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.Solve the inequality 2(x − 1) ≤ 8.
(a)x ≤ 4
(b)x ≤ 5
(c)x < 5
(d)x ≤ 3
2.Which of these quadratic graphs does NOT cross the x-axis at all?
(a)y = (x − 2)² + 3
(b)y = (x + 4)(x − 1)
(c)y = (x − 2)(x + 3)
(d)y = x² − 9
3.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.
(a)x² + y² = 1225
(b)x² + y² = 1369
(c)x² + y² = 144
(d)x² + y² = 2209
4.Make x the subject of the formula y = (x − 4)/5.
(a)x = 5(y + 4)
(b)x = 5y − 4
(c)x = y/5 + 4
(d)x = 5y + 4
5.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.
(a)(3, 7)
(b)(−2, 2)
(c)(8, 2)
(d)(3, −3)
6.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.
(a)n² + 4n + 4
(b)n² + 4n
(c)2n² + 4n + 4
(d)n² + 4
7.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?
(a)Translate +2 in x only (no reflection); roots 1, 6
(b)Solved 2 − x = k as x = k − 2; roots −3, 2
(c)No overall change; roots −1, 4
(d)Reflect in the y-axis, +2 in x; roots 3, −2
8.The graph of y = f(x) passes through the point (2, 7). The graph of y = f(x) + a passes through the point (2, 3). Work out the value of a.
(a)4
(b)10
(c)−4
(d)3
9.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
(a)x + 14
(b)x + 10
(c)5x + 10
(d)x + 13
10.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.
11.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.
(a)4
(b)26
(c)6
(d)2
12.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
13.Solve x² − 6x = 0.
(a)x = 0
(b)x = 3
(c)x = 6
(d)x = 0 or x = 6
14.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).
y = x + 2
(a)1.5
(b)0
(c)−0.5
(d)no solution
15.Solve the simultaneous equations x + y = 1 and 2x + y = 5.
(a)x = 4, y = −3
(b)x = −2, y = 3
(c)x = 6, y = −5
(d)x = 4, y = 5

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