Test Your Skills: Pat Maths Test Sample Questions Quiz!

1. Kate has ten balls in a box. Three balls are red, five are white and two are black. She chooses one ball from the box, without looking. The probability that the ball is black is:

0.5

0.3

0.2

0.1

Explanation

2. A sack of flour that weighs 4.5 kilograms has 300 grams taken from it. What does the sack weigh now?

1.5 kg

4.2 kg

4.47 kg

2.55 kg

29.5 kg

Explanation

3. Jeremy's height is 1.7 meters. Anna's height is 1.63 meters.What is the difference in their height?

4cm

7cm

13cm

56

64

The difference in height between Jeremy and Anna is 7cm. This can be calculated by subtracting Anna's height (1.63 meters) from Jeremy's height (1.7 meters), which gives us a difference of 0.07 meters. Since 1 meter is equal to 100 centimeters, we can convert the difference to centimeters by multiplying 0.07 by 100, resulting in 7cm.

Explanation

The difference in height between Jeremy and Anna is 7cm. This can be calculated by subtracting Anna's height (1.63 meters) from Jeremy's height (1.7 meters), which gives us a difference of 0.07 meters. Since 1 meter is equal to 100 centimeters, we can convert the difference to centimeters by multiplying 0.07 by 100, resulting in 7cm.

4.

White, black, grey

Grey, black, white

Grey, white, black

Black, grey,white

Black, white, grey

To determine the order from most likely to least likely, count the number of sections for each color on the spinner. Grey has the most sections with 5, making it the most likely outcome. White follows with 4 sections, making it the next most likely. Black has the fewest sections with 3, making it the least likely outcome. Therefore, the correct order is grey, white, black based on their respective probabilities.

Explanation

To determine the order from most likely to least likely, count the number of sections for each color on the spinner. Grey has the most sections with 5, making it the most likely outcome. White follows with 4 sections, making it the next most likely. Black has the fewest sections with 3, making it the least likely outcome. Therefore, the correct order is grey, white, black based on their respective probabilities.

5. Nina's plane landed at 7.43pm. What time is this in 24-hour time?

0543

0743

1443

1743

1943

The question asks for the time in 24-hour format, which means that the answer should be in the format of HHMM. The given answer, 1943, represents 7:43pm in 24-hour time.

Explanation

The question asks for the time in 24-hour format, which means that the answer should be in the format of HHMM. The given answer, 1943, represents 7:43pm in 24-hour time.

6. $8048 divided by 8 space equals$

106

1001

1006

1021

7. What is the result of multiplying 7 by 9?

56

72

63

45

To find the result of multiplying 7 by 9, you simply multiply these two numbers together: 7 x 9 = 63. So, option C) is the correct answer.

Explanation

To find the result of multiplying 7 by 9, you simply multiply these two numbers together: 7 x 9 = 63. So, option C) is the correct answer.

8. Nick went for a bike ride. He wanted to ride 20 kilometres. He rode 14.5 kilometres then took a break.
Which one of these shows how much further he needed to go to finish his ride?

20 + 14.5

20 - 14.5

14.5 + 20

14.5 - 20

Nick wanted to ride 20 kilometers, but he only rode 14.5 kilometers before taking a break. To determine how much further he needed to go to finish his ride, we subtract the distance he already rode (14.5 kilometers) from the total distance he wanted to ride (20 kilometers). This can be represented as 20 - 14.5.

Explanation

Nick wanted to ride 20 kilometers, but he only rode 14.5 kilometers before taking a break. To determine how much further he needed to go to finish his ride, we subtract the distance he already rode (14.5 kilometers) from the total distance he wanted to ride (20 kilometers). This can be represented as 20 - 14.5.

9. Which percentage is equal to 0.49?

490%

49%

4.9%

049%

The correct answer is 49%. To convert a decimal to a percentage, we move the decimal point two places to the right and add a percent symbol. In this case, 0.49 becomes 49%.

Explanation

The correct answer is 49%. To convert a decimal to a percentage, we move the decimal point two places to the right and add a percent symbol. In this case, 0.49 becomes 49%.

10.

(R,3) and (S,3)

S,3) and (S,4)

(S,3) and (U,4)

(U,3) and (U,4)

11. Mr Smith buys 72 boxes of candles. Each box contains 24 candles.How many candles does he have?

148

216

432

1476

1728

Mr. Smith bought 72 boxes of candles, and each box contains 24 candles. To find the total number of candles he has, we need to multiply the number of boxes by the number of candles in each box. Therefore, 72 multiplied by 24 equals 1728. So, Mr. Smith has 1728 candles in total.

Explanation

Mr. Smith bought 72 boxes of candles, and each box contains 24 candles. To find the total number of candles he has, we need to multiply the number of boxes by the number of candles in each box. Therefore, 72 multiplied by 24 equals 1728. So, Mr. Smith has 1728 candles in total.

12. Which number is larger than 0.17?

0.025

0.15

0.02

0.3

0.017

To find the number larger than 0.17, compare each option:

0.025 is less than 0.17

0.15 is less than 0.17

0.02 is less than 0.17

0.3 is greater than 0.17

0.017 is less than 0.17

Among these options, 0.3 is the only number that is greater than 0.17, making it the correct answer. This comparison is done by aligning the decimal points and comparing digits.

Explanation

To find the number larger than 0.17, compare each option:

0.025 is less than 0.17

0.15 is less than 0.17

0.02 is less than 0.17

0.3 is greater than 0.17

0.017 is less than 0.17

Among these options, 0.3 is the only number that is greater than 0.17, making it the correct answer. This comparison is done by aligning the decimal points and comparing digits.

13. Sue bought 5 bubblegums for 35 cents each. She gave the shopkeeper two dollars.How much change should she get?

25 cents

35 cents

50 cents

$1.50

$1.75

Sue bought 5 bubblegums for 35 cents each, which means she spent a total of 5 * 35 = 175 cents. She gave the shopkeeper two dollars, which is equal to 200 cents. To find out how much change she should get, we subtract the amount she spent from the amount she gave, which is 200 - 175 = 25 cents. Therefore, she should get 25 cents as change.

Explanation

Sue bought 5 bubblegums for 35 cents each, which means she spent a total of 5 * 35 = 175 cents. She gave the shopkeeper two dollars, which is equal to 200 cents. To find out how much change she should get, we subtract the amount she spent from the amount she gave, which is 200 - 175 = 25 cents. Therefore, she should get 25 cents as change.

14.

WALRUS

WHALES

MONKEY

MANTIS

DONKEY

15.

Square

Parallelogram

Rectangle

Hexagon

Triangle

16. 6.07 million may be written as:

607 000 000

60 700 000

6 070 000

607 000

The correct answer is 6 070 000 because it matches the given number, 6.07 million, when written in standard form. The other options do not match the given number.

Explanation

The correct answer is 6 070 000 because it matches the given number, 6.07 million, when written in standard form. The other options do not match the given number.

17.

The first 20 kilometres took Helen:

About 30 minutes

About 50 minutes

About hours

Helen took about 50 minutes to travel the first 20 kilometres.

Explanation

Helen took about 50 minutes to travel the first 20 kilometres.

18.

3 m

4 m

M

5 m

M

19. Tarek has $5.00 to buy a kilogram of 'Koala' biscuits. Which will give him the most change?

One 1 Kg pack

Two 500 g pack

Two 250 g packs and one 500 g pack

Four 250 g packs

He will get the same change no matter which may he chooses the kilograms

Tarek will get the most change if he buys two 500g packs of biscuits. This is because buying two 500g packs will cost less than buying one 1kg pack. Therefore, he will have more money left over as change.

Explanation

Tarek will get the most change if he buys two 500g packs of biscuits. This is because buying two 500g packs will cost less than buying one 1kg pack. Therefore, he will have more money left over as change.

20. $3.2 space cross times space 3.2 equals space 10.24s o comma space square root of 10.24 end root space equals........$

12.8

9.6

6.4

3.2

1.6

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 10.24 is 3.2 because:

3.2 * 3.2 = 10.24

When you multiply 3.2 by itself (3.2 squared), it equals 10.24. Therefore, the square root of 10.24 is 3.2.

Explanation

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 10.24 is 3.2 because:

3.2 * 3.2 = 10.24

When you multiply 3.2 by itself (3.2 squared), it equals 10.24. Therefore, the square root of 10.24 is 3.2.

21.

24 units

28 units

36 units

44 units

48 units

The total number of squares in the construction is 40. Since they're of unit area, the volume of a single square is 1 unit cube. Thus, 40 squares would mean 40 unit cubes of area. The structures at the top are triangular prisms, the area of a triangle is given by b x h so each triangle has an area of 1sq. units, assuming each whole brick is split into half to get the prisms, their area amounts to 1/2 cubic units and there are 8 such prisms, thus their total volume would amount to 4 cubic units, therefore the total volume of the structure would be 44 cubic units.

Explanation

The total number of squares in the construction is 40. Since they're of unit area, the volume of a single square is 1 unit cube. Thus, 40 squares would mean 40 unit cubes of area. The structures at the top are triangular prisms, the area of a triangle is given by b x h so each triangle has an area of 1sq. units, assuming each whole brick is split into half to get the prisms, their area amounts to 1/2 cubic units and there are 8 such prisms, thus their total volume would amount to 4 cubic units, therefore the total volume of the structure would be 44 cubic units.

22. Alison has an equal number of 5-cent and 10-cent coins. She has no other coins. If she has 90 cents altogether, how many coins must she have?

2

5

10

12

15

Let's call the number of 5-cent coins Alison has "x." Since she has an equal number of 10-cent coins, she also has "x" of those.

Now, let's calculate the total value of the coins she has:

The value of each 5-cent coin is 5 cents, and she has "x" of them, so the total value of 5-cent coins is 5x cents.

The value of each 10-cent coin is 10 cents, and she has "x" of them, so the total value of 10-cent coins is 10x cents.

Altogether, she has 5x cents (from the 5-cent coins) + 10x cents (from the 10-cent coins) = 15x cents.

We know that she has 90 cents altogether, so we can set up the equation:

15x = 90

To solve for x, we can divide both sides of the equation by 15:

15x / 15 = 90 / 15

x = 6

So, Alison has 6 of each coin (5-cent and 10-cent coins), which means she has a total of 6 + 6 = 12 coins. Therefore, she must have 12 coins.

Explanation

Let's call the number of 5-cent coins Alison has "x." Since she has an equal number of 10-cent coins, she also has "x" of those.

Now, let's calculate the total value of the coins she has:

The value of each 5-cent coin is 5 cents, and she has "x" of them, so the total value of 5-cent coins is 5x cents.

The value of each 10-cent coin is 10 cents, and she has "x" of them, so the total value of 10-cent coins is 10x cents.

Altogether, she has 5x cents (from the 5-cent coins) + 10x cents (from the 10-cent coins) = 15x cents.

We know that she has 90 cents altogether, so we can set up the equation:

15x = 90

To solve for x, we can divide both sides of the equation by 15:

15x / 15 = 90 / 15

x = 6

So, Alison has 6 of each coin (5-cent and 10-cent coins), which means she has a total of 6 + 6 = 12 coins. Therefore, she must have 12 coins.

23. $7.5 space divided by space 6 space equals$

1.23

1.25

1.433

1 and 5 remainder

7.5/6 can also be written as 75/60. Simplifying 75/60, we get 15/12 (dividing both numerator and denominator by 5). Now, divide 15 by 12 and you'll get the answer 1.25.

Explanation

7.5/6 can also be written as 75/60. Simplifying 75/60, we get 15/12 (dividing both numerator and denominator by 5). Now, divide 15 by 12 and you'll get the answer 1.25.

24. The time shown on this clock is:

Twenty-five past ten

Five to five

Six to five

Six to six

Six to four

The correct answer is "six to five" because it indicates that the time on the clock is six minutes before five o'clock. The phrase "to" is used to indicate minutes before the next hour.

Explanation

The correct answer is "six to five" because it indicates that the time on the clock is six minutes before five o'clock. The phrase "to" is used to indicate minutes before the next hour.

25. Which set of cards have the numbers in order from smallest to largest?

The set of cards that have the numbers in order from smallest to largest is set B.

Explanation

The set of cards that have the numbers in order from smallest to largest is set B.

26.

A half turn in an anticlockwise direction

A half turn in a clockwise direction

A right angle turn in an anticlockwise direction

A right angle turn in a clockwise direction

27. Use the scale on this map. Which point is 2.5 meters from point X?

P

Q

R

S

T

Using the scale provided on the map, you can measure the distance from point X to the other points. The scale indicates that 2.5 meters is slightly less than three squares on the grid. When measuring from X to each point, point Q is found to be exactly 2.5 meters away from point X. Therefore, point Q is the correct answer, as it matches the required distance using the map's scale.

Explanation

Using the scale provided on the map, you can measure the distance from point X to the other points. The scale indicates that 2.5 meters is slightly less than three squares on the grid. When measuring from X to each point, point Q is found to be exactly 2.5 meters away from point X. Therefore, point Q is the correct answer, as it matches the required distance using the map's scale.

28. What is the average (mean) of the numbers 4,4,4, 5,6,8,11?

4

5

6

7

None of these

The average (mean) of a set of numbers is found by adding up all the numbers and then dividing the sum by the total number of numbers. In this case, the sum of the numbers 4, 4, 4, 5, 6, 8, and 11 is 42. Since there are 7 numbers in total, the average is 42 divided by 7, which equals 6. Therefore, the correct answer is 6.

Explanation

The average (mean) of a set of numbers is found by adding up all the numbers and then dividing the sum by the total number of numbers. In this case, the sum of the numbers 4, 4, 4, 5, 6, 8, and 11 is 42. Since there are 7 numbers in total, the average is 42 divided by 7, which equals 6. Therefore, the correct answer is 6.

29. If f(x) = 3x² + 2x - 5, what is f'(x), the derivative of f(x)?

6x + 2

6x - 2

3x + 2

2x + 6

The derivative f'(x) of the function f(x) = 3x² + 2x - 5 is found by applying the power rule. The derivative of 3x² is 6x, and the derivative of 2x is 2. The constant term -5 has a derivative of 0. Therefore, f'(x) = 6x + 2, making option A the correct answer.

Explanation

The derivative f'(x) of the function f(x) = 3x² + 2x - 5 is found by applying the power rule. The derivative of 3x² is 6x, and the derivative of 2x is 2. The constant term -5 has a derivative of 0. Therefore, f'(x) = 6x + 2, making option A the correct answer.

30. Which one of these numbers is 'five thousandths'?

5000

0.5000

0.005

0.0005

The number "five thousandths" is represented by the decimal 0.005. This is because the zero before the decimal point indicates that there are no whole numbers, the first digit after the decimal point (0) represents tenths, the second digit (0) represents hundredths, and the third digit (5) represents thousandths. Therefore, 0.005 is the correct representation of "five thousandths".

Explanation

The number "five thousandths" is represented by the decimal 0.005. This is because the zero before the decimal point indicates that there are no whole numbers, the first digit after the decimal point (0) represents tenths, the second digit (0) represents hundredths, and the third digit (5) represents thousandths. Therefore, 0.005 is the correct representation of "five thousandths".

31.

The graph shows that between 3:30 and 4:30. Helen:

Rode at constant speed

Rode on flat ground

Rode in an easterly direction

Stopped riding

32. One-third of a cake is to be shared equally among three children.What fraction of the whole cake will each child get?

of the whole cake

Of the whole cake

of the whole cake

When you have a cake that you want to share equally among three children, you are dividing the cake into three equal parts. Each child gets one of these equal parts, and that's exactly what "1 third" represents.

In fractions, "1 third" means dividing something into three equal parts and taking one of those parts. So, when you share a cake equally among three children, each child will get "1 third of the whole cake." This is a fair way to divide the cake, ensuring that each child receives an equal portion, which is a fraction of the whole cake.

Explanation

When you have a cake that you want to share equally among three children, you are dividing the cake into three equal parts. Each child gets one of these equal parts, and that's exactly what "1 third" represents.

In fractions, "1 third" means dividing something into three equal parts and taking one of those parts. So, when you share a cake equally among three children, each child will get "1 third of the whole cake." This is a fair way to divide the cake, ensuring that each child receives an equal portion, which is a fraction of the whole cake.

33. What is the result of the expression 3 m (5 + 2) - 4 ÷ 2?

14

12

19

11

To solve this expression, you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).

Let's calculate it step by step:

First, calculate the expression inside the parentheses: 5 + 2 = 7.

Next, calculate the multiplication: 3 × 7 = 21.

Then, perform the division: 4 ÷ 2 = 2.

Finally, subtract the result of the division from the result of the multiplication: 21 - 2 = 19.

So, the result of the expression is 19.

Explanation

To solve this expression, you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).

Let's calculate it step by step:

First, calculate the expression inside the parentheses: 5 + 2 = 7.

Next, calculate the multiplication: 3 × 7 = 21.

Then, perform the division: 4 ÷ 2 = 2.

Finally, subtract the result of the division from the result of the multiplication: 21 - 2 = 19.

So, the result of the expression is 19.

34. What is the area of the black region?

16

18

35

44

56

Area of the white square is 3m x 4m = 12m²

Area of the black square is 7m x 8m = 56m²

Therefore, area enclosed in the black region is = 56m^{2 -}12m²= 44m²

Explanation

Area of the white square is 3m x 4m = 12m²

Area of the black square is 7m x 8m = 56m²

Therefore, area enclosed in the black region is = 56m^{2 -}12m²= 44m²

35.

12 units

18 units

24 units

30 units

36 units

The line segment RS divides the hexagon into two equal halves, and it represents the length of two sides of the hexagon. Therefore, each side of the hexagon is 6 units / 2 = 3 units long. A hexagon has 6 sides, so the perimeter of the hexagon is 3 units/side * 6 sides = 18 units.

Explanation

The line segment RS divides the hexagon into two equal halves, and it represents the length of two sides of the hexagon. Therefore, each side of the hexagon is 6 units / 2 = 3 units long. A hexagon has 6 sides, so the perimeter of the hexagon is 3 units/side * 6 sides = 18 units.

36.

20

22

24

30

None of these

Expanding on the provided sequence, it's evident that with each additional table, there is an increment of 3 chairs. Extrapolating this pattern to six tables, the total number of chairs would be 20.

Explanation

Expanding on the provided sequence, it's evident that with each additional table, there is an increment of 3 chairs. Extrapolating this pattern to six tables, the total number of chairs would be 20.