Printable · GCSE Higher · ages 14-16

Recognising and sketching graphs worksheet — GCSE Higher

Fifteen questions on "recognising and sketching graphs" — DfE statement A12. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Recognising and sketching graphs worksheet — GCSE Higher

Maths · GCSE Higher · A12 · Recognising and sketching graphs · 15 questions

MathsUKwww.geekhero.co.uk

1.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$
2.Work out the period of the graph of y = cos x, in degrees.
y = cos(x)
(a)180°
(b)90°
(c)360°
(d)720°
3.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?
(a)y = 2x + 1
(b)y = 1/x
(c)y = x²
(d)y = x³
4.A graph has equation y = −2x² + 5. Which statement about its shape is correct?
y = -2x² + 5
(a)It is U-shaped, since x² is always positive.
(b)It is a straight line, because of the constant term +5.
(c)It repeatedly rises and falls, like a wave shape.
(d)It is n-shaped, since the x² coefficient is negative.
5.A graph passes through the point (0, 1). As x increases through positive values, the graph rises more and more steeply, and as x decreases through negative values, the graph gets closer and closer to the x-axis without ever reaching it. Which of these could be the equation of the graph?
(a)y = 2ˣ
(b)y = x² + 1
(c)y = x³ + 1
(d)y = 1 − x²
6.How many turning points does the graph of y = x² − 7x + 10 have?
y = x² − 7x + 10
(a)Four turning points.
(b)One turning point.
(c)Two turning points.
(d)No turning points.
7.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.
y = x
(a)8
(b)−6
(c)−8
(d)6
8.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
(a)The graph has only one branch, in quadrant 1
(b)The graph passes through the origin, (0, 0)
(c)The graph crosses the y-axis but never the x-axis
(d)The graph never crosses either axis
9.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.
y = x
(a)(0, 4)
(b)(4, 0)
(c)(0, 0)
(d)(0, −4)
10.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?
(a)30° and 120°
(b)30° and 210°
(c)45° and 135°
(d)30° and 150°
11.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
12.The diagram shows the graph of a function. Which equation could it represent?
(a) $y = x^{3} + 4 x$
(b) $y = x^{3} - 4 x$
(c) $y = - x^{3} + 4 x$
(d) $y = x^{2} - 4 x$
13.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.
y = tan(x)
(a)270°
(b)0°
(c)90°
(d)45°
14.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) $y = x^{2} + 3$
15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km

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