Substitution Substitute numerical values into formulae and expressions

Substitution Substitute numerical values into formulae and expressions, including scientific formulae If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key vocabulary Substitute Formulae Scientific formulae Value Numerical Expression

Starter 20 – 9 x 2 + 10 Can you make this equal? 8 32 12 -88 Which is correct? Why?

Order of operations We must consider BIDMAS to know which operations in a sum to complete first. B- Brackets I- Indices D- Division M- Multiplication A- Addition S- Subtraction

How to use order of operations 3² + (4 x 5) – 3 3² + (20) – 3 9 + 20 – 3 = 26 25 + (5² + 2) x 3 25 + (25 + 2) x 3 25 + (27) x 3 5 + 81 86

Using BIDMAS 4 + 5 x 10 Jane says the answer is 90 Bill says the answer is 54 Who is correct? Bill is correct because using BIDMAS we should do the multiplication first 4 + 5 x 10 4 + 50 = 54

Practice • Find the value of the following • 20 - 9 x 2 + 10 12 • 20 - 8 ÷ 2 16 • 3 x 5 2 + 10 85 • 23 + 4 x 81 44

Substitute into a formula If x = 7 and we have the expression x + 5 then: - 7 + 5 = 12 If x = 10 and we have the expression 2 x + 5 then: - 20 + 5 = 25 If x = 9 and we have the expression 2(x – 3) then: - 2( 9 - 3) = 2 x 6 = 12

Substitute into a formula If x = 15 and we have the expression √(x + 1) then: - √(15 + 1) = √ 16 = 4 If a = 10 and we have the expression 3 a 2 then: - 3 x 102 = 3 x 100 = 300 If a = -4 and we have the expression 3 a then: - 3 x - 4 = - 12

Substitution practice (1) If a = 5 and b = 6 evaluate: 1) a + b =11 4) b - a =1 2) ab =30 5) 4 b =24 3) 3 a =15 6) 3 ab =90

Substitution practice (2) =12 =16 =80 =26 =14 =3

Substitute into scientific formulae Find the value of v when u = 22. 5, a = 3, t = 5 v = u + at v = 22. 5 + (3 x 5) = 22. 5 + 15 = 37. 5 Find the value of V when r = 3. Answer in terms of π. V= V = 4/3 x π x 27 = 36π

Problem solving and reasoning (1) The profit made by a charity event is given by the formula: Profit = number of tickets sold x £ 5 – cost of expenses Calculate the profit made when 84 tickets were sold and the cost of the expenses was £ 120. Profit = 84 x 5 - 120 Profit = £ 300

Problem solving and reasoning (2) Substitute – explain the mistakes 1) 3 p = 36 18 2) p + q = 8 4 3) p - q = 4 8 4) 2 p 2 = 144 72 5) 4 q² = -16 16 p=6 q = -2

Problem solving and reasoning (3) x+ 7 3 x Show the perimeter of the rectangle is 8 x + 14 Calculate the perimeter when x = 4 Perimeter = 46

Exam specimen questions

Exam specimen questions [2 marks]