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.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
2.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12
3.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
4.By completing the square, find the turning point of the curve y = x² + 6x + 2.
y = x² + 6x + 2
(a)x = 3, y = −7
(b)x = −3, y = −7
(c)x = −3, y = 7
(d)x = −6, y = −34
5.A graph has equation y = −2x² + 5. Which statement about its shape is correct?
y = -2x² + 5
(a)It is U-shaped, since x² is always positive.
(b)It is a straight line, because of the constant term +5.
(c)It repeatedly rises and falls, like a wave shape.
(d)It is n-shaped, since the x² coefficient is negative.
6.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?
(a)18
(b)12n
(c)6n
(d)2n² + 18
7.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
8.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.
(a)(3, −4)
(b)(−4, 3)
(c)(8, 3)
(d)(−4, −5)
9.Work out the value of 3a − 2b when a = 5 and b = 4
(a)52
(b)−7
(c)23
(d)7
10.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.
(a)20
(b)456
(c)0.05
(d)480
11.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.
(a)8
(b)4
(c)2
(d)0
12.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.
(a)(6, 8)
(b)(10, 10)
(c)(5, 5)
(d)(3, 4)
13.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.
(a)−2
(b)18
(c)2
(d)4
14.A proof sets out to show that the sum of the squares of two consecutive odd numbers, written as 2n + 1 and 2n + 3, is always 2 more than a multiple of 8. Four attempts to expand (2n + 1)² + (2n + 3)² and reach a conclusion are shown below. Which attempt correctly proves this claim?
(a)(2n + 1)² + (2n + 3)² = (4n² + 4n + 1) + (4n² + 9) = 8n² + 4n + 10 = 4(2n² + n + 2) + 2, so the sum is always 2 more than a multiple of 4.
(b)(2n + 1)² + (2n + 3)² = (4n² + 4n + 1) + (4n² + 12n + 9) = 8n² + 16n + 10 = 2(4n² + 8n + 5), and 4n² + 8n + 5 is an integer, so the sum is always even, which means it is a multiple of 8.
(c)(2n + 1)² + (2n + 3)² = (4n² + 4n + 1) + (4n² + 12n + 9) = 8n² + 16n + 10 = 8(n² + 2n + 1) + 2, and n² + 2n + 1 is an integer, so the sum is always 2 more than a multiple of 8.
(d)(2n + 1)² + (2n + 3)² = (4n² + 4n + 1) + (4n² + 12n + 9) = 8n² + 16n + 10 = 8(n² + 2n) + 10, so the sum is always 10 more than a multiple of 8.
15.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.
(a)9x − 40y = 1681
(b)9x + 40y = 1681
(c)40x + 9y = 1681
(d)9x + 40y = 41

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