Year 10 Algebra Booklet - Semester One

Name:

Date:

🎯 Part 1: Algebraic Foundations

1. Which expression shows the distributive law applied correctly?

3(x + 2) = 3x + 2

3(x + 2) = 3x + 6

3(x + 2) = x + 6

2. Simplify: 4x + 3x - 2x = _______

3. Factorise: 6x + 9 = _______

4. Real Life Application: Sarah earns $15 per hour plus a $20 bonus. Write an expression for her total pay after h hours:

5. Which of these are like terms? (Check all that apply)

3x and 5x

2y and 7y²

4ab and -2ab

8 and 12

📐 Part 2: Linear Relationships & Coordinate Geometry

6. Find the gradient of the line passing through points A(2, 5) and B(6, 13):

7. The distance between two cities is 450km. A car travels at 90km/h. Write an equation for the distance remaining (d) after t hours:

d = _____________

8. Solve for x: 3x - 7 = 14

9. A mobile phone plan costs $30 per month plus $0.50 per text message. If the total bill is $42, how many text messages were sent?

🔧 Part 3: Formula Manipulation & Problem Solving

10. Rearrange the formula P = 2l + 2w to make w the subject:

11. The area of a triangle is A = ½bh. Find the height when A = 24 and b = 8:

12. Reading Activity: Read this scenario and answer below.

A taxi charges $3.50 for the first kilometre and $1.20 for each additional kilometre. The total fare for a trip is represented by the formula: Fare = 3.50 + 1.20(k-1), where k is the total distance in kilometres.

a) What does the term "1.20(k-1)" represent? _________________________________

b) Calculate the fare for a 7km trip: $ _______

c) If someone paid $15.70, how far did they travel? _______ km

13. Challenge Problem: Two friends start saving money. Emma saves $5 per week starting with $10. Jake saves $3 per week starting with $25. After how many weeks will they have the same amount?