Algebra Worksheet — KS3 — Advanced
Algebra worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Advanced level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Advanced Algebra Challenges
Key Stage 3 / Year 7-9 (Ages 11-14) - Advanced Level
Instructions: This worksheet is designed to challenge your algebraic skills with a variety of problem-solving activities. Each activity requires critical thinking and application of algebraic concepts.
Solving Linear Equations
Solve each equation for x. Show all your working clearly in the space provided.
1. 3x + 4 = 19
2. 5x - 9 = 16
3. 2x + 7 = 3x - 5
4. 4x - 6 = 2x + 8
5. 7x + 3 = 2x + 18
6. 9x - 4 = 5x + 12
7. 6x + 10 = 8x - 4
8. 3x + 5 = 2x + 11
Quadratic Equations
Solve the following quadratic equations using factorisation. Write your solutions in the boxes provided.
1. x² - 5x + 6 = 0
2. x² + 3x - 10 = 0
3. x² - 4x - 12 = 0
4. x² + 7x + 10 = 0
Simultaneous Equations
Solve these pairs of simultaneous equations using the substitution or elimination method. Write your answers in the boxes.
1. 2x + y = 8
x - y = 2
2. 3x - 2y = 7
4x + y = 10
3. x + 3y = 12
2x - y = 3
Algebraic Expressions
Simplify the following algebraic expressions. Show all steps clearly.
1. 3(x + 2) - 4(x - 1)
2. 5x - 3(2x - 4) + 6
3. 2(x - 3) + 4(x + 5) - 7
4. 6(x - 2) - 2(x + 3) + 5
Inequalities
Solve the following inequalities and represent the solution on a number line.
1. 2x - 3 > 7
2. 5x + 4 ≤ 19
3. 3x - 5 < 2x + 4
4. 4x + 1 ≥ 3x + 5
Word Problems
Translate the following word problems into algebraic equations and solve for the unknown. Show all your working.
1. A number is increased by 7 and the result is 15. Find the number.
2. Three times a number decreased by 4 equals 11. Find the number.
3. The sum of a number and twice another number is 18. If the first number is 4, find the second number.
4. A number is divided by 2 and then 5 is subtracted from the result to get 3. Find the number.
Data Analysis with Algebra
Analyse the data in the table and answer the questions below. Use algebra to solve any equations that arise.
| Month | Sales (£) | Costs (£) | Profit (£) |
| Jan | 500 | 300 | 200 |
| Feb | 650 | 320 | 330 |
| Mar | 720 | 340 | 380 |
| Apr | 680 | 310 | 370 |
1. Which month had the highest profit?
2. Calculate the total sales for the quarter.
3. What is the average monthly profit?
Factorising Expressions
Factorise the following expressions completely. Write your answers in the boxes provided.
1. x² - 9
2. x² + 6x + 9
3. x² - 4x - 5
4. x² + 5x + 6
Activity 1: x = 5 ; x = 5 ; x = 12 ; x = 7 ; x = 3 ; x = 4 ; x = 7 ; x = 6
Activity 2: x = 2, x = 3 ; x = 2, x = -5 ; x = 6, x = -2 ; x = -2, x = -5
Activity 3: x = 3, y = 2 ; x = 3, y = 2 ; x = 3, y = 3
Activity 4: x - 2 ; 3x + 18 ; 6x + 9 ; 4x - 1
Activity 5: x > 5 ; x ≤ 3 ; x < 9 ; x ≥ 4
Activity 6: 8 ; 5 ; 7 ; 16
Activity 7: March ; £2550 ; £320
Activity 8: (x - 3)(x + 3) ; (x + 3)² ; (x - 5)(x + 1) ; (x + 2)(x + 3)
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