Formulae www mathsrevision com S 4 Credit Using

Formulae www. mathsrevision. com S 4 Credit Using Formulae Making Formulae Change the Subject of Formula Harder Subject of Formula Understanding Formulae www. mathsrevision. com

Starter Questions S 4 Credit www. mathsrevision. com 1. Calculate 3 + 2 x 4 www. mathsrevision. com

Formulae www. mathsrevision. com S 4 Credit Learning Intention 1. To explain how to evaluate formulae Success Criteria 1. Understand the term formulae. 2. Be able to substitute values into formulae and evaluate properly using BODMAS. www. mathsrevision. com

Formulae www. mathsrevision. com S 4 Credit A formula is the process calculating a quantity based on a known relationship e. g. Length, Area, Volume etc. . . . It is VERY important that we remember a keypoint when working with formulae. B O D M A S Brackets Other squares and square root etc. . Divide Multiplication Addition Subtraction

Formula for Parallelogram www. mathsrevision. com S 4 Credit Example 1 : Find the area of parallelogram. 3 cm 9 cm

Formulae for the Volume of a Sphere www. mathsrevision. com S 4 Credit r D = diameter D Q. If the above sphere has radius 10 cm. Calculate it’s volume.

Formulae for Volume of a Cone www. mathsrevision. com S 4 Credit h r Q. If the above cone has radius 15 cm and height of 10 cm. Calculate it’s volume.

Formulae www. mathsrevision. com S 4 Credit Now try MIA Ex 2. 1 & 2. 2 Ch 4 (page 80)

Starter www. mathsrevision. com S 4 Credit r D = 6 cm D

Making Formulae www. mathsrevision. com S 4 Credit Learning Intention 1. To explain how to construct a formula. Success Criteria 1. Understand the process of constructing a formula. 2. Apply knowledge to construct formulae. www. mathsrevision. com

Making Formulae S 4 Credit www. mathsrevision. com Try and make a formula for the money I have left, £M , after h hour. I started my shopping trip with £ 250. On average, each hour I spent £ 40. M = 250 - 40 h Calculate M for h = 3 M = 250 – 40 x 3 = 250 -120 = £ 130

Making Formulae S 4 Credit www. mathsrevision. com Try and make a formula for the cost C of tiling a kitchen floor. A tile fitter charges £ 20 per hour h. The tiles cost £ 15 per m 2 A. C = 20 h + 15 A Calculate C for h = 5 and A = 10 C = 20 x 5 + 15 x 10 = £ 250

Making Formulae www. mathsrevision. com S 4 Credit A internet café decides to change it’s table design to. 1 Table 2 Tables 3 Tables Task : Find a formula connecting the number of surfers and the number of tables.

Making Formulae www. mathsrevision. com S 4 Credit 1 Table Step 1 : Fill empty boxes 3 Tables 2 Tables Number of Tables 1 2 3 4 5 Number of Surfers 4 6 8 10 12 2 2 Step 2 : Find difference Same difference linear pattern What is the formula

Making Formulae www. mathsrevision. com S 4 Credit Number of Tables 1 2 3 4 5 Number of Surfers 4 6 8 10 12 2 2 Can you write down formula connecting the number of surfers and the number of tables. Find a number Step 3 : Part of the Formula S=2 x. T Step 4 : Correction factor “add on 2” S = 2 T + so formula works 2

Making Formulae www. mathsrevision. com S 4 Credit Now try MIA Ex 3. 1 Ch 4 (page 84)

Starter Questions www. mathsrevision. com S 4 Credit D = 6 cm h = 10 cm h r

Harder Formulae S 4 Credit www. mathsrevision. com Find a formula for the : 1 cm (i) Perimeter (ii) Area 2 x + 2 cm for the shaded shape below. C = πDbig - πDsmall C = π(Db – Ds) C = π(2 x + 2 – 2 x) C = 2π 2 x cm

Harder Formulae S 4 Credit www. mathsrevision. com Find a formula for the : 1 cm (i) Perimeter (ii) Area 2 x + 2 cm for the shaded shape below. A = πr 2 big - π r 2 small 2 x cm A = π(r 2 b – r 2 s) A = π((x + 1)2 – x 2) A = π(x 2 +2 x + 1 – x 2) = π(2 x + 1)

Harder Formulae S 4 Credit www. mathsrevision. com Find a formula for the : 1 cm (i) Perimeter (ii) Area 2 x + 2 cm for the shaded shape below. A = πr 2 big - π r 2 small 2 x cm A = π(r 2 b – r 2 s) A = π((x + 1)2 – x 2) A = π(x 2 +2 x + 1 – x 2) = π(2 x + 1)

Harder Formulae www. mathsrevision. com S 4 Credit Show that for the square with and equilateral triangle cut out has : 2 x (i) Perimeter = 10 x (ii) Area = (4 - √ 3)x 2 for the shaded shape below. √ 3 x P = 2 x + 2 x = 10 x

Harder Formulae www. mathsrevision. com S 4 Credit Show that for the square with an equilateral triangle cut out has : 2 x (i) Area = (4 - √ 3)x 2 for the shaded shape below. Area = Square - Triangle As = 2 x 2 x = 4 x 2 x AT = 0. 5 x 2 x x √ 3 x = √ 3 x 2 AT = 4 x 2 - √ 3 x 2 = (4 - √ 3)x 2 √ 3 x h

Harder Formulae www. mathsrevision. com S 4 Credit Now try MIA Ex 3. 2 Ch 4 (page 87)

Starter www. mathsrevision. com S 4 Credit 5 cm 2. 5 cm 3 cm 4 cm

Formulae www. mathsrevision. com S 4 Credit The Subject of a Formula Learning Intention 1. To explain how to change the subject of a formula using “The balancing Method” www. mathsrevision. com Success Criteria 1. Know “The balancing Method” for solving equations. 2. Apply knowledge to change subject of a formula.

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit The formula below is used to work out the circumference of a circle Since the formula works out C , then C is called the subject of the formula. www. mathsrevision. com

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit We can make D the subject of the formula by simple using “ The Balancing Method “ www. mathsrevision. com

Rearrange What into y = Goes In The Box ? S 4 Credit www. mathsrevision. com Make y the subject of the formulae using x+y=8 “the balancing method” -x + 2 y = 2 y=8 -x y 2 = x x = 4( y + 1 ) y = √x 2 x =√y y = 4 x 2 x = 3( y - k )

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit Now try MIA Ex 4. 1 Ch 4 (page 88)

Starter Questions www. mathsrevision. com S 4 Credit Make g the subject of each formula : www. mathsrevision. com

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit Learning Intention 1. To explain how to change the subject of a formula containing square and square root terms. www. mathsrevision. com Success Criteria 1. Know “ The balancing Method” for solving equations. 2. Apply knowledge to change subject of harder formulae including square and square root terms.

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit Example : The force of the air against a train is given by the formula below. Make the speed (S) the subject of the formula. www. mathsrevision. com

Changing the Subject of a Formula S 4 Credit www. mathsrevision. com Example : The thickness of a rope T cm to lift a weight W tonnes can be worked out by the formula below. Make W the subject of the formula. www. mathsrevision. com

Changing the Subject of a Formula S 4 Credit www. mathsrevision. com Example : The formula below is used to change degrees Celsius to Fahrenheit. Change the subject to C. www. mathsrevision. com

Changing the Subject of a Formula www. mathsrevision. com S 4 Credit Now try MIA Ex 4. 2 Ch 4 (page 91)

Starter Questions www. mathsrevision. com S 4 Credit Make w the subject of each formula : www. mathsrevision. com

Understanding Formulae www. mathsrevision. com S 4 Credit Learning Intention 1. To explain the effect on the subject by changing one or more of the values in the formula. www. mathsrevision. com Success Criteria 1. Understand the meaning of doubling and halving. 2. Apply knowledge so far to work out the effect on the subject by varying one or more values in the formula.

Understanding Formulae www. mathsrevision. com S 4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Circumference of circle is given by the formula : C = πD What happens to the Circumference if we double the diameter New D = 2 D The Circumference doubles C = π(2 D) = 2πD www. mathsrevision. com

Understanding Formulae www. mathsrevision. com S 4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Area of circle is given by the formula : A = πr 2 What happens to the Area if we double the radius r New r = 2 r The Area increasing by a factor of 4. C = π(2 r)2 = 4πr 2 www. mathsrevision. com

Understanding Formulae www. mathsrevision. com S 4 Credit In real-life we often want to see what effect changing the value of one of the variables has on the subject. The Area of circle is given by the formula : A = πr 2 What happens to the Area if we double the radius r New r = 2 r The Area increasing by a factor of 4. C = π(2 r)2 = 4πr 2 www. mathsrevision. com

Understanding Formulae www. mathsrevision. com S 4 Credit The thickness of a rope T cm to lift a weight W tonnes can be worked out by the formula below. If we increase W by a factor of 100. What effect does this have on the thickness of the rope T. The thickness of the rope T increasing by a factor of 10. New W = 100 W www. mathsrevision. com

Understanding Formulae www. mathsrevision. com S 4 Credit Now try MIA Ex 5. 1 Ch 4 (page 94)