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1. Simplify the following: (a) x x + (b) 3 2 2xy (c) 3x+1 2 (d) 3 b−1 (e) 2x+2 y x+1 xy 4 + 4 xy 3 − (6x + 5) − 4 b−2 2. Simplify the follwing: (a) 4(x+1) 3 (b) x2 +3x x+4 (c) 8x−24 4 5(x−2) − 2 × 2x+8 5x x+7 ÷ 12 Exercises for Worksheet 2.3 Page 24 2 (f) x2 4 + −4x x−4 (g) (h) 1 x+1 2−1 (i) 4a 7 1 1 1 − + x+1 x+2 x+3 + 3a+5 2 − 3(a+2) 4 (j) 3p p p 5p − ( − + 12 2 4 6 ) (d) y2 −6y y+5 × 3y+15 2y−12 (e) 5m−7 m+2 ÷ 4m+8 3m+6 (f) 6p−3 4 ÷ −4p+2 12
Worksheet 2.4 Introduction to Inequalities Section 1 Inequalities The sign < stands for less than. It was introduced so that we could write in shorthand things like 3 is less than 5. This becomes 3 < 5. The sign > stands for greater than. In a similar way we can write 5 > 3 in this shorthand form. These statements are called inequalities. Recall the number line (introduced in an earlier worksheet): ✛ ✲ -5 -4 -3 -2 -1 0 1 2 3 4 5 It is drawn so that the numbers increase from left to right. Alternatively the numbers decrease from right to left. Any number which lies to the right of another on the number line is greater than it and any number which lies to the left of another on the number line is less than it. Example 1 : • −6 < 0 • 5 > 2 • −5 < −4 • 2.5 < 3 We can also use inequalities in algebraic expressions. So 21a is less than 30a is written 21a < 30a (only true if a > 0) The expression a > 1 means that a is one of all the numbers to the right of 1 on the number line. We draw this using an open circle and an arrow heading to the right. The open circle sits over 1 and indicates that the actual number 1 is not included. That is a is bigger than 1 but not equal to 1: ❝ ✲ ✛ ✲ -5 -4 -3 -2 -1 0 1 2 3 4 5 Example 2 : x > 2 ✛ ❝ ✲ -5 -4 -3 -2 -1 0 1 2 3 4 5 Page 25 ✲
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 and 20: y a fraction is the same operation
Page 21 and 22: Section 3 Solving Equations Sometim
Page 23: 2. Solve for x in terms of y: (a) 3
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
Page 71 and 72: Section 4 Introductory Trigonometry
Page 73 and 74: Exercises: 1. Find the following ra
Page 75 and 76:
Worksheet 2.9 Introduction to the C
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Exercises: 1. Complete the table of
Page 79 and 80:
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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