Year 9 Algebra Worksheet - Intermediate

Year 9 Algebra worksheet for Year 9 (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 9 Algebra: Expand, Solve and Sketch

Key Stage 3 · Ages 13–14 · Intermediate

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Instructions: Show clear working for each question and check your answers where possible. Use the given formulae and coordinate values carefully. For the graph questions, use the stated points to sketch each curve on squared paper.

Expand and Simplify Double Brackets

Multiply each term in the first bracket by each term in the second bracket. Collect like terms and show your working. Check your result by substituting a simple value for x.

1. Expand and simplify: (x + 3)(x + 5) [3 marks]

2. Expand and simplify: (x - 4)(x + 2) [3 marks]

3. Expand and simplify: (2x + 1)(x - 3) [3 marks]

4. Expand and simplify: (3x - 2)(2x + 5) [3 marks]

Solve Simultaneous Equations

Find the values of both unknowns that satisfy each pair of equations. Use elimination or substitution, and show enough working for your method to be followed. Check each pair by substituting your values into both equations.

1. Solve: x + y = 11; x - y = 3 [3 marks]

2. Solve: 2x + y = 13; x + y = 8 [3 marks]

3. Solve: 3x + 2y = 16; x + 2y = 8 [3 marks]

4. Solve: 2x + 3y = 19; x + y = 7 [3 marks]

Solve Linear Inequalities

Solve each inequality using the same inverse operations as for equations. Remember to reverse the inequality sign if you multiply or divide by a negative number. Give integer solutions where requested.

1. Solve: 3x + 4 < 19 [2 marks]

2. Solve: 5 - 2x ≥ 13 [2 marks]

3. Solve: 4(x - 1) ≤ 2x + 6 [3 marks]

4. List the integer solutions of -2 < x + 1 ≤ 4 [3 marks]

Rearrange Formulae

Make the named letter the subject by using inverse operations on both sides. Keep the formula balanced at every step. Give each final formula in its simplest form.

1. Make x the subject: y = 3x + 7 [2 marks]

2. Make h the subject: A = bh/2 [2 marks]

3. Make r the subject: C = 2πr [2 marks]

4. Make x the subject: y = (x - 4)/3 [2 marks]

Recognise and Sketch Quadratic Graphs

Use the supplied x-values to calculate the corresponding y-values, then plot the coordinates and join them with a smooth curve. Identify the turning point and state whether the parabola opens upwards or downwards. Do not join the points with straight line segments.

1. For y = x² - 4, complete the values for x = -2, -1, 0, 1, 2; write the coordinates and sketch the graph. [4 marks]

2. For y = -(x - 1)² + 4, complete the values for x = -1, 0, 1, 2, 3; write the coordinates and sketch the graph. [4 marks]

3. The graph y = (x + 2)² - 1 is a translation of y = x². State its turning point and whether it opens upwards or downwards. [2 marks]

Answer Key

Activity 1: 1. x² + 8x + 15 ; 2. x² - 2x - 8 ; 3. 2x² - 5x - 3 ; 4. 6x² + 11x - 10

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

Activity 3: 1. x < 5 ; 2. x ≤ -4 ; 3. x ≤ 5 ; 4. x = -2, -1, 0, 1, 2, 3

Activity 4: 1. x = (y - 7)/3 ; 2. h = 2A/b ; 3. r = C/(2π) ; 4. x = 3y + 4

Activity 5: 1. Coordinates (-2, 0), (-1, -3), (0, -4), (1, -3), (2, 0); turning point (0, -4); opens upwards. 2. Coordinates (-1, 0), (0, 3), (1, 4), (2, 3), (3, 0); turning point (1, 4); opens downwards. 3. Turning point (-2, -1); opens upwards.