Graphs 7
4 marks · HardA student is asked to solve the equation by drawing suitable graphs.
Write down:
Which two graphs the student must draw.
Explain how the solutions can be found using these graphs.
If the graphs intersect at one point only, estimate the solution for to one decimal place.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) y = x^3 - 2x and y = 3
(b) The value(s) of x where the graphs intersect are the solutions to the equation.
(c) x = 1.7 (accept 1.7 to 1.8)
Common mistakes: Drawing y = x^3 - 2x and y = x instead of y = 3
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States or identifies both graphs correctly: y = x^3 - 2x and y = 3.
M2 (b) · 1 mark · Explains that the solution(s) are the x-values of intersection points.
A1 (c) · 2 marks · Estimates solution: x = 1.7 (±0.1) (accept any value between 1.7 and 1.8).
Worked solution
(a) The student needs to draw the graphs of y = x^3 - 2x and y = 3.
(b) The solutions are the x-values where the two graphs intersect.
(c) By estimating the x-value at the intersection, x ≈ 1.7 (to 1 decimal place).