f loo

nies

10

20

30

40

50

Number of quarters0 10 20 30 40 50

q

l

58. a) n = f(t), so two points on the graph have coordinates C(25, 458) and D(29, 534).

Use this form for the equation of a linear function:

Substitute: , , , and

In slope-point form, the equation that represents this function is:

b) Use:

Substitute:

When the students sell 325 cups of punch, the approximate temperature is 18°C.

59. a) Let q represent the number of quarters, and l represent the number of loonies.The value of q quarters is 25q cents, and the value of l loonies is 100l cents.Then, a system of equations is: q + l = 3525q + 100l = 2375

b) Since the intersection point is at (15, 20), there are 15 quarters and 20 loonies in the coin box.