Word Problems - GCSE AQA Higher Tier Year 10

Word Problems - GCSE AQA Higher Tier Year 10

• Example 1: Simple Multiplication

• Hailey buys a bag of loaves for £1.25. If she wanted to buy 4, how much would she pay?

• Calculations: £1.25 x 4 = £5.00

• Answer: Hailey would pay £5.00.

• Example 2: Calculating the cost of multiple items

• A shop sells apples at £0.75 each. If a customer buys 6 apples and pays with a £5 note, how much change do they get?

• Calculations: £0.75 x 6 = £4.50 £5.00 - £4.50 = £0.50

• Answer: The customer gets £0.50 change.

• Example 3: Finding the cost per unit

• A box of 12 oranges costs £3.60. Work out the price of one orange.

• Calculations: £3.60 ÷ 12 = £0.30

• Answer: One orange costs £0.30.

• Example 4: Percentage Increase/Decrease

• The price of a jacket increases by 15% from £40. Find the new price.

• Calculations: 15% of £40 = £6 £40 + £6 = £46

• Answer: The new price is £46.

• Example 5: Percentage Increase/Decrease Continued

• A book originally priced at £12 is reduced by 20% in a sale. What is the sale price?

• Calculations: 20% of £12 = £2.40 £12 - £2.40 = £9.60

• Answer: The sale price is £9.60.

• Example 6: Ratio Problems

• The ratio of boys to girls in a class is 3:2. If there are 18 boys, how many girls are there?

• Calculations: 3 parts = 18 boys 1 part = 18 boys ÷ 3 = 6 2 parts = 6 x 2 = 12 girls

• Answer: There are 12 girls.

• Example 7: Finding a fraction of a quantity

• A baker has 30 cakes. 2/5 of the cakes are chocolate. How many chocolate cakes are there?

• Calculations: (2/5) x 30 = 12

• Answer: 12 chocolate cakes.

• Example 8: Compound Measures

• A car travels at a constant speed of 60 mph for 2.5 hours. How far does the car travel?

• Calculations: 60 mph x 2.5 hours = 150 miles

• Answer: The car travels 150 miles.

• Example 9: Simultaneous Equations (Higher Tier)

• 3x + 2y = 11 2x - y = 1 Find the values of x and y.

• Calculations: Solving this system of equations, by elimination, substitution, or graphing, results in x=3 and y=2

• Answer: x = 3, y = 2

• Example 10: Area and Perimeter Problems (Higher Tier)

• A rectangle has a length of 8cm and a width of 5cm. Find its area and perimeter.

• Calculations: Area = length x width = 8cm x 5cm = 40 sq cm Perimeter = 2(length + width) = 2(8cm + 5cm) = 26cm

• Answer: Area = 40 sq cm, Perimeter = 26 cm.

Key Concepts and Strategies

• Understanding the question: Carefully read the word problem to identify the given information and what the problem is asking you to find.
• Identify the operations: Determine the mathematical operations needed (addition, subtraction, multiplication, division, percentage calculations).
• Write equations/formulas Convert the word problem into a mathematical equation, where necessary.
• Show your working: Clearly show each step of your calculations to support your answer.
• Units: Always include units (e.g., pounds (£), miles, centimeters) in your answers.
• Check your answer: Ensure your answer makes sense in the context of the word problem.

This quiz focuses on solving word problems related to basic arithmetic concepts necessary for GCSE AQA Higher Tier Year 10. Students will engage with real-life scenarios that require calculation of costs, unit prices, and percentage changes. Test your skills in multiplication, change calculation, and percentage increase/decrease.