Algebra Worksheet — KS3 — Intermediate
Algebra worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Intermediate Algebra Mastery
Key Stage 3 / Year 7-9 (Ages 11-14) - Intermediate Level
Instructions: This worksheet will help you strengthen your algebra skills through a variety of engaging activities. Each task is designed to challenge your understanding and application of algebraic concepts. Be sure to show all your workings clearly.
Solving Linear Equations
Solve each of the following equations for x. Show all your workings clearly in the space provided.
1. 2x + 5 = 13
2. 3x - 7 = 11
3. 4x + 8 = 20
4. 5x - 10 = 15
5. 6x + 3 = 27
6. 7x - 14 = 21
7. 8x + 12 = 44
8. 9x - 18 = 36
Understanding Algebraic Expressions
Simplify each algebraic expression by combining like terms. Write your simplified expression in the box provided.
1. 3x + 4x - 2x
2. 5y - 3y + 2y
3. 6a + 2b - 3a + b
4. 7m - 2m + 4m - m
5. 3p + 5q - 2p + q
Factoring Quadratic Expressions
Factor each quadratic expression completely. Write your factors in the space provided.
1. x^2 + 5x + 6
2. x^2 - 3x - 10
3. x^2 + 4x + 4
4. x^2 - 7x + 12
5. x^2 + x - 12
Solving Word Problems with Equations
Read each word problem carefully and form an equation to solve it. Write your equation and solution in the space provided.
1. If three times a number is increased by 5, the result is 20. Find the number.
2. A number decreased by 7 is equal to twice the number. Find the number.
3. The sum of a number and its double is 36. Find the number.
Graphing Linear Equations
Plot the graph of each linear equation on a separate graph paper. Identify the slope and y-intercept from the equation.
1. y = 2x + 3
2. y = -x + 4
3. y = 0.5x - 1
Inequalities
Solve each inequality and represent the solution on a number line. Write your solution in the space provided.
1. 3x + 2 > 11
2. 4x - 5 ≤ 7
3. -2x + 3 < 9
Substitution in Algebraic Expressions
Substitute the given values into each expression and simplify. Write your answer in the box provided.
1. For x = 2, y = 3, evaluate 3x + 4y
2. For a = 5, b = -2, evaluate 2a - 3b
3. For p = -1, q = 4, evaluate p^2 + 2q
Understanding Functions
Determine the output of each function for the given input. Write your answer in the space provided.
1. f(x) = 2x + 5, find f(3)
2. g(x) = x^2 - 4x + 1, find g(2)
3. h(x) = 3x - 7, find h(-1)
Activity 1: x = 4 ; x = 6 ; x = 3 ; x = 5 ; x = 4 ; x = 5 ; x = 4 ; x = 6
Activity 2: 5x ; 4y ; 3a + 3b ; 8m ; p + 6q
Activity 3: (x + 2)(x + 3) ; (x - 5)(x + 2) ; (x + 2)^2 ; (x - 3)(x - 4) ; (x + 4)(x - 3)
Activity 4: x = 5 ; x = 7 ; x = 12
Activity 5: Slope = 2, y-intercept = 3 ; Slope = -1, y-intercept = 4 ; Slope = 0.5, y-intercept = -1
Activity 6: x > 3 ; x ≤ 3 ; x > -3
Activity 7: 18 ; 16 ; 15
Activity 8: 11 ; 1 ; -10
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