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Most Common GCSE Maths Questions

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Question 1: Calculating Travel Costs

Alice plans to travel from London to Manchester for a conference. Her train ticket costs £60, and she expects to spend another £45 on meals. If she wants to buy a souvenir that costs £15, how much money will she spend in total?

Answer: £120

Explanation: Add the cost of the train ticket, meals, and the souvenir together: £60 + £45 + £15 = £120. Alice will spend a total of £120 on her trip.

Question 2: Finding the Area of a Garden

John wants to plant a rectangular garden that is 10 meters long and 6 meters wide. How much area will his garden cover?

Answer: 60 square meters

Explanation: The area of a rectangle is found by multiplying its length by its width. So, John’s garden will cover an area of 10×6=60.

Question 3: Sharing a Prize

Three friends win a cash prize of £450 and decide to share it equally. How much money does each friend get?

Answer: £150

Explanation: To find out how much each friend gets, divide the total prize by the number of friends: £450 ÷ 3 = £150. Each friend gets £150.

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Question 4: Calculating Paint Needed for a Wall

If one litre of paint covers 5 square meters, how many litres of paint are needed to cover a wall that is 10 meters long and 4 meters high?

Answer: 8 litres

Explanation: First, calculate the area of the wall:

10×4=40

10×4=40 square meters. Then, divide this by the coverage of one litre of paint:

40÷5=8

40÷5=8. You need 8 litres of paint.

Question 5: Working Out Discounts

A shop offers a 20% discount on all items. If a jacket originally costs £80, how much will it cost after the discount is applied?

Answer: £64

Explanation: Find 20% of £80:

0.20×80=£16

0.20×80=£16. Subtract this from the original price: £80 – £16 = £64. The jacket will cost £64 after the discount.

Question 6: Solving for Speed

A car travels 150 kilometers in 3 hours. What is the average speed of the car in kilometers per hour?

Answer: 50 km/h

Explanation: Average speed is calculated by dividing the total distance by the total time taken. So, the car’s average speed is

150÷3=50

150÷3=50 km/h.

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Question 7: Geometry Problem with a Cylinder

A cylindrical tank has a radius of 4 meters and a height of 10 meters. Calculate the volume of the tank. (Use π = 3.14 for calculations)

Answer: The volume is 502.4 cubic meters.

Explanation: To find the volume of a cylinder, use the formula pi times radius squared times height. Using pi as 3.14, radius as 4 meters, and height as 10 meters, the calculation gives us 502.4 cubic meters.

Question 8: Algebraic Expression Evaluation

Evaluate the expression

2x^2−4x+1 for x=4

Answer: The result is 7.

Explanation: By substituting x with 3 into the expression, we perform the calculation as follows: 2 times 3 squared minus 4 times 3 plus 1, which simplifies to 7.

Question 9: Probability Scenario

A bag contains 5 red balls, 3 green balls, and 2 blue balls. If two balls are drawn at random without replacement, what is the probability that both are red?

Answer: The probability is 4/45.

 Explanation: The probability of drawing two red balls without replacement is calculated by multiplying the chance of drawing one red ball and then another, resulting in 4/45 when simplified.

Question 10: Maths in Physics

In a physics experiment, a light bulb casts a shadow of a solid object onto a screen. If the object is moved closer to the light bulb, how does the size of the shadow change, and why?

Answer: The shadow becomes larger.

Explanation: As the object moves closer to the light source, it blocks more light, causing the shadow it casts to enlarge. This is due to the principles of light rays and how they diverge from a point source; the closer an object is to the source, the larger the angle it subtends from the source, resulting in a larger shadow on the screen.
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