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.Which line of algebra shows that the sum of two consecutive odd numbers is always a multiple of 4?
(a)(2n + 1) + (2n + 3) = 4n + 4 = 4(n + 1)
(b)(2n + 1) + (2n + 1) = 4n + 2 = 2(2n + 1)
(c)(2n + 1) + (2n + 3) = 4n + 3
(d)n + (n + 2) = 2n + 2 = 2(n + 1)
2.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
3.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
(a)23
(b)27
(c)24
(d)20
4.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.
(a)6.6
(b)6.1
(c)6.3
(d)6.0
5.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.
(a)7n − 2
(b)n² + 4n
(c)2n² + 4n
(d)n²
6.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.
(a)9n + 5
(b)5n + 9
(c)5n
(d)5n + 4
7.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.
(a)7.4
(b)6.2
(c)3.2
(d)5
8.f(x) = x + 3 and g(x) = 2x. Work out fg(x).
y = x + 3
(a)2x² + 6x
(b)2x + 3
(c)3x + 3
(d)2x + 6
9.Show that the equation x³ − x − 3 = 0 has a solution between x = 1 and x = 2, by working out f(1) and f(2), where f(x) = x³ − x − 3.
y = x
(a)f(1) = −3 and f(2) = −1
(b)f(1) = −3 and f(2) = 3
(c)f(1) = 3 and f(2) = −3
(d)f(1) = −2 and f(2) = 5
10.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.
(a)x = 3 and x = −3
(b)x = 4
(c)x = 5 and x = −5
(d)x = 4 and x = −4
11.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
(a)88
(b)39
(c)32
(d)25
12.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.
(a)£65, and C = 40 + 25h is an expression
(b)£115, and C = 40 + 25h is a formula
(c)£195, and C = 40 + 25h is a formula
(d)£115, and C = 40 + 25h is an expression
13.The graph of y = f(x) passes through the point (2, 7). The graph of y = f(x) + a passes through the point (2, 3). Work out the value of a.
(a)4
(b)10
(c)−4
(d)3
14.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?
(a)No, because (3 + 4)² = 49, not 25.
(b)Yes, because 3 + 4 = 7, and 7 is less than 25.
(c)No, because 3² + 4² = 17, not 25.
(d)Yes, because 3² + 4² = 25.
15.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.
y = cos(x)
(a)Translate −90° in x, then translate +2 in y.
(b)Translate −90° in x, then translate −2 in y.
(c)Reflect in the x-axis, then translate −90° in x.
(d)Translate +90° in x, then translate −2 in y.

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