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.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.
(a)t = 0 or t = 4
(b)t = 2
(c)t = 0
(d)t = 1 or t = 3
2.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.
(a)xₙ₊₁ = 5(xₙ² + 3)
(b)xₙ₊₁ = (xₙ² + 3) ÷ 5
(c)xₙ₊₁ = (xₙ + 3) ÷ 5
(d)xₙ₊₁ = (xₙ² − 3) ÷ 5
3.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.
y = −x² + 6x − 5
(a)x = 3, y = −4
(b)x = 3, y = 4
(c)x = 6, y = 31
(d)x = −3, y = 4
4.The table shows the velocity, in m/s, of a train at various times, in seconds: 0 at t = 0, 20 at t = 4, 35 at t = 10, 27 at t = 14. Assuming the velocity changes at a constant rate between each pair of readings, estimate the distance the train travels between t = 0 and t = 12, using the trapezium rule.
(a)271 m
(b)275 m
(c)282 m
(d)267 m
5.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?
y = 3x + 1
(a)y = (1/3)x + 2
(b)y = −(1/3)x + 2
(c)y = −3x + 2
(d)y = 3x − 4
6.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
(a)x = 1, y = 3
(b)x = 3, y = 2
(c)x = 3, y = 1
(d)x = 3, y = −1
7.By completing the square, find the turning point of the curve y = x² − 10x + 30.
y = x² − 10x + 30
(a)x = 10, y = −70
(b)x = 5, y = −5
(c)x = 5, y = 5
(d)x = −5, y = 5
8.How many turning points does the graph of y = x² − 7x + 10 have?
y = x² − 7x + 10
(a)Four turning points.
(b)One turning point.
(c)Two turning points.
(d)No turning points.
9.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.
(a)260
(b)319
(c)320
(d)279
10.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
11.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
12.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.
(a)9 m
(b)18 m
(c)37 m
(d)16 m
13.Which expression is equivalent to 0.5(4x + 6) − x?
(a)3x + 3
(b)2x + 3
(c)x + 3
(d)x + 6
14.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
15.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
(a)11
(b)16
(c)96
(d)48

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