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 · 15 questions

MathsUKwww.geekhero.co.uk

1.Which expression means 'triple c, then add double d'?
(a)6cd
(b)2c + 3d
(c)3c + 2d
(d)5(c + d)
2.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
3.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
4.Simplify 5a/6 − a/3
(a)7a/6
(b)2a/3
(c)4a/3
(d)a/2
5.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?
(a)1.76
(b)0
(c)10
(d)6
6.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.
(a)y = −(12/5)x
(b)y = (5/12)x − 25/12
(c)y = (5/12)x − 169/12
(d)y = −(5/12)x − 119/12
7.By completing the square, find the turning point of the curve y = x² − 10x + 30.
y = x² − 10x + 30
(a)x = 10, y = −70
(b)x = 5, y = −5
(c)x = 5, y = 5
(d)x = −5, y = 5
8.Write down the expression that means the same as (x + 7) ÷ 4.
(a)4(x + 7)
(b)4/(x + 7)
(c)(x + 7)/4
(d)(x + 7) − 4
9.p = 4. Work out the value of 2p³.
(a)512
(b)24
(c)64
(d)128
10.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?
y = 2x − 5
(a)Yes, but step 2 should give x = 2(y + 5)
(b)No; it should be x = (y − 5)/2
(c)Yes; x = (y + 5)/2 is right
(d)No; it should be x = y/2 + 5
11.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)
12.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
(a)88
(b)39
(c)32
(d)25
13.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?
(a)x² − 8x + 15 ≥ 0
(b)x² + 2x − 15 ≥ 0
(c)x² − 2x − 15 ≥ 0
(d)x² − 2x − 15 ≤ 0
14.A bath is filled with water; the graph of volume (litres) against time (minutes) is a curve, since the flow rate changes. The tangent to the curve at t = 10 minutes passes through the points (8, 130) and (12, 190), and the volume in the bath at t = 10 minutes is 160 litres. Use the gradient of this tangent to estimate the volume in the bath 5 minutes after t = 10 minutes.
(a)190 litres
(b)235 litres
(c)85 litres
(d)75 litres
15.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.
(a)x = 4 ± √13
(b)x = −4 ± √13
(c)x = 8 ± √13
(d)x = 4 ± √19

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