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.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.
(a)900
(b)50
(c)37.5
(d)1.25
2.Solve 4x − (2x − 6) = 18
(a)x = 6
(b)x = 3
(c)x = 12
(d)x = 24
3.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
4.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
5.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
(a)(2, −5)
(b)(−2, 5)
(c)(2, 5)
(d)(−2, −5)
6.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.
(a)409,600
(b)8
(c)6,400
(d)3,200
7.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.
(a)2.6
(b)2.9
(c)2.4
(d)2.7
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.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² + 2x − 15
(a)x = −3 and x = 5
(b)x = 5 and x = 3
(c)x = 3 and x = −5
(d)x = −15 and x = 1
10.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
11.The line y = 2x + 7 and the circle x² + y² = 4 are given. By finding the discriminant of the resulting quadratic, without solving it fully, work out how many points the line and the circle intersect at.
y = 2x + 7
(a)0 — the line does not intersect the circle
(b)It cannot be found without solving the quadratic.
(c)1 — the line is a tangent to the circle
(d)2 — the line crosses the circle at two points
12.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.
(a)16
(b)17
(c)34
(d)8
13.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.
(a)9x − 40y = 1681
(b)9x + 40y = 1681
(c)40x + 9y = 1681
(d)9x + 40y = 41
14.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.
(a)9n + 5
(b)5n + 9
(c)5n
(d)5n + 4
15.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

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