Printable · GCSE Higher · ages 14-16

Algebra worksheet — GCSE Higher

Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Algebra worksheet — GCSE Higher

Maths · GCSE Higher · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.The equation 7x = x² + 3 can be solved using the iterative formula xₙ₊₁ = (xₙ² + 3) ÷ 7. Taking x₀ = 0.4, x₁ = 0.4514 correct to 4 decimal places. Using the full unrounded value of x₁, work out x₂ correct to 3 decimal places.
(a)0.493
(b)0.458
(c)0.451
(d)0.632
2.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.
(a)(2x + 1)/(x + 3)
(b)(2x + 1)/(x − 3)
(c)2x + 1
(d)(2x + 3)/(x − 3)
3.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
4.Work out the value of a² − 2b when a = −3 and b = 4.
(a)1
(b)−17
(c)−11
(d)17
5.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.
(a)Formula A gives £39 and Formula B gives £39, but the stallholder is wrong because the two formulas use a different number of terms.
(b)Formula A gives £29 and Formula B gives £39, so the stallholder is wrong.
(c)Formula A gives £39 and Formula B gives £39, but this is only true when n = 4, so the stallholder is wrong.
(d)Formula A gives £39 and Formula B gives £39, and since 3(2n + 5) expands to 6n + 15 for every value of n, the stallholder is correct.
6.Solve 4x² − 9 = 0.
(a)x = 3/2 or x = −3/2
(b)x = 3/2 only
(c)x = 3 or x = −3
(d)x = 9/4 or x = −9/4
7.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.
(a)1
(b)3
(c)2
(d)5
8.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?
(a)3x/2
(b)−3x/2
(c)3x²/2
(d)3/2
9.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.
(a)x = 0, y = 3 and x = 6, y = −3
(b)x = 0, y = 3 and x = −3, y = 6
(c)x = 0, y = 3 and x = 3, y = 0
(d)x = 0, y = 3
10.Make x the subject of the formula y = 3(x + 2).
(a)x = (y − 2)/3
(b)x = y/3 − 2
(c)x = 3y − 2
(d)x = y/3 + 2
11.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3
12.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.
y = x² − 7x + 2
(a)x ≈ 6.70
(b)x ≈ 6.30
(c)x ≈ 7.30
(d)x ≈ 0.70
13.The curve y = x² − 1 and the line y = 3x − 3 meet at two points. Work out the x-coordinates of those two points.
y = 3x − 3y = x² − 1
(a)x = −1 and x = −2
(b)x = −1 and x = 4
(c)x = 1 and x = −1
(d)x = 1 and x = 2
14.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.
(a)y = (4/3)x + 25/3
(b)y = −(3/4)x
(c)y = −(4/3)x − 7/3
(d)y = (4/3)x + 16/3
15.Solve the inequality 2(x − 1) ≤ 8.
(a)x ≤ 4
(b)x ≤ 5
(c)x < 5
(d)x ≤ 3

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