 ## 1.6.3 Quadratic Equations, SPM Paper 2 (Long Questions)

Question 9:Solve the following quadratic equation:4x (x + 4) = 9 + 16xSolution: 4x( x+4 )=9+16x 4 x 2 +16x=9+16x    4 x 2 −9=0 ( 2x ) 2 − 3 2 =0 ( 2x+3 )( 2x−3 )=0 2x+3=0  or  2x−3=0  2x=−3 2x=3    x=− 3 2  x= 3 2     Question 10:Solve the following quadratic equation:(x … Read more

## 1.6.2 Quadratic Equations, SPM Paper 2 (Long Questions)

Question 5: Solve the equation: (m + 2)(m – 4) = 7(m – 4).   Solution: (m + 2)(m – 4) = 7(m – 4) m2– 4m + 2m – 8 = 7m – 28 m2– 9m + 20 = 0 (m – 5)(m – 4) = 0 m = 5 or m = 4    … Read more

## 1.6.1 Quadratic Equations, SPM Paper 2 (Long Questions)

Question 1: Solve the quadratic equation, (y + 3)(y – 4) = 30 Solution: (y + 3)(y – 4) = 30 y2 – 4y + 3y– 12 = 30 y2 – y – 12 – 30 = 0 y2 – y – 42 = 0 (y + 6)(y – 7) = 0 y + 6 … Read more

## 1.5 Roots of Quadratic Equations

1.5 Roots of Quadratic Equations 1. A root of quadratic equation is the value of the unknown which satisfies the quadratic equation. 2. Roots of an equation are also called the solution of an equation. 3. To solve a quadratic equation by the factorisation method, follow the steps below: Step 1: Express the quadratic equation in general form ax2 … Read more

## 1.4 Quadratic Equations

1.4 Quadratic Equations 1. Quadratic equations are equations which fulfil the following characteristics: (a) Have an equal ‘=’ sign (b) Contain only one unknown (c) Highest power of the unknown is 2.   For example,  2. The general form of a quadratic equation is written as: (a) ax2 + bx + c = 0, where a ≠ 0, b ≠ 0 … Read more

## 1.3.1 Solving Quadratic Equations – Factorisation

1.3.1 Solving Quadratic Equations – Factorisation 1. If a quadratic equation can be factorised into a product of two factors such that (x – p)(x – q) = 0 Hence  x – p = 0   or  x – q = 0    x = p   or x = q p and q  are the roots of the equation. Notes … Read more

## 1.3 Factorisation of Quadratic Expression

1.3 Factorisation of Quadratic Expression   (A) Factorisation quadratic expressions of the form ax2 + bx + c, b = 0 or c = 0 1. Factorisation of quadratic expressions is a process of finding two linear expressions whose product is the same as the quadratic expression. 2. Quadratic expressions ax2 + c and ax2 + … Read more

## 1.2 Graph of Quadratic Function

1.2 The Graph of Quadratic Function The graph of quadratic function is parabola. When the coefficient of x2 is positive the graph is a parabola with U shape. When the coefficient of x2 is negative the graph is a parabola with ∩ shape. Axis of Symmetry The axis of symmetry is a vertical line passing through the maximum or … Read more

## 1.1.1 Quadratic Expression (Sample Questions)

Example 1: Form a quadratic expression by multiplying each of the following. (a) (6p – 2)(2p – 1) (b)   (m + 5)(4 – 7m) (c)    (x + 2) (2x – 3) Solution: (a) (6p – 2)(2p – 1) = (6p)(2p) + (6p)(-1) + (-2)(2p) +(-2)(-1) = 12p2 – 6p – 4p + 2 = 12p2 – … Read more

## 1.1 Quadratic Expressions

(A) Identifying quadratic expression 1. A quadratic expression is an algebraic expression of the form ax2 + bx + c, where a, b and c are constants, a ≠ 0 and x is an unknown. (a) The highest power of x is 2. (b) For example, 5×2– 6x + 3 is a quadratic expression. Example 1 State whether … Read more