1.	(a)	Complete the table for y = x2 – 3x + 1
x	–2	–1	0	1	2	3	4	
y	11		1	–1		1	5	
(2)
(b)	On the grid, draw the graph of y = x2 – 3x + 1
(2)

(c)	Use your graph to find an estimate for the minimum value of y.

y = ……………………
(1)
(d)	Use a graphical method to find estimates of the solutions to the equation
x2 – 3x + 1 = 2x – 4

	x = …………………… or	x = ……………………
(3)
(Total 8 marks)

2.	Solve	x2 – 3x – 18 = 0

……………………………
(Total 3 marks)

3.	Solve this quadratic equation.
	x2 – 5x – 8 = 0
	Give your answers correct to 3 significant figures.
x = .....................................or x = .....................................
(Total 3 marks)

4.	Given that
x2 – 14x + a = (x + b)2 for all values of x,
find the value of a and the value of b.

a = .........................................
b = .........................................
(Total 3 marks)

5.	Peter cuts a square out of a rectangular piece of metal.

	The length of the rectangle is 2x + 3.
The width of the rectangle is x + 4.
The length of the side of the square is x + 2.
All measurements are in centimetres.
	The shaded shape in the diagram shows the metal remaining.
	The area of the shaded shape is 20 cm2.
(a)	Show that x2 + 7x – 12 = 0

(4)
(b)	(i)	Solve the equation x2 + 7x – 12 = 0
Give your answers correct to 4 significant figures.

……………………………..
(3)
(ii)	Hence, find the perimeter of the square.
Give your answer correct to 3 significant figures.

…………………….. cm
(1)
(Total 8 marks)

6.	

Diagram NOT accurately drawn
	AB = (2x + 1) metres.
BC = (x + 2) metres.
Angle ABC = 30°.
	The area of the triangle ABC is 3 m2.
Calculate the value of x.
	Give your answer correct to 3 significant figures.

……………………………
(Total 5 marks)