Free GCSE MATH Question and Answers — Questions and Answers

Question 1: Choose a word from the list provided to finish the phrase. 10 is _____________ of 5.

A factor
A multiple (Correct answer)
A square
A square root
Half

Correct answer: A multiple

A multiple of a number is the result of multiplying that number by an integer. In this case, 10 is obtained by multiplying 5 by the integer 2 (5 x 2 = 10). Therefore, 10 is a multiple of 5.

Question 2: There are 800 pupils traveling on the school bus. A bus can accommodate 34 students. Determine how many buses will be required to transport all of the pupils.

24 (Correct answer)
23
22
25
34

Correct answer: 24

To determine the number of buses required, divide the total number of pupils by the capacity of one bus: 800 ÷ 34 ≈ 23.53. Since you cannot have a fraction of a bus and all pupils must be transported, you must round up to the next whole number. Therefore, 24 buses are needed.

Question 3: Calculate 9 - 2x = 3 (x + 2)

x = 0.1
x = 5
x = 0.2
x = 3/5 (Correct answer)
x = 3

Correct answer: x = 3/5

First, distribute the 3 on the right side of the equation: 9 - 2x = 3x + 6. Next, gather the x terms on one side by adding 2x to both sides, resulting in 9 = 5x + 6. Then, subtract 6 from both sides to isolate the x term: 3 = 5x. Finally, divide by 5 to solve for x, which gives x = 3/5.

Question 4: Workout 80 times in 4/5.

64 (Correct answer)
32
24
48
60

Correct answer: 64

To 'workout 80 times in 4/5' means to calculate 4/5 of 80. You can do this by multiplying 80 by the fraction 4/5. This calculation is (80 ÷ 5) × 4, which equals 16 × 4. The final result is 64.

Question 5: 9, 10, 25, 32, 49, 55, 69, 80a) Write down two numbers that add up to 57b) Write down an 8 multiple c) Write down a square number from the list

32 and 80 b) 25 c) 69
32 and 25 b) 25 c) 69
32 and 49 b) 80 c) 25
32 and 25 b) 32 c) 25 (Correct answer)
25 and 32 b) 25 c) 80

Correct answer: 32 and 25 b) 32 c) 25

For part a), the numbers 32 and 25 from the list add up to 57 (32 + 25 = 57). For part b), a multiple of 8 is a number that can be divided by 8 without a remainder; 32 is 8 multiplied by 4. For part c), a square number is the result of an integer multiplied by itself; 25 is 5 multiplied by 5.

Question 6: A) How would you write 60% as a fraction? b) Numbers below should be written in the following order: 70%, 3/4, 0.6, and 2/3.

3/5 b) 0.6, 70%, 2/3 , 3/4
6/10 b) 2/3, 0.6 70%, 3/4
6/100 b) 0.6, 2/3, 3/4, 70%
3/5 b) 0.6, 2/3, 70%, 3/4
3/5 b) 2/3, 0.6, 70%, 3/4 (Correct answer)

Correct answer: 3/5 b) 2/3, 0.6, 70%, 3/4

For part a), 60% as a fraction is 60/100, which simplifies to 3/5. For part b), convert all values to decimals for easy comparison: 0.6 = 0.6, 2/3 ≈ 0.667, 70% = 0.7, 3/4 = 0.75. Arranging these in ascending order gives 0.6, 2/3, 70%, 3/4.

Question 7: The following sequence is provided: 3, 7, 11, 15, , , . A) locate the following three terms. B) determine this sequence's n-term rule c) What is the sequence's 100th term.

19, 23, 28 b) 4n-1 c) 398
19, 23, 28 b) 4n - 2 c) 398
19, 23, 27 b) 4n -1 c) 399 (Correct answer)
19, 24, 30 b) 4n + 1 c) 401
19, 22, 25 b) 3n + 1 c) 301

Correct answer: 19, 23, 27 b) 4n -1 c) 399

The sequence increases by 4 each time (3, 7, 11, 15). So, the next three terms are 15+4=19, 19+4=23, 23+4=27. The n-term rule is 4n - 1 (since 4n gives 4, 8, 12, 16, and we need to subtract 1 to get 3, 7, 11, 15). For the 100th term, substitute n=100 into the rule: 4(100) - 1 = 400 - 1 = 399.

Question 8: Mike is skewed like a coin. There is a 0.4 percent chance that it will land on heads. 350 times of the coin will be spun by Mike. Calculate how often the heads will fall.

140 (Correct answer)
175
96
210
120

Correct answer: 140

To calculate how often heads will fall, multiply the total number of coin spins by the probability of landing on heads. The probability is given as 0.4. So, 350 spins multiplied by 0.4 equals 140. Mike can expect the coin to land on heads 140 times.

Question 9: 1 centimeter on a map equals 2 kilometers. Which measurement on the map corresponds to a real distance of a) 10 km, b) 22 km, or c) 7 km?

5cm b) 11cm c) 7cm
5cm b) 11cm c) 3.5cm (Correct answer)
20cm b) 44cm c) 14cm
5cm b) 10cm c) 14 cm
5 cm b) 11cm c) 14cm

Correct answer: 5cm b) 11cm c) 3.5cm

The map scale is 1 cm = 2 km. To find the map distance for a real distance, divide the real distance by 2. For a) 10 km / 2 = 5 cm. For b) 22 km / 2 = 11 cm. For c) 7 km / 2 = 3.5 cm.

Question 10: All regular prices are lowered by 15% during a discount. A jacket usually costs £42. In the transaction, John purchases the jacket. Calculate the jacket's retail price.

£35.70 (Correct answer)
£ 36.50
£ 40.50
£ 38.40
£ 32.50

Correct answer: £35.70

A 15% discount means the jacket's price is 100% - 15% = 85% of its original cost. To find the retail price, multiply the original price (£42) by 0.85. So, £42 × 0.85 = £35.70.

Question 11: What is meant by the word "correlation"?

Inequalty
Equality
Opposite
Relationship (Correct answer)

Correct answer: Relationship

In statistics, 'correlation' describes the statistical relationship between two or more variables. It indicates the extent to which these variables tend to change together. A positive correlation means they increase or decrease in tandem, while a negative correlation means one tends to increase as the other decreases.

Question 12: What does the word "gradient" mean?

The value of a point on a line or a curve on the x-y axes
The distance of a point on a line or curve from the y-axis
The slope of a line or curve at a given point (Correct answer)
The height of a point on a line or curve above the x-axis

Correct answer: The slope of a line or curve at a given point

The 'gradient' of a line or curve, also known as its slope, measures its steepness. For a straight line, it's a constant value representing the change in the y-axis divided by the change in the x-axis. For a curve, the gradient varies and is defined by the slope of the tangent line at a specific point.

Question 13: What exactly does "relative frequency" mean?

The trials in an experiment
The proportion of trials in an experiment
The proportion of succesful trials in a experiment (Correct answer)
The succesful trials in an experiment

Correct answer: The proportion of succesful trials in a experiment

Relative frequency is the proportion of times a specific event or outcome occurs in an experiment or set of trials. It is calculated by dividing the number of successful trials (where the event occurred) by the total number of trials conducted. It provides an estimate of the probability of an event.

Question 14: What exactly is a "hypotenuse"?

the longest side of a right angled triangle (Correct answer)
The shortest side of triangle
the shortest side of a right angled triangle
The longest side of a triangle

Correct answer: the longest side of a right angled triangle

In a right-angled triangle, the hypotenuse is the side that is directly opposite the right angle (90-degree angle). It is always the longest side of the triangle. The Pythagorean theorem relates the lengths of the two shorter sides (legs) to the length of the hypotenuse.

Question 15: What is a list of numbers' "median" defined as?

The sum of the numbers devided the number of numbers in the list
The middle value after the numbers have been arranged in numerical order (Correct answer)
The difference between the highest and lowest number
The value that occurs most often

Correct answer: The middle value after the numbers have been arranged in numerical order

The median of a list of numbers is the middle value when the numbers are arranged in numerical order (either ascending or descending). If there is an odd number of values, the median is the single middle number. If there is an even number of values, the median is the average of the two middle numbers.

Question 16: What exactly does the phrase "transformation" mean?

destruction
swap
change (Correct answer)
movement

Correct answer: change

In a general sense, 'transformation' refers to a significant change in the form, nature, or appearance of something. In mathematics, it describes a function that changes the position, size, or orientation of a geometric figure, such as a translation, rotation, reflection, or dilation.

Free GCSE MATH Question and Answers

Choose a word from the list provided to finish the phrase. 10 is _____________ of 5.