Higher January 2022 Paper 2 Q21

EdexcelHigherCurrent spec5 marksDrawing & Using Graphs Solving Quadratics

21 Part of the graph of \(y = 2x^2 - 4x - 1\) is shown on the grid.

Graph of y = 2x squared − 4x − 1 for x from −1 to 3 on a grid with y from −5 to 5; the curve has its minimum at (1, −3) and crosses the x-axis between −1 and 0 and between 2 and 3

(a) Use the graph to find estimates for the solutions of the equation \(2x^2 - 4x - 1 = 0\)
Give your solutions correct to one decimal place. (2)

(b) By drawing a suitable straight line on the grid, find estimates for the solutions of the equation \(x^2 - x - 1 = 0\)
Show your working clearly.
Give your solutions correct to one decimal place. (3)

Mark scheme (a)

Scheme	Marks
–0.2 and 2.2	B2
	(2)

Notes

B2: Both correct to 1 decimal place
(B1 for (–0.2, 0), (2.2, 0)
or
a single correct value to 1 decimal place
or
both values within –0.2 to –0.23 and 2.2 to 2.23)

Mark scheme (b)

Scheme	Marks
\((y =)\;-2x + 1\) oe seen	M1
\(y = -2x + 1\) drawn	M1
Working required Answer: –0.6 and 1.6	A1
	(3)
	(5 marks)

Notes

M1: Written – could be label on graph

M1: dep on previous M1 for drawing \(y = -2x + 1\) passing through (–1, 3) and (2, –3)
(allow 1 square tolerance)

A1: dep on M2 for both answers to 1 decimal place