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 line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.
y = 3x + 6
(a)(2, 0)
(b)(−2, 0)
(c)(6, 0)
(d)(0, 6)
2.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.
(a)Outside: OQ² = 221 > r² = 169
(b)Outside: OQ = 21 (10 + 11) > r = 13
(c)Inside: OQ ≈ 14.87 < r² = 169
(d)Inside: OQ² = 221 < (2r)² = 676
3.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.
(a)(0, 7) and (0, −7)
(b)(7, 0) and (−7, 0)
(c)(7, 0) only
(d)(0, 7) only
4.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.
(a)4
(b)3
(c)7
(d)18
5.Solve the simultaneous equations y = 2x − 1 and y = x² − x − 1, giving both pairs of solutions.
y = 2x − 1y = x²
(a)x = 0, y = −1 and x = −3, y = −7
(b)x = 0, y = −1
(c)x = −2, y = −5 and x = 1, y = 1
(d)x = 0, y = −1 and x = 3, y = 5
6.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.
(a)5th term
(b)4th term
(c)7th term
(d)6th term
7.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
(a)10
(b)16
(c)12
(d)13
8.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.
(a)100/3
(b)25
(c)24
(d)50/3
9.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
(a)29
(b)25
(c)28
(d)16
10.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.
(a)−2
(b)19
(c)−17
(d)18
11.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
(a)An equation, because solving it gives the value of n
(b)An identity, because it is true for many values of n
(c)A formula, because it works out n from 9
(d)An inequality, because ≤ compares the two sides
12.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.
(a)£0.20
(b)£2.00
(c)£3.20
(d)£1.80
13.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.
(a)a = 8
(b)a = 12
(c)a = −4
(d)a = 4
14.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
15.Solve the simultaneous equations y = x + 1 and x² + y² = 25, giving both pairs of solutions.
y = x + 1
(a)x = 4, y = 5 and x = −3, y = −2
(b)x = −4, y = −3 and x = 3, y = 4
(c)x = 12, y = 13
(d)x = −4, y = −3

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