YEAR 8 TERM 3 REVISION NOTES ALGEBRAIC TECHNIQUES

YEAR 8 – TERM 3 – REVISION NOTES

ALGEBRAIC TECHNIQUES – 1 a List the terms and state the coefficient of the pronumerals for the following expressions 1) 6 a + 4 b + 5 c 2) 2 a 2 +6 b +c Terms 6 a, 4 b and 5 c a=6, b=4 and c=5 Terms 2 a 2, 6 b and c a 2=2, b=6 and c=1 Write an expression for the following 3) 4) 5) 6) 7) 8) 10 more than x 18 less than 2 X x 2 x divided by 3 The product of a and b The product of a and its self The difference of c and a quarter of b x + 10 2 x - 18 2 x / 3 or 2 x ÷ 3 ab a 2 c –b/4

ALGEBRAIC TECHNIQUES 1 b Substitute the following values of x into the expression 9 x +2 1) 4 2) -8 3) 0 38 -70 2 Substitute a= 5 and b = -4 4) 5) 6) 7) 8) 4 a + b 2 a 2 – 4 b (ab/2) + b 3 a 2 –b 2 100 - (a-b) 16 66 -14 59 91

ALGEBRAIC TECHNIQUES -1 b cont. Complete 9) a 1 2 3 3 a 2 + 4 7 16 31 5 – 2 a 3 1 -1 a 3 + 5 6 13 32

ALGEBRAIC TECHNIQUES – 1 c Adding and subtracting like terms - Simplify 1) 14 a + 6 a + 4 – 2 2) 22 b – 6 b 2 +10 b 2 - 4 b 20 a + 2 18 b + 4 b 2 Write an expression for the perimeter and area of the following shapes 3) 4) 2 a 7 a P = 18 a and A = 14 a 2 10 a -2 b 8 a + 4 b 6 P = 18 a + 2 b + 6 A = ½ X 6 X (10 a-2 b) = 30 a – 6 b

ALGEBRAIC TECHNIQUES – 1 d Multiplying and dividing terms - Simplify 1) 2) 3) 4) 3 a X 6 b X 2 c 18 ab X 3 ab 12 y / 6 24 y 3 / 8 y Find the Missing Term 5) 6) 7) 8) 6 x X 3☐☐ X 4 y = 72 x 2 y 3 28 xy 2 / - 2☐☐ = -14 y y☐ = 1 x☐ X y☐ = xy 36 abc 54 a 2 b 2 2 y 3 y 2 ☐ = x and ☐ = y ☐= 0 ☐ = 1 and ☐ = 1

ALGEBRAIC TECHNIQUES – 1 e Adding and subtracting algebraic fractions - Simplify 1) 3 y + y 5 5 4 y 5 2) 2 x + x 3 9 7 x 9 3) 9 x + 23 x 7 14 41 x OR 2 13 x 14 14 4) 6 x - 4 x 20 20 2 x simplifies to x 20 10 5) 13 x – 4 x 14 7 5 x 14 6) 12 x – 6 x 15 30 18 x simplifies to 3 x 30 5

ALGEBRAIC TECHNIQUES – 1 f Multiplying and dividing algebraic fractions - Simplify 1) 2 x X 4 3 5 8 x 15 2) 8 a X 2 b 3 5 16 ab 15 3) 14 a simplifies to 7 54 a 27 7 a X 2 18 3 a 4) 9 x ÷ 1 20 4 36 x simplifies to 9 x 20 5 5) 13 x ÷ 4 14 5 65 x 56 6) 12 x ÷ 6 x 15 30 360 x simplifies to 4 90 x

ALGEBRAIC TECHNIQUES – 1 g Expanding brackets 1) 18 (a + 5) 18 a + 90 2) 48 f + 10 5 (9 f +2) +3 f 3) -3(2 a + 3 b - 4 c) -6 a – 9 b + 12 c 4) 12(5 – 3 a) + 2(a -3) 54 -34 a 5) a(3 a + 4 b + 5 c) 3 a 2 + 4 ab + 5 ac 6) 5 a 2(3 a + b – 5 c) 15 a 3 +5 a 2 b – 25 a 2 c

ALGEBRAIC TECHNIQUES – 1 h Factorising Expression 1) 9 a + 12 3(a + 4) 2) 48 y + 36 xy 12 y(4 +9 x) 3) -10 x - 20 -10 (x-2) 4) 2 x 2 +6 x 2 x(x +3) 5) 15 a 3 + 10 a 2 + 5 a 5 a(3 a 2 + 2 a +5) 6) 10 ax 3 +20 a 2 b – 50 a 2 c 10 a(x 3 +2 ab – 5 ac)

ALGEBRAIC TECHNIQUES – 1 j and 1 k Index laws for multiplication and division 1) 83 X 85 88 2) 65 ÷ 62 62 3) 30 1 4) (23)4 212 5) (3 x 2)3 27 x 6 6) 51 5