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 table shows the speed, in m/s, of a car at times, in seconds, all 2 seconds apart: 0 at t = 0, 3 at t = 2, 8 at t = 4, 15 at t = 6, 24 at t = 8. A student uses the trapezium rule with these five readings to estimate the distance the car travels. By finding the second differences of the speed values, decide whether this trapezium estimate is an overestimate or an underestimate of the true distance.
(a)Underestimate — second differences are constant.
(b)Overestimate — the speed values are increasing.
(c)Underestimate — the curve bends upward (convex).
(d)Overestimate — the curve bends upward (convex).
2.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?
(a)x = 4
(b)x = −4
(c)x = 0
(d)x = 8
3.A circle has centre (0, 0) and passes through the point (5, 12). Work out the equation of the circle.
(a)x² + y² = 119
(b)x² + y² = 169
(c)x² + y² = 17
(d)x² + y² = 13
4.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.
(a)x < 2 or x > 6
(b)2 < x < 6
(c)−6 < x < −2
(d)2 ≤ x ≤ 6
5.f(x) = x + 3 and g(x) = 2x. Work out fg(x).
y = x + 3
(a)2x² + 6x
(b)2x + 3
(c)3x + 3
(d)2x + 6
6.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.
y = 2x + 1y = -2x + 3
(a)Yes, because the gradients 2 and −2 add to 0
(b)No, because their gradients are 2 and −2
(c)Yes, because both gradients have size 2
(d)No, because their y-intercepts are 1 and 3
7.Write down the expression that means 5 more than half of n.
(a)(n + 5)/2
(b)5n/2
(c)2n + 5
(d)n/2 + 5
8.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
(a)28
(b)38
(c)32
(d)33
9.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.
(a)y = 3x − 2
(b)y = x + 4
(c)y = 3x + 2
(d)y = 2x + 3
10.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.
(a)x = −8
(b)x = 1
(c)x = 8
(d)x = 5
11.f(x) = (x + 1)/2. Find f⁻¹(x).
(a)2x − 1
(b)(x − 1)/2
(c)x/2 − 1
(d)2x + 1
12.Solve 5(x + 3) = 40
(a)x = 8
(b)x = 11
(c)x = 7.4
(d)x = 5
13.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).
(a)y = (x − 3)(x − 5)
(b)y = (x − 3)(x + 5)
(c)y = (x + 3)(x + 5)
(d)y = (x + 3)(x − 5)
14.Work out the period of the graph of y = cos x, in degrees.
y = cos(x)
(a)180°
(b)90°
(c)360°
(d)720°
15.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)

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