Printable · GCSE Foundation · ages 14-16

Recognising and sketching graphs worksheet — GCSE Foundation

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 Foundation

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

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1.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?
(a) $y = 2 x + 1$
(b) $y = - 2 x - 1$
(c) $y = x - 1$
(d) $y = 2 x - 1$
2.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) $y = x^{2} - 4 x$
3.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
4.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.
5.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
6.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?
y = 3x + 2
(a)A curve that gets closer to an axis but never reaches it.
(b)A straight line.
(c)A curve that decreases then increases.
(d)A U-shaped curve, like a quadratic.
7.Which of these equations gives a straight-line graph when plotted?
(a)y = 3/x
(b)y = 2x − 3
(c)y = x³ − 3
(d)y = x² − 3
8.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.
9.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) $y = x^{2} - 2 x - 3$
10.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
11.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
12.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.
13.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
(a)−2 and 2
(b)0 and 2
(c)−4 and 4
(d)−2 and 3
14.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?
(a)(2, 3)
(b)(2, 5)
(c)(2, 6)
(d)(3, 2)
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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