Functional Skills Mathematics Level 2 Learning Resource Formulae
Contents Calculations Using Simple Formulae Page 3-5 Create Simple Formulae Page 6-8 Common Mathematical Page - 10 Formulae in Use West Nottinghamshire College 2
Information Calculations Using Simple Formulae A formula is a way of expressing information symbolically; a quick way of writing a general method for solving a problem. It is an equation stating a rule. Formulae can be very simple: Profit = Revenue - Cost P = R C Balance = Income - Expenditure B = I - E Speed = Distance Time S = D T Distance = Speed Time D = S T In each case, a single letter or symbol replaces the words. If you know what the letter or symbol represents, then the formula makes perfect sense. The use of formulae is simply algebraic substitution. These letters/symbols represent variable quantities and are known as variables. For each variable in the formula, simply put in the relevant numerical value. When there is no operator between a number and a variable, or between two variables, multiplication is implied. It is important to do the various stages of the calculation in the correct order (BODMAS). If you are unsure of the order to work out a calculation refer back to Level 2, Learning Resource 8, Using a Calculator. Example 1 Area = Length Width A = L x W Find A when: L = 5 W = 3 Length = 5 m Width = 3 m A = 5 3 A = 15 Area = 15 m 2 West Nottinghamshire College 3
Examples Calculations Using Simple Formulae Example 2 Perimeter = (2 x Length) + (2 x Width) P = (2 x L) + ( 2 x W) Find P when: L = 5 W = 3 Length = 7 m Width = 5 m P = (2 7) + (2 5) P = 14 + 10 P = 24 Perimeter = 24 m Remember you must always work out the sum in brackets first (BODMAS). Example 3 Distance = Speed x Time D = ST Remember ST = S T Find D when: S = 10 T = 2 Speed = 10 m.p.h Time = 2 hours D =10 2 D = 20 Distance = 20 miles Example 4 n = 2 a + 4(b+c) Remember 4(b + c) = 4 (b + c) Find n when: a = 6 b = 2 c = 3 n = 2 6 + 4 (2 + 3) n = 2 6 + 4 x 5 n = 3 + 20 Brackets first followed by divide, then multiply. n = 23 West Nottinghamshire College 4
Exercise 1 Calculations Using Simple Formulae 1) A = L x W Find A when: L = 6 W = 8 2) V = LWH Find V when: L = 4 W = 1 H = 2 3) w = 3a - b 2 Find w when: a = 7 b = 4 4) q = 2(4y + z) Find q when: y = 6 z = 1 5) Calculate the following when: r = 5 s = 6 t = 4 a) r + st b) 3r (s + t) c) 5rs + 2rt 6) The perimeter of a garden is given by the formula P = (2 x L) + (2 x W). What is the perimeter when L = 15 m and W = 7 m? m 7) Speed can be calculated by the formula: speed = distance in miles s = d time in hours t What is the speed of a car when d = 300; t = 5? mph 8) The formula for working out the time (in hours) required to cook a joint of meat or a chicken is: Time = (cooking time per lb (mins) x weight in lb) + extra cooking time (mins) 60 t = cw + e 60 If c = 20; e = 20 and w = 5 when cooking a chicken, what is t (the total time)? hrs ) The conversion of Celsius ( C) to Fahrenheit ( F ) is given by the formula: F = C + 32 5 Use the formula to calculate the Fahrenheit equivalent of: a) 15 o C b) 100 o C c) 0 o C d) - 40 o C West Nottinghamshire College 5
Information Create Simple Formulae We often use formulae in everyday life. You may calculate how long a journey will take; how much several items will cost; how much money you have left to spend. In each of these calculations you are using simple algebraic expressions to form a formulae. You can then use the formulae; substitute different numbers depending on the situation. When you create an algebraic expression, remember that the multiplication sign is often left out. If letters or symbols are to be multiplied by numbers, the numbers always come first. Example 1 Create an algebraic expression for the following: Batteries cost Y pence each. How much will it cost for 7 batteries? 1 battery costs Y pence 7 batteries cost 7 x Y pence = 7Y pence. Remember any numbers always come before letters/symbols in a multiplication and the multiplication sign is left out. Example 2 Create an algebraic expression for the following: Batteries cost Y pence each. How much will it cost for Z batteries? 1 battery costs Y pence Z batteries cost Z x Y pence = ZY batteries. West Nottinghamshire College 6
Examples continued Create Simple Formulae Example 3 Create a formula to check how much money you will be able to save each month. Income = I Expenditure = E Balance = B Balance = Income Expenditure B = I E If your income is 1000 and your expenditure is 825, B = 1000-825 = 175 Example 4 Create a formula to work out your electricity bill. Standing Charge Unit Cost No of units used My bill S C u B My bill = (Unit Cost x No of units used) + Standing Charge B = Cu + S The multiplication sign (x) has been left out. If I use 640 units: Unit Cost 8.37 pence Standing Charge 7.35 B = 8.37 640 + 735 B = 5356.8 + 735 B = 601.8 pence B = 60.2 West Nottinghamshire College 7
Exercise 2 Create Simple Formulae 1) Write expressions for the following: a) 7 x f b) G x H + L c) Rajiv earns 7 per hour. How much would he earn in h hours? d) There are 14 pages in an article. How many pages will you have in total if you photocopy c copies of the article? pages e) If you use F grams of flour to make a cake, how many grams will you need to make C cakes? grams f) If you use F grams of flour to make 12 mince pies, how many grams will you need to make P mince pies? grams 2) a) A litre of petrol costs 3p. Form an equation to find the cost in pounds of any number of litres of petrol. No of litres used n Cost in C b) Use your equation to find the cost of 20 litres of petrol. 3) I want to hire a bouncy castle for the village fête. The cost per day is 35 and I shall have to make a deposit of 35. a) Form an equation to calculate the bill. b) Use your equation to find the cost of 3 days' hire. 4) My phone bill has a quarterly rental charge of 18.72. Each unit costs 3.62p. a) Form an equation to work out my bill. b) Use the equation to find the cost of 860 units. Remember: the quarterly charge and unit charge must be in the same units. West Nottinghamshire College 8
Information Common Mathematical Formulae in Use Throughout mathematics there are many formulae that we use on a regular basis. To calculate the area and volume of a variety of shapes it is necessary to find the relevant formula and substitute the symbols and letters with given measurements. Some common mathematical formulae: Area of a rectangle = length x width A = lw Volume = length x width x height V = lwh Area of a triangle = 1 1 base x height A = bh 2 2 Circumference of a circle = 2 x π x radius C = 2πr Area of a circle = π x (radius) 2 A = πr 2 Volume of a cylinder = π x (radius) 2 x h V = πr 2 h π is a special number and is always 3.14 (to 2 d.p.) Example Volume of cylinder = π r 2 h Find the volume when r = 2 cm; h = 4 cm. r V = π r 2 h Substitute the symbols with the values. V = 3.14 x (2 x 2) x 4 V = 3.14 x 4 x 4 V = 50.24 cm 3 h West Nottinghamshire College
Exercise 3 1) Area of a Trapezium = 2 1 (a+b) h Common Mathematical Formulae in Use a Find the area when: h a) a = 2 b = 6 h = 3 b) a = 3 b = 7 h = 2.5 c) a = 3 b = 6 h = 3.5 b Remember, you must always work out the sum in brackets first. 2) Circumference of a circle = 2π r Find the circumference when: a) r = 5 cm b) r = 10 cm c) r = 2.5 cm 3) Area of a circle = π r 2 Find the area when: a) r = 5 cm b) r = 10 cm c) r = 2.5 cm r π = 3.14 4) Volume of cylinder = π r 2 h Find the volume when: a) r = 5 cm h = 10 cm b) r = 3 cm h = 8 cm c) r = 3.2 cm h = 2.1 cm 5) Total surface area = 2π r 2 + 2π rh Find the total surface area when: a) r = 2 cm h = 4 cm b) r = 10 cm h = 5 cm c) r = 5.3 cm h = 4 cm r h West Nottinghamshire College 10