Onlinetuition.com SPM Mathematics
(E) Converting from One Base to Another 1. The following steps are used to convert a number from one base to another base. (a) convert the number to a number in base 10 by using expended notation. (b) use repeated division to convert the number in base 10 to the respective bases. Example 1: Convert (a) 1101012 … Read more
(D) Converting Numbers in Base Two, Eight and Five to Base Ten and Vice Versa 1. Steps to convert numbers in base 2, 8 and 5 to base 10 are as follows. (a) write the number in expanded notation. (b) simplify the expanded notation into a single number. Example 1: Convert each of the following … Read more
(A) Numbers in Bases Two, Eight and Five 1. The numbers we use daily are in base ten. The ten digits used in numbers in based ten are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. 2. Numbers in base two are numbers that use two digits only. The digits are 0 and 1. Example: 1011012. 3. Numbers in … Read more
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
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
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
1.4 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
1.3 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
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
(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