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.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?
(a)The equation has one solution; the inequality has many.
(b)Both have exactly one solution.
(c)Both have many solutions.
(d)The equation has many solutions; the inequality has one.
2.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.
y = 3x − 8
(a)x = 3(y + 8)
(b)x = (y − 8) / 3
(c)x = y + 8 / 3
(d)x = (y + 8) / 3
3.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.
(a)(1, 3)
(b)(−1, 3)
(c)(9, 4)
(d)(−1, 4)
4.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
5.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
(a)68, and it is an equation
(b)36, and it is a formula
(c)52, and it is a formula
(d)68, and it is a formula
6.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
(a)7.4
(b)1.25
(c)5
(d)4
7.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
8.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?
(a)Third and fourth
(b)First and third
(c)Second and fourth
(d)First and second
9.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
(a)28
(b)35
(c)37
(d)39
10.Factorise fully 56x − 24
(a)8(7x − 16)
(b)8(56x − 3)
(c)8(7x + 3)
(d)8(7x − 3)
11.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.
y = −x² + 6x − 5
(a)x = 3, y = −4
(b)x = 3, y = 4
(c)x = 6, y = 31
(d)x = −3, y = 4
12.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.
(a)12a + 8
(b)8a + 6
(c)8a + 2
(d)5a
13.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
(a)w < 630
(b)w ≥ 630
(c)w > 630
(d)w ≤ 630
14.Solve the inequality 5 − x ≤ 2.
(a)x ≤ −3
(b)x ≥ −3
(c)x ≥ 3
(d)x ≤ 3
15.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.
(a)s = t / d
(b)s = d / t
(c)s = d − t
(d)s = dt

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