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.