Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Graphs 4
17 practice questions
Practice questions
11–17 of 17
Question 11
4 marks · Normal
Answer and see the solution →For the quadratic graph :
(a)[2 marks]Find the x-coordinates where the curve meets the x-axis.
(b)[2 marks]State the coordinates of the turning point.
Question 12
2 marks · Normal
Answer and see the solution →The equation of a straight line is given as . What is the gradient of this line? What does the negative value indicate about its slope?
Question 13
5 marks · Normal
Answer and see the solution →A particle moves along a line. Its distance, s metres, from a point is given by , where t is the time in seconds.
(a)[2 marks]Complete the table for values of t from 0 to 6:
t 0 1 2 3 4 5 6 s (b)[1 mark]State when the particle is closest to the point and what the minimum distance is.
(c)[2 marks]Between which two times is the particle at least 5 metres from the starting point?
Question 14
4 marks · Hard
Answer and see the solution →A projectile is launched so that its height, metres, above the ground after seconds is given by .
(a)[3 marks]Find the maximum height reached by the projectile and the time at which it occurs.
(b)[1 mark]Determine the time when the projectile returns to the ground.
Question 15
3 marks · Hard
Answer and see the solution →A quadratic graph has the general form .
(a)[3 marks]Explain how the values of , , and affect the shape and position of the graph in the coordinate plane.
Question 16
4 marks · Hard
Answer and see the solution →A rectangular field is to be enclosed on three sides with fencing. The fourth side is a hedge and requires no fence. The length of the field is metres and the width is metres. If 160 m of fencing is available, express the total area of the field in terms of , and find the value of that gives the maximum area.
(a)[1 mark]Show that .
(b)[3 marks]Calculate the value of that produces the largest field area, and find this maximum area.
Question 17
4 marks · Hard
Answer and see the solution →Consider the straight line with equation .
(a)[1 mark]For what value of does this line pass through the point (2, 7)?
(b)[1 mark]Find the gradient and explain its meaning in the context of any straight line graph.
(c)[1 mark]Calculate the x-coordinate where the line crosses the x-axis.
(d)[1 mark]Given a second line with equation , what value of would make the two lines parallel and intersect at y = 10?