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ISEB Common Pre-Test study materials
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ISEB Common Pre-Test practice questions

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Question 1Mathematics

A bag contains 3 red, 5 blue and 2 green counters. One counter is taken at random. What is the probability that it is blue?

  1. 1/2 Correct answer.
  2. 5/8
  3. 1/5
  4. 3/10

Explanation

There are 3 + 5 + 2 = 10 counters in total, and 5 of them are blue. The probability is therefore 5/10, which simplifies to 1/2.

Question 2Mathematics

What is 4.7 × 100?

  1. 4700
  2. 47
  3. 470 Correct answer.
  4. 0.47

Explanation

Multiplying by 100 moves every digit two place values to the left, so the decimal point shifts two places to the right. Starting from 4.7 this gives 470.

Question 3Mathematics

A rectangle measures 8 cm by 5 cm. What is its area?

  1. 40 cm² Correct answer.
  2. 13 cm²
  3. 26 cm²
  4. 80 cm²

Explanation

The area of a rectangle is length multiplied by width, so 8 × 5 = 40. The answer is written in square centimetres because two lengths are multiplied.

Question 4Mathematics

Work out 3/4 + 1/8, giving your answer as a fraction in its simplest form.

  1. 7/8 Correct answer.
  2. 4/12
  3. 1/2
  4. 4/8

Explanation

Rewrite 3/4 as 6/8 so both fractions share the denominator 8. Then 6/8 + 1/8 = 7/8, which is already in its simplest form.

Question 5Mathematics

Which number is a multiple of both 6 and 8?

  1. 18
  2. 14
  3. 48 Correct answer.
  4. 36

Explanation

A number is a multiple of both 6 and 8 if it appears in both times tables. 48 = 6 × 8 and 48 = 8 × 6, so it is the lowest common multiple in the list.

Question 6Mathematics

A train leaves at 09:45 and arrives at 11:20. How long does the journey take?

  1. 1 hour 45 minutes
  2. 1 hour 25 minutes
  3. 1 hour 35 minutes Correct answer.
  4. 2 hours 25 minutes

Explanation

From 09:45 to 10:45 is one hour, and from 10:45 to 11:20 is a further 35 minutes. The total journey time is therefore 1 hour 35 minutes.

Question 7Mathematics

Round 6473 to the nearest hundred.

  1. 6500 Correct answer.
  2. 6400
  3. 6000
  4. 6470

Explanation

The hundreds digit is 4, and the next digit is 7, which is 5 or more, so the hundreds digit rounds up to 5. This gives 6500.

Question 8Mathematics

What is the value of 2³ + 5 × 4?

  1. 52
  2. 28 Correct answer.
  3. 44
  4. 17

Explanation

Indices are evaluated first, giving 2³ = 8. Multiplication comes next, giving 5 × 4 = 20, and finally 8 + 20 = 28.

Question 9Mathematics

A number n is multiplied by 4 and then 7 is subtracted. The result is 25. What is n?

  1. 4
  2. 8 Correct answer.
  3. 32
  4. 18

Explanation

Working backwards, add 7 to 25 to get 32, then divide by 4 to get 8. Checking: 4 × 8 − 7 = 32 − 7 = 25.

Question 10Mathematics

A shirt costs £24. In a sale its price is reduced by 15%. What is the sale price?

  1. £20.40 Correct answer.
  2. £21.60
  3. £22.50
  4. £9.00

Explanation

15% of £24 is 0.15 × 24 = £3.60, and subtracting this from £24 gives £20.40. Equivalently, the sale price is 85% of £24.

Question 11Mathematics

The angles in a triangle are in the ratio 2 : 3 : 4. What is the size of the largest angle?

  1. 80° Correct answer.
  2. 40°
  3. 60°
  4. 90°

Explanation

The angles add to 180°, and the ratio has 2 + 3 + 4 = 9 parts, so one part is 180 ÷ 9 = 20°. The largest share is 4 parts, giving 4 × 20 = 80°.

Question 12Mathematics

A sequence begins 3, 7, 11, 15, ... What is the 20th term?

  1. 80
  2. 75
  3. 83
  4. 79 Correct answer.

Explanation

The sequence increases by 4 each time, so the nth term is 4n − 1. Substituting n = 20 gives 80 − 1 = 79.

Question 13Mathematics

A cube has a volume of 64 cm³. What is the total surface area of the cube?

  1. 96 cm² Correct answer.
  2. 384 cm²
  3. 64 cm²
  4. 16 cm²

Explanation

The side length is the cube root of 64, which is 4 cm. Each face has area 4 × 4 = 16 cm², and a cube has 6 faces, so the total surface area is 96 cm².

Question 14Mathematics

Simplify 5a + 3b − 2a + 4b.

  1. 3a + 1b
  2. 10ab
  3. 3a + 7b Correct answer.
  4. 7a + 7b

Explanation

Collect like terms separately: 5a − 2a = 3a and 3b + 4b = 7b. Unlike terms a and b cannot be combined into one term.

Question 15Mathematics

What is the highest common factor of 36 and 60?

  1. 4
  2. 12 Correct answer.
  3. 180
  4. 6

Explanation

The factor pairs of 36 include 1, 2, 3, 4, 6, 9, 12, 18 and 36, and 12 divides 60 exactly (60 ÷ 12 = 5). No larger factor of 36 divides 60, so 12 is the highest common factor.

Question 16Mathematics

On a map with scale 1 : 25 000, a path measures 6 cm. What is the real length of the path in kilometres?

  1. 150 km
  2. 15 km
  3. 0.15 km
  4. 1.5 km Correct answer.

Explanation

Each centimetre represents 25 000 cm, so 6 cm represents 150 000 cm. Dividing by 100 000 to convert centimetres to kilometres gives 1.5 km.

Question 17Mathematics

A fair six-sided dice is rolled once. What is the probability of rolling a prime number?

  1. 1/2 Correct answer.
  2. 1/3
  3. 2/3
  4. 1/6

Explanation

The prime numbers on a dice are 2, 3 and 5, giving 3 favourable outcomes out of 6. The probability is 3/6, which simplifies to 1/2.

Question 18Mathematics

Solve the inequality 3x − 4 < 11.

  1. x < 5 Correct answer.
  2. x < 15
  3. x < 7
  4. x > 5

Explanation

Add 4 to both sides to get 3x < 15, then divide both sides by 3 to get x < 5. Dividing by a positive number keeps the inequality sign unchanged.

Question 19Mathematics

The mean of five numbers is 12. Four of the numbers are 8, 10, 15 and 11. What is the fifth number?

  1. 20
  2. 12
  3. 16 Correct answer.
  4. 14

Explanation

The five numbers must total 5 × 12 = 60. The four known numbers add to 8 + 10 + 15 + 11 = 44, so the fifth number is 60 − 44 = 16.

Question 20Mathematics

A triangle has sides 6 cm, 8 cm and 10 cm. Which statement about the triangle is true?

  1. It is right-angled because 6² + 8² = 10². Correct answer.
  2. It is equilateral because all sides are different.
  3. It cannot be drawn because 6 + 8 > 10.
  4. It is right-angled because 6 + 8 = 14.

Explanation

Squaring the two shorter sides gives 36 + 64 = 100, which equals 10². By the converse of Pythagoras' theorem, a triangle with these side lengths has a right angle opposite the longest side.

Question 21Mathematics

Expand and simplify (x + 3)(x − 5).

  1. x² + 2x − 15
  2. x² − 15
  3. x² − 8x − 15
  4. x² − 2x − 15 Correct answer.

Explanation

Multiplying each term in the first bracket by each term in the second gives x² − 5x + 3x − 15. Collecting the middle terms gives −2x, so the result is x² − 2x − 15.

Question 22Mathematics

Two similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². What is the area of the larger rectangle?

  1. 135 cm²
  2. 75 cm² Correct answer.
  3. 45 cm²
  4. 54 cm²

Explanation

For similar shapes, areas are in the ratio of the squares of the lengths, so the area ratio is 9 : 25. The larger area is 27 × 25/9 = 3 × 25 = 75 cm².

Question 23Mathematics

A car travels 150 km in 2 hours 30 minutes. What is its average speed in km/h?

  1. 37.5 km/h
  2. 50 km/h
  3. 75 km/h
  4. 60 km/h Correct answer.

Explanation

2 hours 30 minutes is 2.5 hours. Average speed is distance divided by time, so 150 ÷ 2.5 = 60 km/h.

Question 24Mathematics

The nth term of a sequence is 3n² − 2. What is the difference between the 5th term and the 4th term?

  1. 21
  2. 27 Correct answer.
  3. 24
  4. 3

Explanation

The 5th term is 3 × 25 − 2 = 73 and the 4th term is 3 × 16 − 2 = 46. Their difference is 73 − 46 = 27.

Question 25Mathematics

In a group of 40 students, 25 study French, 18 study Spanish and 8 study both languages. How many students study neither French nor Spanish?

  1. 7
  2. 5 Correct answer.
  3. 3
  4. 11

Explanation

By the inclusion–exclusion principle, the number studying at least one language is 25 + 18 − 8 = 35. Subtracting from 40 leaves 5 students who study neither.

Question 26Mathematics

A bag contains 5 red counters and 3 blue counters. One counter is taken at random. What is the probability that it is blue?

  1. 1/3
  2. 3/8 Correct answer.
  3. 3/5
  4. 5/8

Explanation

Probability is the number of favourable outcomes divided by the total number of outcomes. There are 3 blue counters and 5 + 3 = 8 counters altogether, so the probability of blue is 3/8.

Question 27Mathematics

What is 0.6 written as a fraction in its simplest form?

  1. 3/50
  2. 1/6
  3. 3/5 Correct answer.
  4. 6/5

Explanation

0.6 means six tenths, so it equals 6/10. Dividing the numerator and denominator by 2 gives 3/5, which cannot be simplified further.

Question 28Mathematics

A rectangle measures 7 cm by 4 cm. What is its perimeter?

  1. 28 cm
  2. 22 cm Correct answer.
  3. 11 cm
  4. 14 cm

Explanation

The perimeter is the total distance around the shape, found by adding all four sides: 7 + 4 + 7 + 4. This gives 22 cm.

Question 29Mathematics

What is 25% of 80?

  1. 20 Correct answer.
  2. 15
  3. 25
  4. 40

Explanation

25% is the same as one quarter, so 25% of 80 is 80 ÷ 4 = 20. Alternatively, 80 × 0.25 = 20.

Question 30Mathematics

A temperature of −6 °C rises by 9 degrees. What is the new temperature?

  1. 15 °C
  2. 3 °C Correct answer.
  3. −3 °C
  4. −15 °C

Explanation

Starting at −6 and rising means moving 9 places up the number line. −6 + 9 = 3, so the new temperature is 3 °C.

Question 31Mathematics

How many lines of symmetry does a square have?

  1. 8
  2. 4 Correct answer.
  3. 1
  4. 2

Explanation

A square has four lines of symmetry: one horizontal, one vertical and two along the diagonals. Each line folds the square exactly onto itself.

Question 32Mathematics

Work out 3/4 + 1/8.

  1. 7/8 Correct answer.
  2. 5/8
  3. 1/2
  4. 4/12

Explanation

Write both fractions with the common denominator 8: 3/4 = 6/8. Then 6/8 + 1/8 = 7/8, which is already in simplest form.

Question 33Mathematics

A number is chosen at random from the whole numbers 1 to 20 inclusive. What is the probability that it is a multiple of 5?

  1. 1/20
  2. 1/5 Correct answer.
  3. 1/10
  4. 1/4

Explanation

The multiples of 5 from 1 to 20 are 5, 10, 15 and 20, giving 4 favourable outcomes out of 20. So the probability is 4/20, which simplifies to 1/5.

Question 34Mathematics

A recipe for 4 people uses 300 g of rice. How much rice is needed for 10 people at the same rate?

  1. 1200 g
  2. 600 g
  3. 750 g Correct answer.
  4. 700 g

Explanation

Find the amount for one person first: 300 ÷ 4 = 75 g. Then multiply by 10 to get 750 g. This is a direct proportion problem.

Question 35Mathematics

The mean of four numbers is 9. Three of the numbers are 6, 8 and 10. What is the fourth number?

  1. 11
  2. 9
  3. 14
  4. 12 Correct answer.

Explanation

If the mean of four numbers is 9, their total is 4 × 9 = 36. The three known numbers add to 24, so the fourth is 36 − 24 = 12.

Question 36Mathematics

Solve the equation 5x + 7 = 32.

  1. x = 7.8
  2. x = 6
  3. x = 25
  4. x = 5 Correct answer.

Explanation

Subtract 7 from both sides to get 5x = 25, then divide both sides by 5 to get x = 5. Substituting back gives 5 × 5 + 7 = 32, which checks.

Question 37Mathematics

A straight line passes through the points (0, 3) and (4, 11). What is the gradient of the line?

  1. 2 Correct answer.
  2. 4
  3. 8
  4. 1/2

Explanation

Gradient is the change in y divided by the change in x. The y-value rises from 3 to 11, a change of 8, while x rises by 4, so the gradient is 8 ÷ 4 = 2.

Question 38Mathematics

Expand 4(2x − 3).

  1. 8x + 12
  2. 2x − 12
  3. 8x − 12 Correct answer.
  4. 8x − 3

Explanation

Multiply each term inside the bracket by 4: 4 × 2x = 8x and 4 × (−3) = −12. The expanded expression is therefore 8x − 12.

Question 39Mathematics

A cuboid has length 5 cm, width 3 cm and height 4 cm. What is its volume?

  1. 60 cm³ Correct answer.
  2. 47 cm³
  3. 12 cm³
  4. 94 cm³

Explanation

The volume of a cuboid is length × width × height. Here 5 × 3 × 4 = 60, so the volume is 60 cm³.

Question 40Mathematics

A triangle has two angles of 65° and 48°. What is the size of the third angle?

  1. 113°
  2. 57°
  3. 67° Correct answer.
  4. 77°

Explanation

The angles in any triangle add up to 180°. The two known angles total 113°, so the third angle is 180 − 113 = 67°.

Question 41Mathematics

What is 3/5 of 45?

  1. 27 Correct answer.
  2. 30
  3. 9
  4. 15

Explanation

First find one fifth of 45 by dividing by 5, which gives 9. Then multiply by 3 to get 27, so 3/5 of 45 is 27.

Question 42Mathematics

A fair coin is tossed twice. What is the probability of getting two heads?

  1. 3/4
  2. 1/4 Correct answer.
  3. 1/3
  4. 1/2

Explanation

The four equally likely outcomes are HH, HT, TH and TT. Only one of these is two heads, so the probability is 1/4. The two tosses are independent, and 1/2 × 1/2 = 1/4.

Question 43Mathematics

The cost of hiring a hall is £40 plus £12 per hour. Which formula gives the total cost C in pounds for h hours?

  1. C = 40 + 12h Correct answer.
  2. C = 12 + 40h
  3. C = 52h
  4. C = 40h − 12

Explanation

The fixed charge of £40 is paid once, whatever the number of hours, so it is the constant term. The hourly charge of £12 is multiplied by h, giving C = 40 + 12h.

Question 44Mathematics

A car travels 84 km in 1 hour 30 minutes. What is its average speed in km/h?

  1. 42 km/h
  2. 63 km/h
  3. 84 km/h
  4. 56 km/h Correct answer.

Explanation

1 hour 30 minutes is 1.5 hours. Speed is distance divided by time, so 84 ÷ 1.5 = 56 km/h.

Question 45Mathematics

A jacket is priced at £60. Its price is reduced by 20%, and then the reduced price is reduced by a further 10%. What is the final price?

  1. £42.00
  2. £45.60
  3. £48.00
  4. £43.20 Correct answer.

Explanation

A 20% reduction leaves 80%, so the first price is 60 × 0.8 = £48. A further 10% reduction leaves 90% of £48, which is £43.20. The two reductions cannot simply be added.

Question 46Mathematics

Two similar triangles have corresponding sides in the ratio 2 : 5. The area of the smaller triangle is 12 cm². What is the area of the larger triangle?

  1. 30 cm²
  2. 75 cm² Correct answer.
  3. 60 cm²
  4. 150 cm²

Explanation

For similar shapes, areas are in the ratio of the squares of the side lengths, so the area ratio is 2² : 5² = 4 : 25. The larger area is 12 × 25/4 = 75 cm².

Question 47Mathematics

Make x the subject of the formula y = 3x − 7.

  1. x = 3y + 7
  2. x = y/3 + 7
  3. x = (y + 7)/3 Correct answer.
  4. x = (y − 7)/3

Explanation

Add 7 to both sides to get y + 7 = 3x, then divide both sides by 3. This gives x = (y + 7)/3. The whole of y + 7 must be divided by 3.

Question 48Mathematics

Solve the simultaneous equations 2x + y = 11 and x − y = 1.

  1. x = 4, y = 3 Correct answer.
  2. x = 2, y = 7
  3. x = 3, y = 4
  4. x = 5, y = 1

Explanation

Adding the two equations eliminates y: 3x = 12, so x = 4. Substituting into x − y = 1 gives 4 − y = 1, so y = 3. Checking in 2x + y gives 8 + 3 = 11, which is correct.

Question 49Mathematics

A sequence has nth term n² + 3n. What is the difference between the 10th term and the 9th term?

  1. 22 Correct answer.
  2. 40
  3. 19
  4. 21

Explanation

The 10th term is 10² + 3 × 10 = 130, and the 9th term is 9² + 3 × 9 = 108. Their difference is 130 − 108 = 22.

Question 50Mathematics

A bag contains 5 red counters and 3 blue counters. One counter is taken from the bag at random and not replaced. A second counter is then taken at random. What is the probability that both counters are red?

  1. 5/14 Correct answer.
  2. 5/8
  3. 25/64
  4. 3/28

Explanation

For the first counter the probability of red is 5/8. Since that red counter is not replaced, 4 red remain out of 7 counters, so the second probability is 4/7. Multiplying gives 5/8 × 4/7 = 20/56 = 5/14, which is the probability of red followed by red.