Formulae Change the Subject of Formula Harder Subject of Formula Understanding Formulae Making Formulae Using Formulae S4 Credit

Starter Questions 1.Does x 4 = 11 or 20 S4 Credit

Learning Intention Success Criteria 1.To explain how to evaluate formulae 1.Understand the term formulae. Formulae 2.Be able to substitute values into formulae and evaluate properly using BODMAS. S4 Credit

Formulae 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 S4 Credit

Formula for Parallelogram Example 1 : Find the area of parallelogram. 9cm 3cm S4 Credit

Formulae for the Volume of a Sphere S4 Credit r D D = diameter Q.If the above sphere has radius 10cm. Calculate it’s volume.

Q.If the above cone has radius 15cm and height of 10 cm.Calculate it’s volume. Formulae for Volume of a Cone r h S4 Credit

Now try MIA Ex 2.1 & 2.2 Ch4 (page 80) Formulae S4 Credit

Starter D = 6 cm r D S4 Credit

Learning Intention Success Criteria 1.To explain how to construct a formula. 1.Understand the process of constructing a formula. Making Formulae 2.Apply knowledge to construct formulae. S4 Credit

Try and make a formula for the money I have left, £M, after h hour. S4 Credit Making Formulae I started my shopping trip with £250. On average, each hour I spent £40. M =250-40h Calculate M for h = 3 M = 250 – 40 x 3 = = £130

Try and make a formula for the cost C of tiling a kitchen floor. S4 Credit Making Formulae A tile fitter charges £20 per hour h. The tiles cost £15 per m 2 A. C =20h+15A Calculate C for h = 5 and A = 10 C = 20 x x 10 =£250

A internet café decides to change it’s table design to. 1 Table 3 Tables 2 Tables Task :Find a formula connecting the number of surfers and the number of tables. S4 Credit Making Formulae

Number of Tables Number of Surfers Step 1 : Fill empty boxes 2222 Same difference linear pattern What is the formula 1 Table 3 Tables 2 Tables Step 2 : Find difference S4 Credit Making Formulae

S4 Credit 24513Number of Tables Number of Surfers 2222 Can you write down formula connecting the number of surfers and the number of tables. S = 2T + 2 S = 2 x T Part of the Formula Correction factor “add on 2” Find a number so formula works Step 3 : Step 4 : Making Formulae

Now try MIA Ex 3.1 Ch4 (page 84) Making Formulae S4 Credit

Starter Questions D = 6 cm h = 10 cm r h S4 Credit

Find a formula for the : (i)Perimeter (ii)Area for the shaded shape below. S4 Credit Harder Formulae 2 x cm 1 cm C = π(D b – D s ) C = π(2 x + 2 – 2 x ) C = 2π 2 x + 2cm C = πD big - πD small

Find a formula for the : (i)Perimeter (ii)Area for the shaded shape below. S4 Credit Harder Formulae 2 x cm 1 cm A = π(r 2 b – r 2 s ) A = π(( x + 1) 2 – x 2 ) 2 x + 2cm A = πr 2 big - π r 2 small A = π( x 2 +2 x + 1 – x 2 ) = π(2 x + 1)

Find a formula for the : (i)Perimeter (ii)Area for the shaded shape below. S4 Credit Harder Formulae 2 x cm 1 cm A = π(r 2 b – r 2 s ) A = π(( x + 1) 2 – x 2 ) 2 x + 2cm A = πr 2 big - π r 2 small A = π( x 2 +2 x + 1 – x 2 ) = π(2 x + 1)

Show that for the square with and equilateral triangle cut out has : (i)Perimeter = 10 x (ii)Area = (4 - √3) x 2 for the shaded shape below. S4 Credit Harder Formulae √3 x P = 2 x 2x2x + 2 x + 2 x + 2 x + 2 x = 10 x P =

A T = 0.5 x 2 x x √3 x Show that for the square with an equilateral triangle cut out has : (i)Area = (4 - √3) x 2 for the shaded shape below. S4 Credit Harder Formulae √3 x A s = 2 x x 2 x = 2x2x Area = Square - Triangle 4 x 2 √3 x 2 h A T = 4 x 2 - √3 x 2 =(4 - √3) x 2 =

Now try MIA Ex 3.2 Ch4 (page 87) Harder Formulae S4 Credit

Starter 5 cm 2.5 cm 3 cm 4 cm 3 cm S4 Credit

Learning Intention Success Criteria 1.To explain how to change the subject of a formula using “The balancing Method” 1.Know “The balancing Method” for solving equations. Formulae 2.Apply knowledge to change subject of a formula. The Subject of a Formula S4 Credit

Changing the Subject of a Formula 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. S4 Credit

Changing the Subject of a Formula We can make D the subject of the formula by simple using “ The Balancing Method “ S4 Credit

What Goes In The Box ? Make y the subject of the formulae using “the balancing method” x + y = 8 y 2 = x -x + 2y = 2 x = 4( y + 1 ) y = 8 - x y = √x Rearrange into y = 2x =√yx = 3( y - k ) y = 4x 2 S4 Credit

Now try MIA Ex 4.1 Ch4 (page 88) S4 Credit Changing the Subject of a Formula

Starter Questions Make g the subject of each formula : S4 Credit Nothing new ! simply use the “balancing method”

Learning Intention Success Criteria 1.To explain how to change the subject of a formula containing square and square root terms. 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 S4 Credit

Changing the Subject of a Formula Example : The force of the air against a train is given by the formula below. Make the speed (S) the subject of the formula. S4 Credit

Changing the Subject of a Formula 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. S4 Credit

Changing the Subject of a Formula Example : The formula below is used to change degrees Celsius to Fahrenheit. Change the subject to C. S4 Credit

Now try MIA Ex 4.2 Ch4 (page 91) S4 Credit Changing the Subject of a Formula

Starter Questions Make w the subject of each formula : S4 Credit Nothing new ! simply use the “balancing method”

Learning Intention Success Criteria 1.To explain the effect on the subject by changing one or more of the values in the formula. 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 S4 Credit

S4 Credit Understanding Formulae The Circumference of circle is given by the formula : C = πD What happens to the Circumference if we double the diameter C = π(2D) New D = 2D The Circumference doubles In real-life we often want to see what effect changing the value of one of the variables has on the subject. = 2πD

In real-life we often want to see what effect changing the value of one of the variables has on the subject. S4 Credit Understanding Formulae The Area of circle is given by the formula : A = πr 2 What happens to the Area if we double the radius r C = π(2r) 2 New r = 2r The Area increasing by a factor of 4. = 4πr 2

In real-life we often want to see what effect changing the value of one of the variables has on the subject. S4 Credit Understanding Formulae The Area of circle is given by the formula : A = πr 2 What happens to the Area if we double the radius r C = π(2r) 2 New r = 2r The Area increasing by a factor of 4. = 4πr 2

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. S4 Credit Understanding Formulae New W = 100W The thickness of the rope T increasing by a factor of 10.

Now try MIA Ex 5.1 Ch4 (page 94) S4 Credit Understanding Formulae