chapter 4 ii quadratic equations enrich

5/12/2018 Chapter 4 II Quadratic Equations ENRICH - slidepdf.com

http://slidepdf.com/reader/full/chapter-4-ii-quadratic-equations-enrich 1/4

Enrich

4.1 Quadratic ExpressionA quadratic expression is an expression of the form ax2 + bx + c where a, b and c are

constants, a ≠ 0 and x is an unknown.

Factorisation of Quadratic Expressions using the cross method.

Quadratic Expressions and Equations

Example :

Factorise each of the following :

Exercise

1 x2 + 5x + 6 = (x + 2)(x + 3)

x 2 2x

x 3 3x

x2 +6 5x

(i) x2 + 7 x + 10

(ii) x2 + 6 x + 8

2 x2 – 7x + 12 = (x –3)(x – 4)

x –3 –3x

x – 4 – 4x

x2 +12 –7x

(i) x2 – 5x + 6

(ii) y2 – 8y + 15

1

CHAPTER 4

QUADRATIC EXPRESSIONS AND EQUATIONS



Enrich

Solution of Quadratic EquationsFirst, write the quadratic equation in the form ax2 + bx + c = 0 , a ≠ 0.

Then factorise and write in the form of (x + a)(x + b) = 0

Thus x + a = 0 or x + b = 0

And x = - a, x = - b.

Questions based on the examination format

1. Solve (f – 1)(f – 2) – 6 = 0

2. Solve the equation 15

32 2

=−

n

n

3. Solve the following equation

3m2

= 2(m-3) + 11.

4. Solve the equation )1(732−=+ y y

5. Solve the equation 26

32 2

=

+

−

m

mm

6. Solve the equation7

32 2+

=k

k .

7. Solve the equations ( ) p p 532

12−= .

8 . Solve the equationh

hh

35

2−

=− .

9. Solve equation ( ) 111

62 2

=+

n

n

10. Solve the equation

x2 - 3 x + 2 = 2( x - 1)

Past Year SPM Questions

1. November 2003

Solve the equation 3x2 = 2(x – 1) + 7.

2. July 2004

Solve the quadratic equation .224

3 2+=

p p

3. November 2004

Solve the equation.2

1

522

=

+

+

m

mm

4. July 2005

Solve the quadratic equation mm2

712

2−=− .

5. November 2005

Quadratic Expressions and Equations 2



Enrich

Solve the quadratic equation k k

33

522

=

−

.

6. July 2006

Solve the quadratic equation .21532 2 x x x +=+

7. November 2006

Solve the quadratic equation 62

)1(3+=

− x

x x

8. June 2007

Using factorization, solve the following quadratic equation 25 8 6 5 x x x+ = −

9. Nov 2007

Using factorization, solve the following quadratic equation 24 15 17 x x− = −

10. June 2008

Solve the quadratic equation2(2 1) 2 x x x+ = −

11 Nov 2008

Solve the quadratic equation6 3

12

x x

x

−− =




Enrich

ANSWERS

Questions based on examination format

1 f = -1, 4 2n =

2

1

−

, 33

m =3

5

, -14 y = 5, 2

5m =

2

3−, 4

6k =

2

1, -3

7P =

2

1, -3

8h =

2

1− , 3

9n =

2

3, 4

10 x = 1, 4

SPM Past Year Questions

11,

3

5−= x

22,

3

4−= p

32,

2

1−=m

42,

4

1−=m

55,

2

1−=k

63,

2

5−= x

73,

3

4−= x

8 2, 3

5

x = −

9 3, 5

4 x = −

10 2, 1

3 x = −

11 3, 2

2 x = −


chapter 4 ii quadratic equations enrich

Documents