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 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.
2.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.
(a)y = 200x − 8
(b)y = −8x − 200
(c)y = 200 − 8x
(d)y = 8x + 200
3.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).
(a)(4, 1)
(b)(4, −1)
(c)(−4, 1)
(d)(−4, −1)
4.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
5.Solve the simultaneous equations y = x + 1 and x² + y² = 25, giving both pairs of solutions.
y = x + 1
(a)x = 4, y = 5 and x = −3, y = −2
(b)x = −4, y = −3 and x = 3, y = 4
(c)x = 12, y = 13
(d)x = −4, y = −3
6.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
(a)7n
(b)12n + 7
(c)7n + 12
(d)7n + 5
7.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.
(a)9
(b)25
(c)18.75
(d)15
8.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
9.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.
(a)(0, 7) and (0, −7)
(b)(7, 0) and (−7, 0)
(c)(7, 0) only
(d)(0, 7) only
10.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
11.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
(a)An identity, because it is true for every value of x
(b)An identity, because the brackets can be expanded
(c)An equation, because solving it gives x = 3
(d)A formula, because it works out 4x + 12 from x
12.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.
(a)0
(b)8
(c)3
(d)1
13.Which of these pairs of lines are perpendicular to each other?
(a)y = 2x and y = 2x + 1
(b)y = 2x and y = −(1/2)x + 1
(c)y = 2x and y = −2x + 1
(d)y = 2x and y = (1/2)x + 1
14.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
15.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)

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