Year 8 Algebra Worksheet - Intermediate

Year 8 Algebra worksheet for Year 8 (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.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Algebraintermediate

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Year 8 Algebra: Expand, Solve and Graph

Ages 12–13 | Key Stage 3 | Intermediate

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Instructions: Work through each activity, showing clear algebraic working in the answer spaces. Check expansions by multiplying back and check equation solutions by substitution. For the graph activity, use the coordinate pairs provided to plot each line on squared paper.

Expand and Factorise

Expand each single bracket by multiplying every term inside the bracket by the term outside it. Then factorise each expression by taking out the highest common factor. Check each factorisation by expanding it again.

Expand:

1. 3(x + 4)

2. 5(2x - 3)

3. -2(x - 6)

Factorise fully:

4. 6x + 18

5. 8y - 12

Equations with x on Both Sides

Collect the x-terms on one side and the number terms on the other. Use inverse operations to find the value of the unknown, and show your working in each space. Substitute your solution into the original equation to check it.

Solve for x:

1. 5x + 4 = 2x + 19

2. 7x - 6 = 3x + 10

3. 4x + 13 = 6x - 1

4. 9x - 8 = 5x + 20

Equations with Brackets

First expand the bracket, then collect like terms and solve. Keep each step on a separate line in your working space. Check your answer in the original equation.

Solve for x:

1. 3(x + 2) = 21

2. 2(x - 4) + 5 = 13

3. 4(x + 1) = 2x + 14

4. 5(x - 2) = 3x + 6

Find the nth Term

For each linear sequence, find the common difference and use it to determine the nth-term rule. Check your rule by substituting n = 1 and n = 2 and comparing with the sequence.

Find the nth term of each sequence:

1. 4, 7, 10, 13, …

2. 11, 16, 21, 26, …

3. 20, 17, 14, 11, …

4. 2, 8, 14, 20, …

Plot Straight-Line Graphs

For each rule, complete the table by calculating y for every given x-value. Plot the resulting coordinate pairs on squared paper and join them with a straight line. Label each line with its equation.

For each equation, calculate the missing y-values.

1. y = 2x + 1

x	-1	0	1	2
y

2. y = -x + 3

x	-1	0	1	2
y

Gradient and Intercept

In y = mx + c, identify m as the gradient and c as the y-intercept. Use the equation and the plotted points to answer each question. Give the intercept as a coordinate where requested.

1. For y = 3x + 2, state the gradient.

2. For y = 3x + 2, state the y-intercept as a coordinate.

3. For y = -2x + 5, state the gradient.

4. For y = -2x + 5, state the y-intercept as a coordinate.

5. A straight line passes through (0, -1) and (1, 2). Find its gradient and y-intercept.

Answer Key

Activity 1: 1. 3x + 12 ; 2. 10x - 15 ; 3. -2x + 12 ; 4. 6(x + 3) ; 5. 4(2y - 3)

Activity 2: 1. x = 5 ; 2. x = 4 ; 3. x = 7 ; 4. x = 7

Activity 3: 1. x = 5 ; 2. x = 8 ; 3. x = 5 ; 4. x = 8

Activity 4: 1. 3n + 1 ; 2. 5n + 6 ; 3. 23 - 3n ; 4. 6n - 4

Activity 5: 1. y-values: -1, 1, 3, 5; points: (-1, -1), (0, 1), (1, 3), (2, 5) ; 2. y-values: 4, 3, 2, 1; points: (-1, 4), (0, 3), (1, 2), (2, 1)

Activity 6: 1. 3 ; 2. (0, 2) ; 3. -2 ; 4. (0, 5) ; 5. Gradient = 3, y-intercept = (0, -1)