Algebra Worksheet - A-Level - Intermediate
Algebra worksheet for A-Level / Vocational (Ages 16-18). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Advanced Algebra Practice for A-Level Students
Ages 16-18, Intermediate Difficulty
Instructions: This worksheet is designed to enhance your algebra skills through a variety of challenging problems. You will solve equations, explore functions, and apply algebraic techniques. Read each question carefully and show all your workings.
Quadratic Equations
Solve each quadratic equation by factorising, completing the square, or using the quadratic formula. Show all steps clearly.
1. x² - 5x + 6 = 0
2. 2x² + 3x - 2 = 0
3. x² - 4x - 5 = 0
4. 3x² - 12x + 9 = 0
5. x² + 6x + 9 = 0
Solving Inequalities
Solve the following inequalities and represent the solutions on a number line. Ensure to show your workings and provide the solution set.
1. 3x - 4 > 5
2. 2x + 7 ≤ 3x - 5
3. -x/2 + 3 < 1
4. 4(x - 1) ≥ 2(x + 3)
Functions and Graphs
For each function, find the domain, range, and any asymptotes. Sketch the graph of each function.
1. f(x) = 1/(x - 2)
2. g(x) = x² - 4x + 3
3. h(x) = √(x + 1)
Binomial Expansion
Expand the following expressions using the binomial theorem. Write out the first four terms of the expansion.
1. (2x + 3)⁵
2. (1 - x)⁶
Partial Fractions
Decompose the following rational expressions into partial fractions. Show all steps clearly.
1. (3x + 5)/(x² - x - 2)
2. (4x - 1)/(x² + 2x - 3)
Algebraic Long Division
Perform algebraic long division on the following polynomials. Write down the quotient and remainder.
1. Divide x³ - 6x² + 11x - 6 by x - 2
2. Divide 2x³ + 3x² - x + 5 by x + 1
Activity 1: x = 2, 3 ; x = -2, 0.5 ; x = 5, -1 ; x = 2 ; x = -3
Activity 2: x > 3 ; x ≤ -12 ; x > 4 ; x ≥ 4
Activity 3: Domain: x ≠ 2, Range: y ≠ 0 ; Domain: all real numbers, Range: y ≥ 0 ; Domain: x ≥ -1, Range: y ≥ 0
Activity 4: 32x⁵ + 240x⁴ + 720x³ + 1080x² ; 1 - 6x + 15x² - 20x³
Activity 5: 3/(x-2) + 2/(x+1) ; 4/(x-1) + 3/(x+3)
Activity 6: Quotient: x² - 4x + 3, Remainder: 0 ; Quotient: 2x² + x - 2, Remainder: 3
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