Write the following in the form (x + p)^2 + q
x^2 + 5x - 5
(x + 2.5)^2 - 11.25
100
solve the equations. Give solutions correct to 3 significant figures.
x^2 + 4x + 2 = 0
x = -0.586 or -3.41
100
4x + 6y = 5 and 3x + 4y = 4
y = -0.5 and x = 2
200
x^2 - 5x - 36 = 0
(x + 4)(x - 9) so x=-4 or x=9
200
Solve the equations. Give your answer to 2 decimal places.
x^2 + 10x - 12 = 0
x = 1.08 or -11.08
200
Solve the equation. Give answer to 3 significant figures
5x^2 - 9x + 2 = 0
x = 1.54 or 0.260
200
Solve the simultaneous equations
5x - y = -4
y = 2x + 1
x=-1 and y=-1
300
2x^2 + 7x - 4 =0
(2x - 1)(x + 4) so x=1/2 or -4
300
Solve the equation correct to 3 significant figures
1/x+4 - 2/x+5 = 4
x = -3.83 or -5.43
300
Solve the equation. Give answers to 3 significant figures
x(2x + 3) = 4 - 7x
x = 0.372 or -5.37
300
A gas bill consists of a fixed charge (f pounds) and a charge (g pence) for each unit used. Mrs Anwar used 350 units and paid 30 pounds. Mr White used 450 units and paid 35 pounds. Find the fixed charge and the charge per unit.
g = 5p and f = $12
400
Solve the quadratic equation.
2/x-1 + 3/x+1 = 1
x = 0 or 5
400
Give your solution in surd form.
x^2 - 6x - 2 = 0
x = 3 +/- square root of 11
400
Solve the quadratic equation.
2/x+1 + 4/3x-1 = 3
x = 1 or -5/9
400
Solve the simultaneous equations
2y = 4x^2 - 7
y = 6x
(3.5, 21) and (-0.5, -3)
500
x(x - 3) = x + 21
(x + 3)(x - 7) so x= -3 or 7
500
Solve the equation. Give answer to 2 decimal places
6x^2 - 3x - 2 = 0
x = 0.88 or -0.38
500
The length of a rectangular wall is 5m greater than the height of the wall. The area of the wall is 16m squared. What is the length of the wall?
7.22m
500
Solve the simultaneous equations
x^2 + y^2 = 34
y = 1 + 2x