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.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
2.n = 3. Work out the value of (2n)².
(a)12
(b)9
(c)18
(d)36
3.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
(a)9
(b)7
(c)1
(d)11
4.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
5.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).
(a)(−1, 9)
(b)(2, 6)
(c)(−1, 3)
(d)(−4, 6)
6.A student uses the iterative formula xₙ₊₁ = √(7xₙ + 3) to find an approximate solution of an equation. Work out which equation this iterative formula solves.
(a)x² + 7x − 3 = 0
(b)x² − 7x + 3 = 0
(c)x² − 7x − 9 = 0
(d)x² − 7x − 3 = 0
7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.
(a)(3, 5)
(b)(−3, 9)
(c)(3, 9)
(d)(3, 7)
8.The diagram shows two curves drawn on the same grid. Curve A is the graph of $y = x^{2}$ . Which equation could represent curve B?
(a) $y = (x - 3)^{2}$
(b) $y = x^{2} - 3$
(c) $y = x^{2} + 3 x$
(d) $y = x^{2} + 3$
9.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?
y = x
(a)y ≥ 2, y ≥ x, x ≤ 6
(b)y ≥ 2, y ≤ x, x ≤ 6
(c)y ≤ 2, y ≤ x, x ≤ 6
(d)y ≥ 2, y ≤ x, x ≥ 6
10.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.
y = x
(a)4 and 5
(b)2 and 3
(c)0 and 1
(d)3 and 4
11.A curve has equation y = x² − 9. Which statement about its graph is correct?
y = x² − 9
(a)It crosses the x-axis only once, at x = 9.
(b)It does not cross the x-axis, since −9 is negative.
(c)It crosses the x-axis at x = 9 and x = −9.
(d)It crosses the x-axis at x = 3 and x = −3.
12.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.
(a)9
(b)6
(c)7
(d)8
13.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
14.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
15.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

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