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.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Algebra worksheet — GCSE Higher

Maths · GCSE Higher · Algebra · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.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
2.By completing the square, show that the curve y = x² − 14x + 50 never crosses the x-axis. Which statement gives the correct reason?
y = x² − 14x + 50
(a)The turning point is above the x-axis at (7, −1)
(b)50 is positive, so y is always positive
(c)The discriminant is positive, so y is never zero
(d)(x − 7)² + 1 is at least 1 for every x, so y is never 0
3.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.
(a)(−4, 3)
(b)(4, −9)
(c)(3, 4)
(d)(4, 3)
4.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)
5.Solve 2x² − 7x + 3 = 0.
(a)x = 6 or x = 1
(b)x = 3/2 or x = 1
(c)x = 3 or x = 1/2
(d)x = −3 or x = −1/2
6.f(x) = x³ − 5x − 6. Given that f(2.6) = −1.424 and f(2.7) = 0.183, work out what this shows about the equation x³ − 5x − 6 = 0.
y = x
(a)It has a solution between x = 2.6 and x = 2.7
(b)There is no root in this interval
(c)It has a solution between x = −2.6 and x = −2.7
(d)It shows that x = 2.6 is a solution of the equation
7.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?
y = x − 2y = x² − 4x + 2
(a)Right — x² − 3x + 4 = 0 is correct.
(b)Right — subtracting is the same as adding.
(c)Wrong — the correct equation is x² − 5x + 4 = 0.
(d)Wrong — it should be x² − 5x − 4 = 0.
8.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.
y = cos(x)
(a)Positive x-direction, 90°; image is y = sin x.
(b)Negative x-direction, 90°; image is y = sin x.
(c)Positive x-direction, 90°; image is y = −sin x.
(d)Positive y-direction, 90°; image is y = sin x.
9.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.
(a)n + 5
(b)5n + 4
(c)5n
(d)5n − 1
10.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.
(a)y = −2x + 3
(b)y = 2x + 3
(c)y = −2x − 3
(d)y = −x + 4
11.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)
12.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.
(a)x = 0, y = 3 and x = 6, y = −3
(b)x = 0, y = 3 and x = −3, y = 6
(c)x = 0, y = 3 and x = 3, y = 0
(d)x = 0, y = 3
13.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
14.Factorise x² − 64.
(a)(x − 4)(x + 16)
(b)(x − 8)(x − 8)
(c)(x + 8)(x + 8)
(d)(x − 8)(x + 8)
15.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

Build your own mix at the worksheet builder.