NCC Education Limited. Substitution Topic NCC Education Limited. Substitution Topic NCC Education Limited

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1 Topic 3 - Lecture 2: Substitution Substitution Topic Learning Objective To be able to substitute positive and negative values into algebraic expressions and formulae. Substitution Topic Key Words Expression Formula Substitute V 1.0 Visuals Handout - Page 1

2 Substitution Topic Substitution Substitution means to replace one thing with another. - 3a + 2b is an expression. If you know the values of a and b, you can substitute the letters in the expression and find its value. For example, if a = 4 and b = 5-3 x x 5 = = 22 BODMAS - 1 Substitution Topic a) 3 x = b) x 2 = Work these 2 sums out. Is there a difference in their answers? The answer is no. - Using the rules of operations (BODMAS) the answers are the same. - The rules state that multiplication should always be done before addition. - Part a) should be carried out as 3 x 2 = 6 followed by =10. - And in part b) 3 x 2 = 6 should also be done first followed by = 10. Substitution Topic BODMAS 2 BODMAS helps us to remember the order that operations should be done in. - Brackets - Of You need to remember - Division - Multiplication - Addition - Subtraction to use BODMAS when doing substitution. V 1.0 Visuals Handout - Page 2

3 Substitution Topic Exercise 1 - BODMAS Use BODMAS to carry out these calculations: 1. 2 x x 2 3. (2 + 4) x x (6-3) 5. 7 x x (4-2) x (10-5) 9. 6 x (7-3) (45-5) (34-6) (12-8) Example Substitution Topic The Rugged Walk outdoor centre organises walking trips. They always take 3 sandwiches for each person plus 4 for emergencies. - p = number of people - s = number of sandwiches a) Write a formula for the number of sandwiches. - s = 3p + 4 b) Find s when: i) p = 4 ii) p = 1 s = 3 x s = 3 x = 16 = 7 Exercise 2 - The Right Order Substitution Topic Work out the value of each expression when a = 2: a) a b) 10-3a c) 3a + 10 d) 3a Use the rule h = 4(12 - k) to work out h when: a) k = 5 b) k = 3 c) k = 0 d) k = Use the rule a = 6 - b to work out a when: 3 a) b = 3 b) b = 12 c) b = 0 d) b = 9 4. Work out m in each of these rules when n = 6. a) m = 12 + n b) m = 3 + n c) m = 3(8 - n) 3 3 V 1.0 Visuals Handout - Page 3

4 Including Powers a 2 means a x a y 3 means y x y x y 2a 2 means 2 x a x a 2a 2 y 3 means 2 x a x a x y x y x y Examples: a) Work out 5 + k 2 when k = k 2 = 5 x 3 2 = = 14 Do the squaring first. b) Work out 4a when a = 5 4a = 4 x = 4 x = = 107 Substitution Topic Substitution Topic Negative Numbers If p = -2, q = 4 and r = -3 find: a) p + q b) q p c) 3r + q d) 4p q e) 4r 2p f) p 2 g) 3r Tip: Write your working down to = 2 avoid mistakes with negative = 6 signs. 3x -3+4= -5 4 x -2-4 = x -3 2 x -2 = = = 4 3 x = 3 x = 29 Substitution Topic Substituting Into Formulae 1. The formula v = u + at is used in the study of motion. Work out v when: a) u = 12, a = 4, t = 5 b) u = 1.2, a = -0.4 and t = Another formula is s = ut + ½at2. Work out s when: a) u = 11, a = 4 and t = 5 Answers: b) u = 4.5, a = -2, and t = a) 32 b) a) 105 b) -310 V 1.0 Visuals Handout - Page 4

5 Exercise 3 Substitution Topic If a = 10, b = -4 and c = 2, work out: a) abc b) ab c c) a(b c) d) ab e) a - b c c 2. P = x 2 + y 2, Q = x 3 + y 3, R = 2x 2 + 3y 2, T = (2x) 2 + (3y) 2 Work out the values P, Q, R and T when: a) x = 3, y = 4 b) x = -3, y = -4 c) x = 3, y = A = 5x 3 B = 4x 2 (x - 5) C = 2x 3 (x + 2) 2 4 8x Find the values of A, B and C when: a) x = 1 b) x = -1 Substitution Topic Recap I can use the order of operations. I can substitute positive and negative values into algebraic expressions and formulae. Substitution Topic Topic 3 Lecture 2 Substitution Any questions? V 1.0 Visuals Handout - Page 5