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Example 4 : Exercises: Example 5 : Example 6 : ( x x−1 4 xy x+2 6 3 y × xy 6 − y y−1 ) 3 xy = 4 6 × xy x + 2 24 = xy(x + 2) 3 y = × x× y 3 × 2 1. Simplify the following algebraic expressions: (a) m 5m ÷ 16 12 (b) 3m 8 (c) 6x+3 8 (d) 9xy 7 (e) 6pq 5 (f) 3(x+1) 8 ÷ 15m 20 ÷ 2x+1 12 ÷ 6x 3 ÷ 12p 7 5(x+1) ÷ 16 = 1 2x = ( (y−1)x (x−1)y − (y−1)(x−1) (x−1)(y−1) ) 3 xy (x−1)(y−1) ) = ( xy−x−xy+y = = 3 xy −x + y xy × (x − 1)(y − 1) 3 (y − x)xy 3(x − 1)(y − 1) Page 20 (g) 4x 7 6xy 5 (h) m+1 2 m−1 − 3 m+1 5 3 4p (i) × pq p+1 (j) 8(x+3) 9 12(x+1) × 4(x+3)
Section 3 Solving Equations Sometimes we are asked to solve an equation for a particular variable. This means that only the variable should be on one side of an equality sign and the other information in the equation should be on the other side. This is similar to solving equations in one variable as in Worksheet 2.2. However, you may end up with an algebraic expression on one side involving other variables rather than just a number. You should attack these questions in the same way as solving equations for one variable. The following examples and exercises use some of the techniques given in sections one and two of this worksheet. Example 1 : x − 2 x + 1 + = 3 3 5 Multiply each side by 15 - this will eliminate the fractions: x − 2 x + 1 15 × ( + ) 3 5 x − 2 + 1 15 + 15x 3 3 = = 15 × 3 45 5(x − 2) + 3(x + 1) = 45 5x − 10 + 3x + 3 = 45 8x − 7 = 45 Page 21 8x = 52 x = 52 8 = 13 2
Page 1 and 2: Table of Contents Module 1 1.1 Orde
Page 3 and 4: Worksheet 2.1 Factors of Algebraic
Page 5 and 6: By factorizing we can make a slight
Page 7 and 8: Example 3 : 4a + 2ab = 2a 2a(2 + b)
Page 9 and 10: 1. What are the factors of 18? 2. W
Page 11 and 12: In each of the above calculations,
Page 13 and 14: Solution 1 Solution 2 Putting in J
Page 15 and 16: Exercises: 1. Solve the following e
Page 17 and 18: Worksheet 2.3 Algebraic Fractions S
Page 19: y a fraction is the same operation
Page 23 and 24: 2. Solve for x in terms of y: (a) 3
Page 25 and 26: Worksheet 2.4 Introduction to Inequ
Page 27 and 28: Example 7 : The number of matches i
Page 29 and 30: Example 6 : Exercises: Example 7 :
Page 31 and 32: Example 3 : this is the same as Exa
Page 33 and 34: Exercises for Worksheet 2.4 1. (a)
Page 35 and 36: Note: After expansion of this expre
Page 37 and 38: Example 2 : Example 3 : √ √ 7 +
Page 39 and 40: Example 4 : Example 5 : Example 6 :
Page 41 and 42: 1. (a) √ 2 × √ 2 (b) ( √ 5)
Page 43 and 44: Exercises: 1. Factorize the followi
Page 45 and 46: Exercises: 1. Expand the following,
Page 47 and 48: Section 4 Factorizing Quadratics Be
Page 49 and 50: Example Factorize 6x 2 − x − 12
Page 51 and 52: the quadratic formula. Note that a
Page 53 and 54: Example 3 : Solve (x + 3) 2 = x + 5
Page 55 and 56: Section 7 Multiplication and Divisi
Page 57 and 58: Worksheet 2.7 Logarithms and Expone
Page 59 and 60: Note that for all of the above prop
Page 61 and 62: exactly in decimal form, but it is
Page 63 and 64: 1. Evaluate (a) log 10 1000 (b) log
Page 65 and 66: Example 4 : If CD and AB are parall
Page 67 and 68: The triangle ABC in the above examp
Page 69 and 70: Section 3 Pythagoras’ Theorem All
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Section 4 Introductory Trigonometry
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Exercises: 1. Find the following ra
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Worksheet 2.9 Introduction to the C
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Exercises: 1. Complete the table of
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Example 1 : y = 2x + 3. The gradien
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Example 8 : The lines y = 10x + 3 y
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which doesn’t make sense as we ca
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2. (a) Plot the points X(−1, 2) a
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Worksheet 2.1 Section 1 1. (a) 6 (b
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2. (a) -1 (b) 46,47 (c) 22,24 Works
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Exercises 2.4 1. (a) i. ii. iii. iv
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2. (a) 13 √ 3 (b) −12 √ 5 (c)
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2. (a) 5x2 +13x+9 (x+2)(x+3) (b) 2(
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Exercises 2.7 1. (a) 3 (b) 0 (c) 3
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2. (a) Section 2 1. (a) & (d) Secti
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