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.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?
(a)3x/2
(b)−3x/2
(c)3x²/2
(d)3/2
2.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.
(a)s/f
(b)sf
(c)f/s
(d)s − f
3.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.
(a)11
(b)16
(c)96
(d)48
4.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.
y = x² − 7x + 2
(a)x ≈ 6.70
(b)x ≈ 6.30
(c)x ≈ 7.30
(d)x ≈ 0.70
5.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.
y = x
(a)(0, 4)
(b)(4, 0)
(c)(0, 0)
(d)(0, −4)
6.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5
7.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
8.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.
(a)6 s
(b)8 s
(c)32 s
(d)12 s
9.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.
(a)9 m
(b)18 m
(c)37 m
(d)16 m
10.Simplify (x² − 9) ÷ (x² + 5x + 6).
(a)(x + 3)/(x + 2)
(b)(x − 3)/(x + 2)
(c)x − 3
(d)−9/(5x + 6)
11.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.
(a)12.5
(b)8
(c)10
(d)3.5
12.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.
(a)−1/2
(b)3/2
(c)−3/2
(d)2/3
13.By completing the square, find the turning point of the curve y = x² − 4x + 9.
y = x² − 4x + 9
(a)x = 4, y = −7
(b)x = 2, y = −5
(c)x = 2, y = 5
(d)x = −2, y = 5
14.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
15.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.
y = x²y = x² + 3
(a)A translation by vector (0, 3)
(b)A translation by vector (0, −3)
(c)A translation by vector (3, 0)
(d)A stretch parallel to the y-axis, scale factor 3

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