Algebra in Real Life Quiz

Name:

Date:

📋 Instructions

WALT: We Are Learning To solve real-life problems using algebraic methods

Instructions:

• Answer all questions in the spaces provided

• Show your working where useful

• Keep answers short and clear

• Use correct units in your final answers

💡 Differentiation Support: Look for hint boxes (💭) if you need extra guidance. Remember: when solving equations, do the same operation to both sides.

🔢 Part A: Linear Equations & Expressions (Questions 1-6)

1. A mobile phone contract costs £25 per month plus £0.10 per text message. If the total monthly bill is £32.50, how many text messages were sent?

💭 Hint: Let t = number of texts. Write an equation: 25 + 0.10t = 32.50

2. Write an algebraic expression for: "Three times a number, minus 7"

3. A taxi charges £3.20 plus £1.80 per mile. Solve the equation 3.20 + 1.80m = 12.80 to find how many miles were travelled.

4. Sarah saves £15 per week. Write an expression for the total amount she saves after w weeks, then calculate how much she saves in 8 weeks.

5. A rectangular garden has length (2x + 3) metres and width x metres. Write an expression for the perimeter.

💭 Hint: Perimeter = 2 × length + 2 × width

6. Extension: A plumber charges £45 call-out fee plus £30 per hour. If a job costs £165, write and solve an equation to find how many hours the job took.

📐 Part B: Formulas & Context (Questions 7-12)

7. The formula for the area of a triangle is A = ½bh. Find the area when b = 12 cm and h = 8 cm.

8. Rearrange the formula v = u + at to make t the subject.

9. A cinema ticket costs £x. A group booking for 15 people costs £135. Which equation represents this situation?

15x = 135

x + 15 = 135

x - 15 = 135

15 + x = 135

10. The temperature in Celsius (C) converts to Fahrenheit (F) using: F = 1.8C + 32. Find F when C = 25°C.

11. A car rental costs £25 per day plus £0.20 per mile. If someone has a budget of £80, which inequality shows the maximum miles (m) they can drive in one day?

25 + 0.20m ≤ 80

25 + 0.20m ≥ 80

0.20m - 25 ≤ 80

25m + 0.20 ≤ 80

12. Extension: The cost (£C) to hire a hall is given by C = 150 + 8n, where n is the number of people. Rearrange to make n the subject, then find how many people attended if the cost was £294.