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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.
(a)5p + 7q
(b)5p + 6q
(c)2p + 7q
(d)12pq
2.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
3.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.
(a)11 — 6 and (4x + 3) are correct factors of 24x + 18.
(b)66 — 6 and (4x + 3) are not correct factors of 24x + 18.
(c)84 — 6 and (4x + 3) are correct factors of 24x + 18.
(d)66 — 6 and (4x + 3) are correct factors of 24x + 18.
4.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2
5.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
6.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.
(a)£24
(b)£14
(c)£12
(d)£8
7.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
8.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
9.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).
(a)(4, 1)
(b)(4, −1)
(c)(−4, 1)
(d)(−4, −1)
10.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.
(a)8
(b)32
(c)5
(d)13
11.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).
(a)(−10, −2)
(b)(−5, −2)
(c)(−4, −2)
(d)(5, −2)
12.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.
(a)h = 2A / a + b
(b)h = (a + b) / (2A)
(c)h = A / (a + b)
(d)h = 2A / (a + b)
13.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.
(a)5n + 2
(b)5n + 12
(c)5n + 7
(d)7n + 5
14.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
15.Work out the value of 2x² when x = −3
(a)18
(b)36
(c)−18
(d)−12

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