Quadratic Equations
50 min
38 marks
1.
Showing all your working, solve
(a)
5x
– 9 = 0,
2
Answer (a) x = ………………….…………
[2]
(b)
x2 + 12x + 3 = 0, giving your answers correct to 1 decimal place.
Answer (b) x = ……..…… or x = …………
[4]
1
2.
(x + 4) cm
R
4x cm
Q
(x + 2) cm
(x + 12) cm
(a)
(i)
NOT TO SCALE
Write down an expression for the area of rectangle R.
Answer (a) (i) …….…………………. cm2
[1]
(ii)
Show that the total area of rectangles R and Q is 5x2 + 30x + 24 square centimetres.
[1
(b)
The total area of rectangles R and Q is 64 cm2.
Calculate the value of x correct to 1 decimal place.
Answer (b) x = …………………………….
[4]
2
3.
150 cm
7x cm
24x cm
NOT TO SCALE
The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 150 cm.
(a)
Show that x2 = 36
[2]
(b)
Calculate the perimeter of the triangle.
Answer (b) ……..….………………… cm
[1]
3
4.
2y – 1
y
y+2
NOT TO SCALE
The diagram shows a right-angled triangle.
The lengths of the sides are given in terms of y.
(i)
Show that 2y2 – 8y – 3 = 0.
[3]
(ii)
Solve the equation 2y2 – 8y – 3 = 0, giving your answers to 2 decimal places.
[4]
(iii)
Calculate the area of the triangle.
[2]
4
5.
B
(x + 1) cm
A
(x + 6) cm
D (x + 2) cm
C
NOT TO SCALE
In triangle ABC, the line BD is perpendicular to AC.
AD = (x + 6) cm, DC = (x + 2) cm and the height BD = (x + 1) cm.
The area of triangle ABC is 40 cm2.
(i)
Show that x2 + 5x – 36 = 0.
Answer (i) ……..……….………
[3]
(ii)
Solve the equation x2 + 5x – 36 = 0.
Answer (ii) x = ….… or x = ……
[2]
(iii)
Calculate the length of BC.
Answer (iii) BC = ……..…… cm
[2]
5
6.
2x + 4
x+2
x
x2 – 40
NOT TO SCALE
The diagram shows a trapezium.
Two of its angles are 90°.
The lengths of the sides are given in terms of x
The perimeter is 62 units.
(i)
Write down a quadratic equation in x to show this information. Simplify your equation.
[2]
(ii)
Solve your quadratic equation.
[2]
(iii)
Write down the only possible value of x.
[1]
(iv)
Calculate the area of the trapezium.
[2]
6