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Essentials and Mathematics grade 10 part 1

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; Subject: ; Class: ; with 45 questions; test in 60 minutes; update 18/06/2018
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Question 1.

The following equation represents the cost, C, in dollars, of printing flyers, where n represents the number of flyers being printed.

Cn n ( ) = + 0 01 50 .

The fixed cost is $50

(A)

True

(B)

False

(C) (D)

Question 2.

Joanne has a part-time job in the restaurant. She receives an hourly wage plus commission based on tips. Her gross monthly pay, P, is represented by the equation:

P= 8h + 0.75t 

where h is the number of hours worked and t is the monthly tips in dollars. Joanne’s gross monthly pay in December was $1200.00. Her customers left $400.00 in tips. How many hours did she work?

(A)

100 h

(B)

112.5 h

(C)

150 h

(D)

187.5 h

Question 3.

The number of ants in a colony doubles every fifteen days (d). The colony started with 250 ants and was observed for 90 d.

If the population were graphed in equal divisions of 500, how many divisions would be needed for 90 d?

(A)

6

(B)

15

(C)

32

(D)

90

Question 4.

A sandwich shop’s profit, P, is represented by the function P = 6n - 180, where n represents the number of sandwiches sold. What is the slope of the function and what does it best represent?

(A)

slope = 6; it represents the store’s cost for supplies.

(B)

slope = 6; it represents the customer’s cost per sandwich.

(C)

slope = 30; it represents when the store breaks even.

(D)

slope = 180; it represents the store’s cost for supplies.

Question 5.

To convert a temperature from degrees Fahrenheit, F, to degrees Celsius, C, the formula F(C )= \({9 \over 5}\)C + 32 can be used. What is the Celsius equivalent if  F(C) = 15?

(A)

59

(B)

40.3

(C)

-5

(D)

-9.4

Question 6.

Sara opened a savings account with $25 and added $15 each week for 8 weeks. The savings, S, in dollars, as a function of time in weeks, w, is given by the equation:

                                                                  S =15w + 25

What is the domain?

(A)

{ 0, 1, 2,...,8}

(B)

{ 1, 2, 3,...,8}

(C)

{ 0, 15, 30,...150}

(D)

{ 25, 40, 55,...145}

Question 7.

. What is the range of the relation in the graph below?

 

(A)

0 to 7

(B)

0 to 40

(C)

10 to 40

(D)

all numbers

Question 8.

Cell-Tel charges the restaurant a flat rate of $29.95 per month for 100 min of telephone use, plus $0.24 for each additional minute. Wally’s last bill totaled $43.87 before tax. For how many minutes did he use the phone that month?

(A)

158

(B)

124

(C)

83

(D)

58

Question 9.

Loan-A-Car charges an initial fee for every car rented plus a charge for every kilometre driven. If the car is driven for 120 km, the cost is $53.00. If the car is driven for 340 km, the cost is $86.00.

What is the agency’s initial fee?

(A)

0

(B)

0.15

(C)

33

(D)

35

Question 10.

The Yearbook Club decides to cut costs for the yearbook by reducing the picture size of personal photos. The original pictures have dimensions of 3.5 cm by 4.0 cm.

If each dimension is reduced by a scale factor of 1:2, what is the area of the final reduced photo?

(A)

3.5 cm2

(B)

7 cm2

(C)

28 cm2

(D)

56 cm2

Question 11.

. Tim and Kristen are standing near the dock.

If the height of the cliff is 30 m and Tim is 20 m from the dock, how far is Kristen from the dock, in metres?

(A)

36.55 m

(B)

48.01 m

(C)

54.89 m

(D)

74.89 m

Question 12.

A lighthouse has a height of 20 m. The angles from each boat to the top of the lighthouse are 7.2° and 14° respectively.

What is the distance, in metres, between the boats?

(A)

76.90 m

(B)

78.10 m

(C)

158.32 m

(D)

238.54 m

Question 13.

What value(s) of\(\measuredangle A\) would give cos A = 0.5879, where \(\measuredangle A\) is between 0° and 180°?

(A)

0.99°

(B)

54°

(C)

126°

(D)

54° and 126°

Question 14.

Consider the following diagram:

What method is used to find side AC?

(A)

Sine Law

(B)

Cosine Law

(C)

Tangent Law

(D)

Pythagorean Theorem

Question 15.

If the dimensions of a cube are doubled, the surface area is increased by a factor of 2.

(A)

Always True

(B)

Sometimes True

(C)

Never True

(D)

Question 16.

Which of the following instruments would best measure the height of a door?

(A)

ruler

(B)

micrometer

(C)

tape measure

(D)

trundle wheel

Question 17.

A device measured a distance to be 4.26 m. What is the precision of the measuring device?

(A)

0.005 m

(B)

0.01 m

(C)

0.05 m

(D)

0.1 m

Question 18.

A school bus is travelling at a rate of 50 km/h. It takes ten seconds for the bus to cross a bridge. To the nearest metre, how long is the bridge?

(A)

8

(B)

14

(C)

83

(D)

139

Question 19.

A diagram of a window is shown below. The top of the window is a semi-circle and the bottom part is a rectangle.

What is the total area of the window?

(A)

8.57 m

(B)

10.14 m

(C)

13.28 m

(D)

19.57 m

Question 20.

. The endpoints of a diameter of a circle are A (-5, 7) , and B(1, -1) . What are the coordinates of the centre of the circle?

(A)

(-2, 3)

(B)

(3, -2)

(C)

(1, 0)

(D)

(-3, 4)

Question 21.

Which statement best describes the slopes of parallel lines?

(A)

equal slopes

(B)

undefined slopes

(C)

positive reciprocal slopes

(D)

negative reciprocal slopes

Question 22.

On a map, the corners of a farmer’s field have coordinates of

A (-1, 4),  B(-3, -2), C(3, -1) , and D(4, 5).

Which of the following is true about the line segments enclosing the field?

 

(A)

II only

(B)

III only

(C)

I and III only

(D)

None of the statements are true

Question 23.

Which of the following are properties of the line y =2x + 3?

 

(A)

I and II only

(B)

I and III only

(C)

II and III only

(D)

I, II and III

Question 24.

Rebecca plots two points: A (-32, 40) , and B(10, 124). What is the equation of the line that passes through these points?

(A)

y= \({1\over 2}\)x + 56

(B)

y =2x + 104

(C)

y = 0.5x - 52

(D)

y = 1.6x + 60.7

Question 25.

Points A, B, C, D and E are all on the same line.

• C is the midpoint of A and E

• B is the midpoint of A and C

• D is the midpoint of C and E

What are the coordinates of point E?

(A)

(7, 9)

(B)

(12, 3)

(C)

(12, 9)

(D)

(14.5, 0)

Question 26.

The following table represents several students’ homework marks compared to their final report card marks.

What is the value of the correlation coefficient for this data?

(A)

0.68

(B)

0.98

(C)

1.41

(D)

25.22

Question 27.

If a linear regression gives an r value of 0.92, this would indicate that the data is

(A)

not linear.

(B)

perfectly linear.

(C)

approximately linear with a positive slope.

(D)

approximately linear with a negative slope.

Question 28.

A ramp 20 feet long and 12 feet high is pushed against a box of the same height and 40 feet long (as shown below).

What is the slope of the ramp from A to B?

(A)

\({1 \over 5}\)

(B)

\({2 \over 5}\)

(C)

\({3\over 5}\)

(D)

\({4 \over 5}\)

Question 29.

A spreadsheet is created to track a loan.

If the interest rate in Year 4 is changed, which of the following cells would change?

(A)

B5

(B)

D4

(C)

D5

(D)

E5

Question 30.

A table is created to track a loan.

What is the interest charged on the loan in Year 3?

(A)

$898.20

(B)

$934.13

(C)

$970.06

(D)

$9700.59

Question 31.

Ming needs four new tires for his car. He finds the following ads in the newspaper.

At which store would Ming get the best price?

(A)

Can City Tires

(B)

Julie’s Tires

(C)

Tire Town

(D)

Wheels & Tires

Question 32.

Kirsten decides to go to Japan. She needs to convert $250 US to Japanese yen.

Which exchange rate would she use?

(A)

0.011280

(B)

1.36724

(C)

88.6500

(D)

121.21212

Question 33.

A spreadsheet is created to track a loan.

Which formula would calculate G4?

(A)

= B3 + D3 -E3

(B)

= B4 + D4 + E4 -F4

(C)

= B4 + D4 - E4

(D)

= B4 + D4 - E4 - F4

Question 34.

The two locations of Lily’s Flowers sell roses, tulips and carnations. The two locations sold the following amounts of flowers and made $0.12 profit per flower.

What was Lily’s Flowers total profit?

(A)

$21.84

(B)

$23.52

(C)

$44.64

(D)

$372.00

Question 35.

The volume of a cube is 5 cm3

 

 

 

.

What is the length of each side?

(A)

1.67 cm

(B)

1.71 cm

(C)

2.24 cm

(D)

125 cm

Question 36.

A cone and a cylinder both have a height of 10 cm. Their volumes are below.

Which of the following statements is correct about the radii of the shapes?

(A)

The radius of the cone is greater.

(B)

The radius of the cylinder is greater.

(C)

The radii of both shapes are equal.

(D)

The relationship cannot be determined from the information given.

Question 37.

Which situation best describes the graph?

(A)

Distance over time on a one-way car trip.

(B)

Cost of parking in a pay parking lot over time.

(C)

Cars in the school parking lot during one day.

(D)

Cost of renting a car for an initial fee plus a charge per kilometre travelled

Question 38.

A factory makes tables. The cost of running the factory is $300 per day plus $50 for each table made. What is the total cost (C), in dollars, as a function of the number of tables (t) made?

(A)

C = 350t

(B)

C = 50t + 300

(C)

C = 300t + 50

(D)

t = 300 + 50C

Question 39.

Students sell tickets for a raffle. If the students sell 500 tickets, they lose $250. If the students sell 1500 tickets, they make a profit of $250. How many tickets do they need to sell to “break even” (no loss or gain)?

(A)

0 tickets

(B)

250 tickets

(C)

1000 tickets

(D)

2000 tickets

Question 40.

Data for various bridges is plotted, where the number of support beams depends on the length of the bridge

What is the domain of the above graph?.

(A)

{1, 2, 3, 4, 5}

(B)

{3, 7, 11, 15, 19}

(C)

All numbers between 1 and 5 inclusive.

(D)

All numbers.

Question 41.

. Given the function y=-2x + 8, what is the y-intercept?

(A)

(-2, 0)

(B)

(0,-2)

(C)

(0, 8)

(D)

(8, 0)

Question 42.

Given the function y = -2x + 8, what is the x-intercept?

(A)

(-4, 0)

(B)

(4, 0)

(C)

(0, 8)

(D)

(8, 0)

Question 43.

Wally wants to advertise his restaurant in the local newspaper. The cost in dollars (C) to run an advertisement for (d) days is given by the formula:

C = 12 + 5.5d

Which of the following represents the cost per day to run an advertisement?

(A)

$5.50

(B)

$12

(C)

$17.50

(D)

C

Question 44.

The equation representing a flare’s height, h in metres, when shot in the air over time t, in seconds, is h = -4.9t2 + 40t . Which window settings below would be the most appropriate for this situation?

(A)

x min = -10   y min = -890

x max = 10,  ymax = 81.6

(B)

x min = -10   y min = -10

x max = 10   y max = 10

(C)

x min = 0   y min = -90

x max = 10  y max = 81.6

(D)

x min = 0    y min = 0

x max = 10   y max = 85

Question 45.

What is the correct formula for calculating the surface area of the sphere below?

 

(A)

SA = \({4 \over 3}\)\(\pi\)(15)3

(B)

SA = 4\(\pi\)(30)

(C)

SA = 4\(\pi\)(15)2

(D)

SA = 4\(\pi\)(30)2

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37    Question 38    Question 39    Question 40    Question 41    Question 42    Question 43    Question 44    Question 45   
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