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 curve y = x² − 6 and the line y = 2x − 3 intersect at two points. Which pair of points is correct?
y = 2x − 3y = x² − 6
(a)(3, 9) and (−1, 1)
(b)(3, 3) and (−1, −5)
(c)(3, 3)
(d)(3, 3) and (1, −1)
2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.
(a)r = A/π
(b)r = √A/π
(c)r = √(A/π)
(d)r = (A/π)²
3.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
(a)6 years
(b)12 years
(c)14 years
(d)28 years
4.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.
5.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?
(a)Statement (iii)
(b)Statement (i)
(c)Statement (ii)
(d)The proof does not assume anything it is trying to prove
6.The point (4, 2) lies on the circle x² + y² = 20. Work out the equation of the tangent to the circle at (4, 2).
(a)y = −0.5x + 4
(b)y = −2x − 10
(c)y = 2x − 6
(d)y = −2x + 10
7.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
8.Solve the inequality 2(x − 1) ≤ 8.
(a)x ≤ 4
(b)x ≤ 5
(c)x < 5
(d)x ≤ 3
9.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
(a)2.5
(b)0
(c)20
(d)5
10.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
11.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.
(a)53
(b)41
(c)48
(d)47
12.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?
(a)30° and 120°
(b)30° and 210°
(c)45° and 135°
(d)30° and 150°
13.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.
14.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.
(a)k = 3
(b)k = −3
(c)k = 4
(d)k = 1.5
15.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$

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