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 sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
(a)38
(b)36
(c)64
(d)14
2.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?
y = x − 2y = x² − 4x + 2
(a)Right — x² − 3x + 4 = 0 is correct.
(b)Right — subtracting is the same as adding.
(c)Wrong — the correct equation is x² − 5x + 4 = 0.
(d)Wrong — it should be x² − 5x − 4 = 0.
3.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.
(a)£14.50
(b)£13.50
(c)£12.50
(d)£24.50
4.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
5.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.
(a)(15, 0)
(b)(6, 0)
(c)(0, 0)
(d)(0, 7.5)
6.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
(a)x + 14
(b)x + 10
(c)5x + 10
(d)x + 13
7.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.
8.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.
(a)18.67
(b)12
(c)15.33
(d)4.3
9.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.
(a)x² + y² = 49
(b)x² + y² = 625
(c)x² + y² = 31
(d)x² + y² = 576
10.n = 3. Work out the value of (2n)².
(a)12
(b)9
(c)18
(d)36
11.Solve 2x + 7 = x + 13
(a)x = 2
(b)x = 20
(c)x = −6
(d)x = 6
12.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.
(a)(0, 36) and (0, −36)
(b)(0, 6) and (0, −6)
(c)(0, 18) and (0, −18)
(d)(6, 0) and (−6, 0)
13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
14.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?
(a)Translate +2 in x only (no reflection); roots 1, 6
(b)Solved 2 − x = k as x = k − 2; roots −3, 2
(c)No overall change; roots −1, 4
(d)Reflect in the y-axis, +2 in x; roots 3, −2
15.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.
(a)(3, 7)
(b)(−2, 2)
(c)(8, 2)
(d)(3, −3)

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