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 graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.
(a)a = 7; turning point (4, −5)
(b)a = 7; turning point (4, 2)
(c)a = 2; turning point (4, 2)
(d)a = −7; turning point (4, 2)
2.f(x) = x³ − 3x − 20, and the equation f(x) = 0 has exactly one solution. Work out the pair of consecutive integers between which that solution lies.
y = x
(a)2 and 3
(b)3 and 4
(c)4 and 5
(d)6 and 7
3.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.
(a)5/L − 3
(b)(L − 3)/5
(c)L/5 − 3
(d)L − 3/5
4.Work out the period of the graph of y = cos x, in degrees.
y = cos(x)
(a)180°
(b)90°
(c)360°
(d)720°
5.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
6.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.
y = x
(a)y = −x³ + 5x
(b)y = x³ − 5x
(c)y = x³ + 5x
(d)y = −x³ − 5x
7.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
8.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.
y = 3x² + 12x + 7
(a)x = −2, y = 5
(b)x = −4, y = −41
(c)x = 2, y = −5
(d)x = −2, y = −5
9.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.
(a)375 m/s
(b)14 m/s
(c)8750 m/s
(d)0.07 m/s
10.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
(a)68, and it is an equation
(b)36, and it is a formula
(c)52, and it is a formula
(d)68, and it is a formula
11.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6
12.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
13.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.
(a)0.5
(b)−1.2
(c)−2
(d)2
14.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.
(a)8 m
(b)24 m
(c)16 m
(d)12 m
15.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.
(a)y = x + 3
(b)y = 3x − 1
(c)y = 3x + 1
(d)y = 3x + 4

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