# National technical training program (NTTP)—Examples of prerequisite exam questions

The questions below were developed based on previous exam versions. Measurement Canada has chosen to release these questions so that potential alternative service providers may have access to questions similar to those that will appear in the actual Candidate Evaluation Prerequisites Exam. These sample questions reflect only a small part of the range of questions which might be asked to measure a student's basic mathematics and reading skills.

• Circle only one answer per question.
• No marks are deducted for wrong answers.
• Each question has a value of two points.
• Calculators are permitted.
• The use of a laptop computer, cellular telephones and smartphones is not permitted in the exam room.
• A pass mark of 70% is required.
• You are allotted 90 minutes to complete the exam.

## Sample prerequisite exam 1

Rounding

One type of rounding is to round to the nearest integer. To round a decimal number to the nearest integer, look at the value of the digit in the tenths place (i.e. the first digit to the right of the decimal point):

• If it is less than 5, the number is rounded down, which means the unit digit remains the same.

Example: 7.49 is rounded down to 7.

• If it is equal to or greater than 5, the number is rounded up, which means the unit digit is increased by one. Do not double round.

Example: 7.69 is rounded up to 8.

Round the following numbers to the nearest integer:

1. 126.3
2. 87.48
3. 3.525
4. 52.14 − 36.3 (Round the answer to the nearest integer.)
5. -6.23
1.
126
2.
87
3.
4
4.
16
5.
-6
Order of operations
1. 6 × 2 − 33 ÷ 3
2. 6 × 4 + 2 × (9÷3)
3. 4 + 50 ÷ 2 − 32
4. (9 × 4)2 − 6 × 3
5. 101 − 52 + (3 × 7)
1.

6 × 2 − 33 ÷ 3
= (6 × 2) − (33 ÷ 3)
= 12 − 11
= 1

2.

6 × 4 + 2 × (9 ÷ 3)
= (6 × 4) + (2 × ( 9 ÷ 3)
= 30

3.

4 + 50 ÷ 2 − 32
= 4 + (50 ÷ 2) − 32
= 4 + 25 − 9
= 20

4.

(9 × 4)2 − 6 × 3
= (36)2 − (6 × 3)
= 1296 − 18
= 1278

5.

101 − 52 + (3 × 7)
= 101 − 25 + 21
= 97

Units and conversions

### Solve the following.

1. Convert 0.5 L to millilitres (mL).
2. If 0.4 kg of clay is divided evenly to create 8 equal sized pots, how many grams of clay is each pot?
3. One pound (1 lb) is equivalent to 0.454 kg. If a person has a mass of 71 kg, then what is the person's mass in pounds? (Round the answer to one decimal place.)
4. What is the total area of this figure?

5. Three snowballs are stacked on top of each other to make a snowman. The snowball diameters are 0.7 m, 0.5 m and 38 cm. What is the total height of the snowman in centimetres?
6. 350 L − 625 mL (Express the answer in millilitres.)
7. 200 g − 60 mg (Express the answer in kilograms.)
8. 4.72 km ÷ 80 (Express the answer centimetres.)
1.

1 L = 1000 mL and 1 mL = 0.001 L
Therefore, 0.5 × 1000 mL = 500 mL

2.

If 0.4 kg ÷ 8 = 0.05 kg per pot
0.05 kg × 1000 g/kg = 50 g per pot

3.

1 lb = 0.454 kg and the reciprocal (1 ÷ 0.454) is 1 kg = 2.20 lb
71 kg × 2.20 lb / kg = 156.4 lb

4.

(4m × 5m) + (2m × 3m) = 26 m2

5.

0.7 m × 100 cm/m = 70 cm
0.5 m × 100 cm/m = 50 cm
38 m + 50 cm + 70 cm = 158 cm

6.

350 L − 625 mL = 350,000 mL − 625 mL = 349,375 mL

7.

200 g − 60 mg = 200,000 mg − 60 mg = 199,940 mg = 0.19994 kg

8

4.72 km ÷ 80 = 0.059 km × 1000 m/km × 100 cm/m = 5900 cm

Binomial and algebraic equations

### Simplify the following equations.

1. 1 + 2x + 2 − 9
2. 4n + 6 + n − 2
3. 1 + 5(y − 1) − y
4. (-6d + 6) (2d − 2)
5. (b + 4)2
1.

1 + 2x + 2 − 9
Same as 2x + (1 + 2 − 9)
= 2x − 6

2.

4n + 6 + n − 2
Same as (4n + n) + (6 − 2)
= 5n + 4

3.

1 + 5(y − 1) − y
= 1 + 5y − 5 − y
= (5y − y ) + (1 − 5)
= 4y − 4

4.

(-6d + 6) (2d − 2)
= -12d2 + 12d + 12d − 12
= -12d2 +24d − 12

5.

(b + 4)2
= (b + 4) (b+4)
= b2 +4b + 4b + 16
= b2 + 8b + 16

Percentages, averages and scientific notation

## Solve each problem.

1. What is the average of the following readings: 15.3, 15.8, 16.1, 16.0?
2. In a video game, Val scored 30% fewer points than Mike. If Mike scored 1060 points, then how many points did Val score?
3. The sale price of an item is $30. If the provincial sales tax is 4.4%, how much money do you need to purchase the item? 4. A pumpkin had a mass of 6.5 kg before it was carved and a mass of 3.9 kg after it was carved. What is the decrease in the mass of the pumpkin? Express the answer as a percentage. 5. Write 2.756 × 10-3 as a decimal. Answers 1. (15.3 + 15.8 + 16.1 + 16.0) ÷ 4 = 15.8 2. 1060 × 0.3 = 318 fewer points than Mike 1060 − 318 = 742 points scored by Val 3.$30 × 4.4% = 30 × 0.044 = $1.32 (sales tax) Total price =$30 + $1.32 =$31.32

4.

6.5 kg − 3.9 kg = 2.6 kg
2.6 kg ÷ 6.5 kg = 0.4 × 100 = 40%

5.

0.002756

Using formulas

### Solve each problem.

1. If a liquid has a density of 0.856 kg/L, what is the mass of 25 L of that liquid? Use this formula: Density (ρ) = mass ÷ volume
2. Using the formula below, find the flow rate (Q) of gasoline which when dispensed takes 37 seconds to fill a 20 L test measure. Provide the answer in litres per minute (L/min).

Q = volume ÷ time

3. Using the formula below, determine the percent error of a device whose indication of volume is 20.12 L and actual volume is 20.01 L.

% error = [(indicated volume – actual volume) ÷ actual volume] × 100

4. Determine the volume of a cylinder whose radius (r) is 50 cm and height (h) is 1.3 m, using the formula below. Provide the answer in litres (L).

Vcylinder = πr2h
(π = 3.141 and 1 L = 1000 cm3)

1.

0.856 kg/1 L = ? kg/21.4 L
0.856 kg/L × 25 L = 21.4 kg

2.

37s ÷ 60 s/min = 0.61666 min
Q = 20 L ÷ 0.61666 min = 32.4 L/min

3.

[(20.12 − 20.01) ÷ 20.01] × 100
= [0.11 ÷ 20.01] × 100
= 0.005497 × 100
= 0.5497%

4.

h = 1.3 m × 100 cm/m = 130 cm
Vcylinder = 3.141 × (50 cm)2 × 130 cm
= 3.141 × 2500 cm2 × 130 cm
= 1,020,825 cm3 (or 1.0208 × 106 cm3 in scientific notation)
1 L = 1000 cm3, therefore 1,020,825 cm3 ÷ 1000 = 1020.825 L

### Solve the following.

In the graph, the x-axis represents time in seconds (s) and the y-axis represents distance in metres (m).

1. What is the distance at 1 s?
2. How much time has elapsed at 7 m?
3. What is the proportional relationship between x and y?
4. Given the relationship is constant, what would the distance be at 4 s? (extrapolate)
5. Given the relationship is constant, what is the distance at 1.4 s? (interpolate)

1.
3.5 m
2.
2 s
3.
3.5:1 (also expressed as y = 3.5x)
4.
3.5 × 4 = 14 m
5.
3.5 × 1.4 = 4.9 m

## Sample prerequisite exam 2

Solve each problem.
1. 524.1 is 280% of what?
1. 505.8
2. 187.2
3. 146748
4. 1467.5
5. 50580
2. 423 is 65% of what?
1. 650.8
2. 9.5
3. 945
4. 27495
5. 101
3. 904 is 210% of what?
1. 248.7
2. 2.5
3. 148
4. 71.1
5. 430.5
4. What percent of 981 is 828?
1. 192.8%
2. 118.5%
3. 84.4%
4. 1.36%
5. 73.4%
5. What is 44% of 2?
1. 0.88
2. 393.8
3. 226800
4. 4.5
5. 88
1.
b
2.
a
3.
e
4.
c
5.
a
Find each product.
1. (p+ 2)(p− 2)
1. p² − 1
2. p² + 4p+ 4
3. p² − 4p+ 4
4. p² − 4
5. p² + 10 p + 25
2. (r+ 4)(r− 4)
1. r + 4
2. r² − 4r + 4
3. r² − 16
4. r² + 8r + 16
5. r² + 4r + 4
3. (m − 4)(m+ 4)
1. m² − 1
2. m² + 8m+ 16
3. m² − 25
4. m² − 16
5. m² − 8m+ 16
4. (m − 2)²
1. m² − 4
2. m² + 4
3. m² + 6m+ 9
4. m² − 9
5. m² − 4m+ 4
5. (b + 4)²
1. b² − 16
2. b² + 8b + 16
3. b² + 16
4. b² − 9
5. b² + 4b + 4
6. (−20)(−13)
1. −260
2. 265
3. 268
4. 260
5. −33
7. (9)(−10)
1. 90
2. −84
3. −1
4. −90
5. −98
8. (−4)(−6)
1. 36
2. 12
3. 34
4. 24
5. 7
9. (−14)(16)
1. −108
2. −224
3. −220
4. −210
5. 2
10. (−14)(2)
1. −39
2. −47
3. −28
4. 28
5. −12
1.
d
2.
c
3.
d
4.
e
5.
b
6.
d
7.
d
8
d
9.
b
10.
c
Solve the following.
1. How is 68.6 × 10−6 expressed in decimal notation?
1. −0.000 068 6
2. 0.000 686
3. 0.000 068 6
4. 0.000 006 86
5. −0.000 006 86
2. How is 0.000000584 expressed in scientific notation?
1. 58.4 × 10-6
2. 5.84 × 10-7
3. 5.84 × 10-8
4. 5.84 × 108
5. 0.584 × 10-6
3. 35 L − 620 mL
1. 34.380 L
2. 3.438 0 L
3. 35 620 mL
4. 3 438.0 mL
5. 35.620 L
4. 302 mL + 200 L
1. 20 302 L
2. 302.2 L
3. 200.302 mL
4. 302 200 mL
5. 200 302 mL
5. 3 kg − 210 mg
1. 2.999 99 kg
2. 2 999.79 g
3. 2 999.79 mg
4. 2 790 g
5. 3 002.10 g
6. A 40 L measure is reduced by 0.29%, and the measure obtained is then increased by 0.42%. What is the new measure to the nearest hundredth in millilitre (mL)?
1. 397.26 mL
2. 39 726.49 mL
3. 400 515.13 mL
4. 4 005.15 mL
5. 40 051.51 mL
7. To convert pounds into kilograms, we use a conversion factor of 0.453 592 kg. If something weighs 546.39 kg, how much does it weigh in pounds? Round to the nearest hundredth.
1. 247.84 pounds
2. 2 478.38 pounds
3. 1 204.58 pounds
4. 12 045.85 pounds
5. 120.46 pounds
8. To convert pounds into kilograms, we use a conversion factor of 0.453 592 kg. If something weighs 35 pounds, how much does it weigh in grams? Round to the nearest hundredth.
1. 15 875.72 g
2. 1 587.57 g
3. 158 757.25 g
4. 158.76 g
5. 1 587 572.51 g
9. A scale's reading shows 602.9 kg when a 601 kg proof mass (actual weight) is placed on it. Calculate the percentage of error (the answer has been rounded).

% error = ((value displayed − value of proof mass) ÷ value of proof mass) × 100

1. 1.11%
2. 1.38%
3. 0.28%
4. 0.32%
5. 0.99%
10. When a 10 kg weight is placed on a scale ten different times, the following readings are obtained: 10.034, 9.998, 10.022, 10.205, 9.865, 10.150, 10.004, 9.999, 10.003 and 10.015. What is the average of the readings (the answer has been rounded)?
1. 10.00
2. 10.03
3. 9.99
4. 10.10
5. 10.08
1.
c
2.
b
3.
a
4.
e
5.
b
6.
e
7.
c
8
a
9.
d
10.
b
Simplify each expression.
1. −2(3 + 4m) + 3
1. −4 − 8m
2. −3 − 8m
3. −8m + 45
4. −6m + 43
5. −8m + 43
2. 6(−4m + 3) + 5m
1. 8 − 20m
2. −19m + 18
3. 2 − 20m
4. 1 + 8m
5. −1 + 8m
1.
b
2.
b
Evaluate each expression.
1. 28 − (−1) − 3
1. 66
2. 49
3. 31
4. 32
5. 26
2. 16 + 17 − (−36)
1. 82
2. 86
3. 57
4. 35
5. 69
3. (−32) + 47 + 24
1. 43
2. 54
3. 39
4. −7
5. −9
4. (−40) − 8 − 23
1. −58
2. −66
3. −71
4. −84
5. −101
5. (−42) + 14 − (−20)
1. 11
2. 24
3. −2
4. 38
5. −8
6. 29 − 38 − 4
1. −5
2. −57
3. 16
4. −13
5. −35
7. (−25) − 34 + 20
1. −87
2. −76
3. −58
4. −86
5. −39
8. 42 − 40 − 40
1. −11
2. −15
3. −38
4. −87
5. −65
9. 6 ÷ 3 + 1
1. 3
2. 1
3. 5
4. 6
5. 9
10. 4 + 2 − 1
1. 9
2. 4
3. 10
4. 5
5. 2
11. 6 − (5 − 4)
1. 9
2. 1
3. 8
4. 7
5. 5
1.
e
2.
e
3.
c
4.
c
5.
e
6.
d
7.
e
8
c
9.
a
10.
d
11.
e
Find each percent change. State if it is an increase or a decrease.
1. From 32 to 102
1. 70% decrease
2. 218.8% increase
3. 70% increase
4. 218.8% decrease
5. 318.8% increase
2. From 207 to 114
1. 78.9% increase
2. 55.1% decrease
3. 44.9% decrease
4. 81.6% decrease
5. 81.6% increase
3. From 335 to 49
1. 286% increase
2. 286% decrease
3. 14.6% decrease
4. 85.4% decrease
5. 583.7% decrease
4. From 59 to 9
1. 15.3% decrease
2. 84.7% decrease
3. 50% decrease
4. 655.6% decrease
5. 50% increase
5. From 99 to 45
1. 54% increase
2. 120% increase
3. 220% decrease
4. 54.5% decrease
5. 39.1% decrease
6. From 20.5 to 3
1. 14.6% decrease
2. 683.3% decrease
3. 85.4% increase
4. 85.4% decrease
5. 583.3% increase
7. From 62 to 27
1. 35% increase
2. 56.5% increase
3. 43.5% decrease
4. 35% decrease
5. 56.5% decrease
1.
b
2.
c
3.
d
4.
b
5.
d
6.
d
7.
e

## Sample prerequisite exam 3

Solve the following.
1. (−46) + 42 + (−9)
1. −40
2. −32
3. −47
4. −13
5. 34
2. 49.635 − 36.984 − 27.386
1. −14.735
2. 34.735
3. −33.285
4. −6.285
5. −51.335
3. (−47) − (−35) − 38
1. −56
2. −43
3. −84
4. −50
5. −80
4. (2 + 5) × 6
1. 60
2. 32
3. 45
4. 42
5. 46
5. (6 ÷ 3)3
1. 14
2. 6
3. 11
4. 5
5. 12
1.
d
2.
a
3.
d
4.
d
5.
b
Solve the following (some answers have been rounded).
1. What percent of 981 is 828?
1. 192.8%
2. 118.5%
3. 84.4%
4. 1.36%
5. 73.4%
2. What percent of 163 is 170?
1. 1.04%
2. 267.3%
3. 95.9%
4. 0.96%
5. 104.3%
1.
c
2.
e
Find each product.
1. (a + 3)(a − 3)
1. a2 − 1
2. a2 + 2a + 1
3. a2 + 6a + 9
4. a2 − 6a + 9
5. a2 − 9
2. (n + 3)2
1. n2 + 9
2. n2 − 4n + 4
3. n2 − 9
4. n2 − 4
5. n2 + 6n + 9
3. (k − 1)2
1. k2 − 4
2. k2 − 2k + 1
3. k2 − 1
4. k2k + 1
5. k + 1
4. (x + 5)(x − 5)
1. x2 − 25
2. x2 − 10x + 25
3. x2 − 9
4. x2 − 6x + 9
5. x2 + 10x + 25
5. (a − 3)(a + 3)
1. a2 − 2a + 1
2. a + 1
3. a2 − 9
4. a2 − 6a + 9
5. a2 − 16
1.
e
2.
e
3.
b
4.
a
5.
c
Simplify each expression.
1. −7a − 4(1 − 7a)
1. 21a − 4
2. 19 + 42a
3. 23 + 36a
4. 23 + 42a
5. 30 + 36a
2. −5 + 7(x + 6)
1. 29 + 7x
2. 6x + 17
3. 6x + 10
4. 37 + 7x
5. 56 + 42x
3. 4(p − 2) + 1
1. −55 − 21p
2. 4p − 6
3. −11 + 46p
4. −10 + 46p
5. 4p − 7
4. 6k − 2(7k + 6)
1. −8k − 12
2. 32 − 48k
3. 4 + 5k
4. −13k − 12
5. −20 − 6k
5. 2m(3 + 4m) + 4m
1. 8m + 6m + 3
2. 2m(4m + 5)
3. 8m2 + 8m
4. 8m2 + 10m
5. 2m(2m + 6)
1.
a
2.
d
3.
e
4.
a
5.
d

## Sample prerequisite exam 4

Solve each problem (some answers are rounded).
1. Working alone, Sarah can tar a roof in 12 hours. John can tar the same roof in 17 hours. If they worked together, how long would it take them?
1. 7.03 hours
2. 6.05 hours
3. 8.82 hours
4. 7.28 hours
5. 8.95 hours
2. Eugene can harvest a field in 16 hours. Ted can harvest the same field in 13 hours. If they worked together, how long would it take them?
1. 5.04 hours
2. 6.2 hours
3. 7.7 hours
4. 9.13 hours
5. 7.17 hours
3. Stefan can clean an attic in 14 hours. One day, his friend Paul helped him and it only took 6.74 hours. How long would it take Paul to do it alone?
1. 15.7 hours
2. 15.86 hours
3. 10.68 hours
4. 13 hours
5. 12.1 hours
4. Working alone, Matt can harvest a field in 13 hours. One day, his friend Micaela helped him and it took 5.96 hours. How long would it take Micaela to do it alone?
1. 12.61 hours
2. 10.75 hours
3. 9.24 hours
4. 13.58 hours
5. 11.01 hours
5. Working alone, Huong can mop the floor of a warehouse in 10 hours. Maria can mop the same floor in 11 hours. If they worked together, how long would it take them?
1. 3.77 hours
2. 4.78 hours
3. 4.77 hours
4. 5.88 hours
5. 5.24 hours
6. Lea and Norachai are selling cheesecakes for a school fundraiser. Customers can buy New York-style cheesecakes and strawberry cheesecakes. Lea sold 10 New York-style cheesecakes and 3 strawberry cheesecakes for a total of $58. Norachai sold 5 New York-style cheesecakes and 10 strawberry cheesecakes for a total of$80. Find the price of one New York-style cheesecake and one strawberry cheesecake.
1. New York-style cheesecake: $3, strawberry cheesecake:$8
2. New York-style cheesecake: $6, strawberry cheesecake:$4
3. New York-style cheesecake: $2, strawberry cheesecake:$2
4. New York-style cheesecake: $3, strawberry cheesecake:$2
5. New York-style cheesecake: $4, strawberry cheesecake:$6
7. Carlos's school is selling tickets to the annual dance competition. On the first day of ticket sales, the school sold 4 adult tickets and 5 child tickets for a total of $60. The school took in$23 on the second day by selling 3 adult tickets and 1 child ticket. Find the price of one adult ticket and one child ticket.
1. adult ticket: $3, child ticket:$10
2. adult ticket: $8, child ticket:$5
3. adult ticket: $5, child ticket:$8
4. adult ticket: $3, child ticket:$11
5. adult ticket: $6, child ticket:$12
8. The sum of the digits of a certain two-digit number is 8. When you reverse its digits, you increase the number by 36. Find the number.
1. 32
2. 26
3. 33
4. 14
5. 24
9. A jet left Paris and flew north at an average speed of 242.7 km/h. A passenger plane left at the same time and flew in the opposite direction with an average speed of 242.7 km/h. How long does the passenger plane need to fly before the planes are 3883.2 km apart?
1. 12.6 hours
2. 8 hours
3. 2.1 hours
4. 11.1 hours
5. 2.4 hours
10. A container ship left the Dania Pier and travelled toward the dry dock at an average speed of 13.8 km/h. An aircraft carrier left 0.6 hours later and travelled in the same direction, but with an average speed of 23 km/h. Find the number of hours the container ship travelled before the aircraft carrier caught up.
1. 2.3 hours
2. 1.5 hours
3. 1.2 hours
4. 1 hour
5. 1.7 hours
11. Farmer Mary's Produce Stand sells 26 lb. bags of mixed nuts that contain 35% peanuts. To make her product, she combines brand A mixed nuts, which contain 50% peanuts and brand B mixed nuts, which contain 30% peanuts.

How many pounds of each brand of mixed nuts does she need to use?

1. 8.8 lb. of brand A, 17.2 lb. of brand B
2. 11.4 lb. of brand A, 14.6 lb. of brand B
3. 7.2 lb. of brand A, 18.8 lb. of brand B
4. 9.1 lb. of brand A, 16.9 lb. of brand B
5. 6.5 lb. of brand A, 19.5 lb. of brand B
12. Carlos asked you to make 14 L of fruit punch that contains 46% fruit juice by mixing together some amount of brand A fruit punch and some amount of brand B fruit punch. Brand A contains 60% fruit juice and brand B contains 20% fruit juice. How much of each brand do you need?
1. 12.9 L of brand A, 1.1 L of brand B
2. 9.1 L of brand A, 4.9 L of brand B
3. 13.5 L of brand A, 0.5 L of brand B
4. 4.5 L of brand A, 9.5 L of brand B
5. 4 L of brand A, 10 L of brand B
13. Jaidee wants to make 7.2 qt. of a 40% acid solution by mixing together a 30% acid solution and a 90% acid solution. How much of each solution must she use?
1. 3 qt. of 30% solution, 4.2 qt. of 90% solution
2. 6 qt. of 30% solution, 1.2 qt. of 90% solution
3. 4.5 qt. of 30% solution, 2.7 qt. of 90% solution
4. 5.3 qt. of 30% solution, 1.9 qt. of 90% solution
5. 5.6 qt. of 30% solution, 1.6 qt. of 90% solution
14. To build the garden of your dreams you need 13.5 m³ of soil containing 34% silt. You have to combine two types of soil to achieve this: soil with 50% silt and soil with 20% silt. How much of each soil should you use?
1. 6.3 m3 with 50% silt, 7.2 m3 with 20% silt
2. 4.9 m3 with 50% silt, 8.6 m3 with 20% silt
3. 5 m3 with 50% silt, 8.5 m3 with 20% silt
4. 4.5 m3 with 50% silt, 9 m3 with 20% silt
5. 2.1 m3 with 50% silt, 11.4 m3 with 20% silt
15. Ndiba wants to make 18 qt. of a 48% alcohol solution by mixing together a 40% alcohol solution and a 55% alcohol solution. How much of each solution must he use?
1. 5.5 qt. of 40% solution, 12.5 qt. of 55% solution
2. 4.5 qt. of 40% solution, 13.5 qt. of 55% solution
3. 13.2 qt. of 40% solution, 4.8 qt. of 55% solution
4. 8.4 qt. of 40% solution, 9.6 qt. of 55% solution
5. 4.1 qt. of 40% solution, 13.9 qt. of 55% solution
1.
a
2.
e
3.
d
4.
e
5.
e
6.
e
7.
c
8.
b
9.
b
10.
b
11.
e
12.
b
13.
b
14.
a
15.
d