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Foundations of Mathematics and pre-calculus level 3

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; Subject: ; Class: ; with 30 questions; test in 45 minutes; update 04/07/2018
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Subjects Update 04/07/2018
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Question 1.

The length of a fireplace mantle is 6'– 9" . Express this length in metres.

(A)

2.1

(B)

4.5

(C)

20.6

(D)

205.9

Question 2.

How many British gallons are equivalent to 24 US gallons?

(A)

20.0

(B)

23.2

(C)

26.4

(D)

28.8

Question 3.

The top of a 20 foot long railing is to be painted. The diameter of the roller to be used is 8.9 cm. Paint needs to be replenished after 6 rotations of the roller. How many times does the painter have to add paint to his roller?

(A)

12

(B)

9

(C)

5

(D)

4

Question 4.

The diameter of a tray is 42 cm and the diameter of a glass is 56 mm. Based on math calculations, a server thought he would be able to fit 56 glasses onto the tray. In fact, he is able to fit only 37 glasses. Approximately how much space on the tray is not covered by glasses?

(A)

1800 cm2

(B)

475 cm

(C)

185 cm2

(D)

155 cm2

Question 5.

The quilt shown below was created with two different fabric colours. Estimate the ratio of dark fabric to light fabric.

(A)

1:1

(B)

1:3

(C)

2:3

(D)

3:4

Question 6.

The Vernier calliper shown below is calibrated in SI units. What is the measurement on the calliper?

(A)

2.01 cm

(B)

2.12 cm

(C)

2.55 cm

(D)

3.05 cm

Question 7.

he foundation walls of a cabin are constructed as follows:

• 8\({1\over 4}\)" thick concrete

• 2\({7 \over 8}\)" thick insulation board on both interior and exterior sides

• \({1 \over 2}\) " thick cedar on the exterior side only

Which solution would be used to determine the total thickness of the foundation walls?

(A)

2(2\({7 \over 8}\) + \({1 \over 2}\)) + 8\({1 \over 4}\)

(B)

8\({1 \over 4}\) - (2\({7 \over 8}\) + \({1 \over 2}\))

(C)

8\({1 \over 4}\) + 2\({7 \over 8}\) + \({1 \over 2}\)

(D)

\({1 \over 2}\) + 2(2\({7 \over 8}\)) + 8\({1 \over 4}\)

Question 8.

How many sheets of \({5\over 8}\) " plywood are in a sling load (or stack) 5' high?

(A)

37

(B)

38

(C)

80

(D)

96

Question 9.

The area of a picture is 2925 mm2 . Express this area in cm2.

(A)

2.925

(B)

29.25

(C)

292.5

(D)

29 250

Question 10.

A basketball key is a painted area on the floor that consists of a semicircle plus a rectangle, as shown below. Find the area of the semicircle.

(A)

2.65 m2

(B)

5.31 m2

(C)

10.62 m2

(D)

21.24 m2

Question 11.

Find the surface area of the cone drawn below.

(A)

75.4 sq in

(B)

120.13 sq in

(C)

245.0 sq in

(D)

468.2 sq in

Question 12.

Which statement correctly expresses a similarity between two triangles in the diagram below?

(A)

\(\Delta\)AGB ~ \(\Delta\)CED

(B)

\(\Delta\)AGB ~ \(\Delta\)ACF

(C)

\(\Delta\)ACF ~ \(\Delta\)ADE

(D)

\(\Delta\)AFC - \(\Delta\)ADE

Question 13.

The shape of the top two layers of the wedding cake shown below are similar. Find the length, x, of the middle layer.

(A)

3.5 in

(B)

4.7 in

(C)

8.0 in

(D)

10.5 in

Question 14.

Which property proves that \(\Delta\) ABC is similar to \(\Delta\)DEF ?

(A)

\({AB\over DE}\) = \({AC \over DF}\)

(B)

AC = ED

(C)

\(\measuredangle\)A = \(\measuredangle\)D

(D)

\({AC\over BC}\) = \({DE \over EF}\)

Question 15.

Gina drew a scale representation of a field (see Polygon C). For instance, she drew a line 2.2 cm to represent the actual measure (20 m) of this side (AD). Gina needs to complete the drawing of Polygon D so that both polygons are similar.

What is the measure of line FG?

(A)

5.6 cm

(B)

6.1 cm

(C)

8.25 cm

(D)

9.5 cm

Question 16.

Which of the triangles below are similar?

(A)

I and II only

(B)

II and IV only

(C)

I, II and III only

(D)

II, III and IV only

Question 17.

What is the length of the stringer of the staircase below?

(A)

4.0 ft

(B)

7.2 ft

(C)

11.4 ft

(D)

15.8 ft

Question 18.

Part of a quilting pattern is shown below.

What is the value of x in the diagram?

(A)

3 cm

(B)

\( \sqrt{12} \) cm

(C)

5 cm

(D)

\(\sqrt{29}\)

Question 19.

In which of the following situations is there enough information given to calculate x?

(A)

(B)

(C)

(D)

Question 20.

Consider the similar triangles shown below. Select the relationship that could be used to generalize the formula for the tangent ratio for \(\measuredangle\)A.

(A)

\({BG \over AG}\) = \({CF \over AF}\) = \({DE \over AE}\)

(B)

\({AB\over AG}\) = \({AC\over AF}\) = \({AD \over AE}\)

(C)

BG = CF = DE

(D)

\(\Delta\)ABG \(\cong\) \(\Delta\)ACF \(\cong\) \(\Delta\)ADE 

Question 21.

Which set has two true statements about the diagram below?

(A)

\(\measuredangle\)2 \(\cong\) \(\measuredangle\)5

\(\measuredangle\)3 and \(\measuredangle\)4 are corresponding angles

(B)

• there are two transversals and one parallel line

\(\measuredangle\)3 and \(\measuredangle\)4 are alternate interior angles

(C)

\(\measuredangle\)\(\cong\)  \(\measuredangle\)5

\(\measuredangle\)3 and \(\measuredangle\)4 are alternate interior angles

(D)

• there are two parallel lines and one transversal

\(\measuredangle\)3 and \(\measuredangle\)4 are alternate interior angles

Question 22.

In the diagram below, the wall is supported by a brace cut from 2 '× 4 ' lumber.

What is the relationship between \(\measuredangle\)1 and \(\measuredangle\)2 ?

(A)

corresponding angles

(B)

alternate exterior angles

(C)

vertically opposite angles

(D)

exterior angles on the same side of the transversal

Question 23.

The diamond pattern of the golf vest has parallel lines as shown below. Which angle(s) is (are) congruent to \(\measuredangle\)3 ?

(A)

\(\measuredangle\)2 only

(B)

\(\measuredangle\)2 and \(\measuredangle\)7 only

(C)

\(\measuredangle\)2 , \(\measuredangle\)6 and \(\measuredangle\)8 only

(D)

\(\measuredangle\)2 , \(\measuredangle\)6 , \(\measuredangle\)7 and \(\measuredangle\)4 only

Question 24.

In the diagram below, which lines are parallel?

(A)

\(\parallel\) p only

(B)

\(\parallel\) o only

(C)

\(\parallel\)\(\parallel\) p

(D)

no parallel lines

Question 25.

In the diagram below, what are the measures of \(\measuredangle\)a , \(\measuredangle\)b and \(\measuredangle\)c ?

(A)

\(\measuredangle\)a = 25°, \(\measuredangle\)b = 155°, \(\measuredangle\)c = 25°

(B)

\(\measuredangle\)a = 155°, \(\measuredangle\)b = 25°, \(\measuredangle\)c = 155°

(C)

\(\measuredangle\)a = 155°, \(\measuredangle\)b = 25°, \(\measuredangle\)c = 25°

(D)

\(\measuredangle\)a = 25°, \(\measuredangle\)b = 165°, \(\measuredangle\)c = 15°

Question 26.

A carpenter’s square is placed on a board. What is the relationship between \(\measuredangle\)1 and \(\measuredangle\)2 in the diagram below?

(A)

corresponding

(B)

supplementary

(C)

complementary

(D)

alternate interior

Question 27.

What is the measure of \(\measuredangle\)BAC using the protractor shown below?

(A)

28°

(B)

32°

(C)

150°

(D)

152°

Question 28.

Rank the following types of angles from having the smallest to the greatest measure:

(A)

I, IV, II, V, III

(B)

I, IV, V, III, II

(C)

III, I, IV, V, II

(D)

III, I, V, IV, II

Question 29.

A cruise ship travelling parallel to the shoreline turns 25° to the right. It continues in this direction before making a sharp right hand turn so it is now pointing at a 10° angle to the shoreline.

What is the measure, in degrees, of the second turn?

(A)

145

(B)

165

(C)

325

(D)

345

Question 30.

Organize the items below from lowest to highest unit price.

(A)

I, III, II

(B)

II, I, III

(C)

II, III, I

(D)

III, I, II

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   
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