Mathematics: summary chapter 11B
11B – refresh
Solve (find the value of x)
3x + 10 = x2
3x + 10 – x2 = 0
x2 – 3x – 10 = 0
(x – 5)(x + 2) = 0
x = 5 or x = -2
11B.1 – Fractional equations
Solve (find the value of p)
45
+ 2=7
2 p−7
45
=5
2 p−7
45
=5
9
2p – 7 = 9
2p = 16
p =8 so, p = 8
solve (find the value of x)
6
x= −1
x+ 2
, 6
x +1=
x+2
(x + 2)(x + 1) = 6
x2 + 1x + 2x + 2 = 6
x2 + 3x – 4 = 0
(x + 4)(x – 1) = 0 In case you can’t factorise, use the quadratic formula:
x + 4 = 0 and x -1 = 0
D=b2−4 ac
x = -4 or x= 1
−b ± √ D
x=
2a
so, x = -4 or x = 1
11B.2 – exponential and square root equations
Solve the exponential equation
3x – 5 + 4 = 85 23x – 3 – 2 = 62
3x – 5 = 81 23x – 3 = 64
34 = 81 26 = 64
x–5 =4 3x – 3 =6
x =9 so, x = 9 3x =9
x =3 so, x = 3
Square root equation (1) Square root equation (2)
√ 125−4 x +1=8 44
=11
√ k−7
44
=11
4
44
=11
√16
11B – refresh
Solve (find the value of x)
3x + 10 = x2
3x + 10 – x2 = 0
x2 – 3x – 10 = 0
(x – 5)(x + 2) = 0
x = 5 or x = -2
11B.1 – Fractional equations
Solve (find the value of p)
45
+ 2=7
2 p−7
45
=5
2 p−7
45
=5
9
2p – 7 = 9
2p = 16
p =8 so, p = 8
solve (find the value of x)
6
x= −1
x+ 2
, 6
x +1=
x+2
(x + 2)(x + 1) = 6
x2 + 1x + 2x + 2 = 6
x2 + 3x – 4 = 0
(x + 4)(x – 1) = 0 In case you can’t factorise, use the quadratic formula:
x + 4 = 0 and x -1 = 0
D=b2−4 ac
x = -4 or x= 1
−b ± √ D
x=
2a
so, x = -4 or x = 1
11B.2 – exponential and square root equations
Solve the exponential equation
3x – 5 + 4 = 85 23x – 3 – 2 = 62
3x – 5 = 81 23x – 3 = 64
34 = 81 26 = 64
x–5 =4 3x – 3 =6
x =9 so, x = 9 3x =9
x =3 so, x = 3
Square root equation (1) Square root equation (2)
√ 125−4 x +1=8 44
=11
√ k−7
44
=11
4
44
=11
√16
