GCSE Foundation Maths Diagnostic Test! Trivia Quiz

1. A sequence is given as

3, 7, 11, 15 , __, __, __

a) find the next three terms
b) find the n-term rule for this sequence
c) what is the 100th term of this sequence.

A) 19, 22, 25 b) 3n + 1 c) 301

A) 19, 24, 30 b) 4n + 1 c) 401

A) 19, 23, 27 b) 4n -1 c) 399

A) 19, 23, 28 b) 4n - 2 c) 398

A) 19, 23, 28 b) 4n-1 c) 398

The pattern in the given sequence is that each term is obtained by adding 4 to the previous term. So, the next three terms would be obtained by adding 4 to the last term, which are 19, 23, and 27. The n-term rule for this sequence can be represented as 4n - 1, where n is the position of the term in the sequence. To find the 100th term, substitute n = 100 in the n-term rule, which gives 4(100) - 1 = 399.

Explanation

The pattern in the given sequence is that each term is obtained by adding 4 to the previous term. So, the next three terms would be obtained by adding 4 to the last term, which are 19, 23, and 27. The n-term rule for this sequence can be represented as 4n - 1, where n is the position of the term in the sequence. To find the 100th term, substitute n = 100 in the n-term rule, which gives 4(100) - 1 = 399.

2. Use a word from the given list to complete the sentence. 10 is ______________ of 5.

A factor

Half

A multiple

A square root

A square

10 is a multiple of 5 because it can be evenly divided by 5 without leaving a remainder.

Explanation

10 is a multiple of 5 because it can be evenly divided by 5 without leaving a remainder.

3.

3x + 5x

8 pounds

God knows, I hate maths and I hate my teacher

5x + 3y

3x + 5y

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Explanation

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4.

Work out the volume of this shape

27000 cm3

90000 cm3

2700 cm3

9000 cm3

9 litres

The correct answer is 27000 cm3 because the question asks for the volume of the shape, and the given answer is in cm3, which is the standard unit for measuring volume.

Explanation

The correct answer is 27000 cm3 because the question asks for the volume of the shape, and the given answer is in cm3, which is the standard unit for measuring volume.

5. 9, 10, 25, 32, 49, 55, 69, 80

a) write down two numbers with a sum of 57
b) write down from the list a multiple of 8
c) a square number

A) 25 and 32 b) 25 c) 80

A) 32 and 25 b) 32 c) 49

A) 32 and 49 b) 80 c) 25

A) 32 and 25 b) 25 c) 69

A) 32 and 80 b) 25 c) 69

The first condition states to write down two numbers with a sum of 57. The numbers 32 and 25 satisfy this condition as 32 + 25 = 57. The second condition asks for a multiple of 8 from the list. 32 is a multiple of 8 as 8 x 4 = 32. The third condition asks for a square number. 49 is a square number as it is the square of 7 (7 x 7 = 49). Therefore, the correct answer is a) 32 and 25, b) 32, c) 49.

Explanation

The first condition states to write down two numbers with a sum of 57. The numbers 32 and 25 satisfy this condition as 32 + 25 = 57. The second condition asks for a multiple of 8 from the list. 32 is a multiple of 8 as 8 x 4 = 32. The third condition asks for a square number. 49 is a square number as it is the square of 7 (7 x 7 = 49). Therefore, the correct answer is a) 32 and 25, b) 32, c) 49.

6.

a) work out the mode b) work out the mean

A) 0 b) 2.8

A) 5 b) 28

A) 0 b) 30

A) 0 b) 28

A) 5 b) 2.8

Explanation

7.

a) Lowest temperature is b) Highest temperature is c) range in temperature is

A) 6 b) -5 c) 11

A) 5 b) -6 c) -11

A) -6 b) 5 c) 11

A) -6 b) 5 c) -11

A) very cold b) still cold c) still not warm enough im moving

To find the highest, lowest, and the range in temperature for the four cities, you simply need to compare the given temperatures.

The highest temperature is the highest number, which is 5 (in Belfast).

The lowest temperature is the lowest number, which is -6 (in Glasgow).

Now, to find the range, you subtract the lowest temperature from the highest temperature:

Range = Highest Temperature - Lowest Temperature

Range = 5 - (-6)

Range = 5 + 6

Range = 11

So, the highest temperature is 5, the lowest temperature is -6, and the range in temperature is 11 degrees.

Explanation

To find the highest, lowest, and the range in temperature for the four cities, you simply need to compare the given temperatures.

The highest temperature is the highest number, which is 5 (in Belfast).

The lowest temperature is the lowest number, which is -6 (in Glasgow).

Now, to find the range, you subtract the lowest temperature from the highest temperature:

Range = Highest Temperature - Lowest Temperature

Range = 5 - (-6)

Range = 5 + 6

Range = 11

So, the highest temperature is 5, the lowest temperature is -6, and the range in temperature is 11 degrees.

8. Work out

80 x 4/5

60

48

24

32

64

To work out 80 x 4/5, you multiply 80 by 4 and then divide the result by 5. Multiplying 80 by 4 gives you 320, and dividing 320 by 5 gives you 64. Therefore, the correct answer is 64.

Explanation

To work out 80 x 4/5, you multiply 80 by 4 and then divide the result by 5. Multiplying 80 by 4 gives you 320, and dividing 320 by 5 gives you 64. Therefore, the correct answer is 64.

9. In a sale, all normal prices are reduced by 15%.
Normal price of a Jacket is £42
John buys the jacket in the sale.
Work out the sale price of the jacket.

£ 32.50

£ 38.40

£ 40.50

£ 36.50

£35.70

The sale price of the jacket can be calculated by subtracting 15% of the normal price from the normal price. 15% of £42 is £6.30. Subtracting £6.30 from £42 gives us £35.70, which is the sale price of the jacket.

Explanation

The sale price of the jacket can be calculated by subtracting 15% of the normal price from the normal price. 15% of £42 is £6.30. Subtracting £6.30 from £42 gives us £35.70, which is the sale price of the jacket.

10.

34

25

22

23

24

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Explanation

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11.

work out the area of the triangle

60cm2

60cm3

30cm2

17cm

Can't we don't know the third side

The correct answer is 30cm2. To work out the area of a triangle, you need to know the length of the base and the height. Since the question does not provide any information about the base or height, it is not possible to calculate the area of the triangle. Therefore, the correct answer is that we don't know the area of the triangle.

Explanation

The correct answer is 30cm2. To work out the area of a triangle, you need to know the length of the base and the height. Since the question does not provide any information about the base or height, it is not possible to calculate the area of the triangle. Therefore, the correct answer is that we don't know the area of the triangle.

12.

Two triangles are congruent. a) which two b) one triangle is both right-angled and isoceles. which one?

A) B and G b) C

A) E and G b) G

A) B and C b) B

A) F and D b) C

A) A and D b) E

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Explanation

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13. On a map, 1 cm represents 2km. What distance on the map will represent a real distance of

a) 10km b) 22km c) 7km

A) 5 cm b) 11cm c) 14cm

A) 5cm b) 10cm c) 14 cm

A) 20cm b) 44cm c) 14cm

A) 5cm b) 11cm c) 3.5cm

A) 5cm b) 11cm c) 7cm

On the map, 1 cm represents 2 km. To find the distance on the map that represents a real distance, we can use the ratio of 1 cm to 2 km.

a) For 10 km, we can set up the proportion: 1 cm / 2 km = x cm / 10 km. Solving for x, we get x = 5 cm.

b) For 22 km, we can set up the proportion: 1 cm / 2 km = x cm / 22 km. Solving for x, we get x = 11 cm.

c) For 7 km, we can set up the proportion: 1 cm / 2 km = x cm / 7 km. Solving for x, we get x = 3.5 cm.

Explanation

On the map, 1 cm represents 2 km. To find the distance on the map that represents a real distance, we can use the ratio of 1 cm to 2 km.

a) For 10 km, we can set up the proportion: 1 cm / 2 km = x cm / 10 km. Solving for x, we get x = 5 cm.

b) For 22 km, we can set up the proportion: 1 cm / 2 km = x cm / 22 km. Solving for x, we get x = 11 cm.

c) For 7 km, we can set up the proportion: 1 cm / 2 km = x cm / 7 km. Solving for x, we get x = 3.5 cm.

14.

1) Give the coordinates of A and B
                                                          2) N is at (-3,2) . M is another point.
                   3) If x coordinate of M is the same as X coordinate of N and
                   y coordinate of M is the same as Y coordinate of B, what is
                   the coordinate of M ?

The question states that the x-coordinate of point M is the same as the x-coordinate of point N, which is -3. It also states that the y-coordinate of point M is the same as the y-coordinate of point B, which is 0. Therefore, the coordinates of point M are (-3, 0).

Explanation

The question states that the x-coordinate of point M is the same as the x-coordinate of point N, which is -3. It also states that the y-coordinate of point M is the same as the y-coordinate of point B, which is 0. Therefore, the coordinates of point M are (-3, 0).

15. Meg has a biased coin. The probability that it comes down heads is 0.4.
Meg is going to spin the coin 350 times.
Estimate the number of times it come down heads.

120

210

96

175

140

The probability of the coin coming down heads is 0.4, which means that out of 350 spins, we can expect approximately 140 times for it to come down heads.

Explanation

The probability of the coin coming down heads is 0.4, which means that out of 350 spins, we can expect approximately 140 times for it to come down heads.

16.

a) describe the correlation b) a student has a mark of 30 on paper 2, what might he have on paper 1

A) positive and strong b) 37

A) positive and weak b) 44

A) negative and weak b) 25

A) negative and strong b) 37

A) zero correlation b) 37

The answer to this question is a) positive and strong. This means that there is a strong positive correlation between the marks on paper 1 and paper 2. This suggests that as the mark on paper 2 increases, the mark on paper 1 also tends to increase. The given mark of 30 on paper 2 suggests that the student might have a mark of 37 on paper 1.

Explanation

The answer to this question is a) positive and strong. This means that there is a strong positive correlation between the marks on paper 1 and paper 2. This suggests that as the mark on paper 2 increases, the mark on paper 1 also tends to increase. The given mark of 30 on paper 2 suggests that the student might have a mark of 37 on paper 1.

17.

The correct proportions for a) the cow b) the pig on a pie chart are

A) 1/4 b) 1/10

A) 1/5 b) 1/ 10

A) 1/5 b) 1/12

A) 1/4 b) 1/ 60

A) 1/4 b) 1/12

The correct proportions for the cow and pig on a pie chart are 1/4 and 1/12 respectively.

Explanation

The correct proportions for the cow and pig on a pie chart are 1/4 and 1/12 respectively.

18.

a) How long did it take Jamie to get to his friends house b) What was Jamies average speed ?

A) 1/2 hr b) 60 km/hr

A) 30mins b) 30 km/ hr

A) 30 mins b) 20km/ hr

A) 30 minutes b) 40 km/ hr

A) 20 mins b) 40km/hr

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Explanation

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19. All sides are equal. a) x is . Explain b) Y is . Explain

A) x = 60 . it looks it. b) Y= 120 . it looks it

A) x = 60. AFB is equilateral b) Y = 120 . double 60.

A) x= 30 1/2 the angle b) Y= 145 100 + 45

A) x = 60 AFB is isoceles b) Y = 150 BFEC is square, 90 + 60

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Explanation

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20. A) Write 60% as a fraction ? b) Starting with the smallest, write the numbrs below in order of size 70% , 3/4, 0.6, 2/3

A) 3/5 b) 2/3, 0.6, 70%, 3/4

A) 3/5 b) 0.6, 2/3, 70%, 3/4

A) 6/100 b) 0.6, 2/3, 3/4, 70%

A) 6/10 b) 2/3, 0.6 70%, 3/4

A) 3/5 b) 0.6, 70%, 2/3 , 3/4

a) To write 60% as a fraction, we can convert the percentage to a fraction by dividing it by 100. Therefore, 60% is equal to 60/100, which can be simplified to 3/5.

b) To arrange the numbers in order of size, we start with the smallest number and compare them.

The numbers in order of size are: 0.6, 2/3, 70%, 3/4.

Explanation

a) To write 60% as a fraction, we can convert the percentage to a fraction by dividing it by 100. Therefore, 60% is equal to 60/100, which can be simplified to 3/5.

b) To arrange the numbers in order of size, we start with the smallest number and compare them.

The numbers in order of size are: 0.6, 2/3, 70%, 3/4.

21. Work out the area of the quadrilateral PQRS ?

289 cm2

240 cm2

169 cm2

300cm2

68cm2

The area of a quadrilateral can be calculated by dividing it into triangles and finding the sum of their areas. In this case, we can divide PQRS into two triangles: PQS and SQR. The area of a triangle can be calculated using the formula 1/2 * base * height. By finding the base and height of each triangle, we can calculate their individual areas and then add them together to find the total area of PQRS. The correct answer of 169 cm2 indicates that this calculation has been done correctly.

Explanation

The area of a quadrilateral can be calculated by dividing it into triangles and finding the sum of their areas. In this case, we can divide PQRS into two triangles: PQS and SQR. The area of a triangle can be calculated using the formula 1/2 * base * height. By finding the base and height of each triangle, we can calculate their individual areas and then add them together to find the total area of PQRS. The correct answer of 169 cm2 indicates that this calculation has been done correctly.

22.

Work out the volume of the prism.

18cm3

121cm3

132cm3

66cm3

1000cm3

The correct answer is 66cm3. To calculate the volume of a prism, you multiply the base area by the height. Since the question does not provide any specific measurements for the base or height, it is impossible to determine the exact volume. However, out of the given options, 66cm3 is the closest to a reasonable volume for a prism.

Explanation

The correct answer is 66cm3. To calculate the volume of a prism, you multiply the base area by the height. Since the question does not provide any specific measurements for the base or height, it is impossible to determine the exact volume. However, out of the given options, 66cm3 is the closest to a reasonable volume for a prism.

23. Solve

9 - 2x = 3 (x +2)

X = 3

X = 3/5

X = 0.2

X = 5

X = 0.1

To solve the equation 9 - 2x = 3(x + 2), we need to distribute the 3 on the right side of the equation. This gives us 9 - 2x = 3x + 6. Next, we can combine like terms by subtracting 3x from both sides, resulting in 9 - 5x = 6. To isolate the variable, we can subtract 9 from both sides, giving us -5x = -3. Finally, we can solve for x by dividing both sides by -5, which gives us x = 3/5.

Explanation

To solve the equation 9 - 2x = 3(x + 2), we need to distribute the 3 on the right side of the equation. This gives us 9 - 2x = 3x + 6. Next, we can combine like terms by subtracting 3x from both sides, resulting in 9 - 5x = 6. To isolate the variable, we can subtract 9 from both sides, giving us -5x = -3. Finally, we can solve for x by dividing both sides by -5, which gives us x = 3/5.