This week Algebra recap: New Algebra: Problem Solving Rearranging Using brackets General syntax New Algebra: FOIL Factorising quadratics Problem Solving Assessment revision

Answer 1 monkey can eat 4.5 bananas in 1 minute. 13 monkeys can eat 58.5 bananas in 1 minute. How long would it take 3 monkeys to eat 81 bananas? 1 monkey can eat 4.5 bananas in 1 minute 3 monkeys can eat 13.5 bananas in 1 minute - 81 ÷ 13.5 = 6 times as many bananas – so it will take 6 minutes Monkeys to bananas is direct proportion – the more monkeys there are, the more bananas they eat Bananas to time is direct proportion – the more bananas a monkey eats, the more time it takes Monkeys to time is inverse proportion – the more monkeys there are, the less time it will take to eat 4.5 bananas

5x -7y + 2x + 7y = 7x + 14y 3 x a x b = 9ab 3x + 5x = 15x 3 x f = f3 a x a = 2a 5y + 4y – 3y = 12y 3x – 2y – 7x + 3y = y – 4x 3x + 5y – 2x + y = 5x + 6y

Solving equations 1. 2x = 18 3. 3x + 2 = 23 2. 2x – 1 = 7 5. x + 5 = 7 3 4. t + t + t = 4.5 6. 2(x – 4) = 12 7. 3(3x + 1) ≥ 21 8. 3x + 7 = x + 12 9. 2x - 4 < 5x - 16

Inequalities < > ≤ ≥ Can be solved as an equation Can be shown on a number line:

Rearranging a formula How would you find x when 5x + 3 = 23? How would you find x when 5x + y = 23? How would you find x when 5x + y = z? 3g – 4 = 20 3g – j = 20 3g – j = r

Make 𝒙 the subject of the equation 𝒚=𝟑𝒙+𝟐 𝑥= 𝑦 3 −2 𝑥= 𝑦−2 3

v = u + at Rearranging a formula Make u the subject of the formula Make a the subject of the formula Make t the subject of the formula

You know how to expand a single bracket… Expand: 2(3x + 5)

Expand brackets (FOIL) (x + 6)(x + 3) x2 + 9x + 18 (x – 6)(x – 3) x2 - 9x + 18 (x + 6)(x – 3) x2 + 3x - 18

Factorising quadratic equations Factorise x2 + 6x + 8 Which two numbers add up to 6 and multiply to 8? (x + 2)(x + 4) Factorise x2 + 6x – 16 Which two numbers add up to 6 and multiply to -16? (x – 2)(x + 8) Factorise x2 - 7x + 12 Which two numbers add up to -7 and multiply to 12? (x - 3)(x - 4)

Mary and John have £50 altogether. Mary has £12 more than John Mary and John have £50 altogether. Mary has £12 more than John. Write an equation for the money they have altogether and using the equation, work out how much money they have each. t = (t – e / 2) + (j + e) 50 = (50 – 12 / 2) + (19 + 12) 50 = (19) + (31)

The perimeter of a rectangle is 56 cm The perimeter of a rectangle is 56 cm. One side is 4cm longer than the other. Write an equation to show this information and find the length of the sides. p = (p – 8 / 4 + 4) + (p – 8 / 4 + 4) + (p – 8 / 4) + (p – 8 / 4) 56 = (56 – 8 / 4 + 4) + (56 – 8 / 4 + 4) + (p – 8 / 4) + (p – 8 / 4) 56 = (16) + (16) + (12) + (12)

Problem Solving Three numbers have a total of 30 Two of the numbers are equal. The third is half the size of the other two. Find the numbers.

Problem Solving Three whole numbers have a total of 100 Two of the numbers have a difference of 7 Two of the numbers are the same Find the numbers  

6x + 12 A : Identity B : Equation C : Expression D : Formula

4x + 2 = 18 A : Identity B : Equation C : Expression D : Formula

6x + 12 = 3(2x + 4) A : Identity B : Equation C : Expression D : Formula

v = u + at A : Identity B : Equation C : Expression D : Formula

a² + 2a = a ( a + 2 ) A : Identity B : Equation C : Expression D : Formula

A = π r² A : Identity B : Equation C : Expression D : Formula

9b - l0 A : Identity B : Equation C : Expression D : Formula

2x² + 3x – 7 = 0 A : Identity B : Equation C : Expression D : Formula

An expression is … A : 8x + 2 = 12 B : 8x + 2 C : 8x + 2 = C D : 8x + 2 = 2(4x + 1)

A formula is … A : 8x + 2 = 12 B : 8x + 2 C : 8x + 2 = C D : 8x + 2 = 2(4x + 1)

An identity is … A : 8x + 2 = 12 B : 8x + 2 C : 8x + 2 = C D : 8x + 2 = 2(4x + 1)

An equation is … A : 8x + 2 = 12 B : 8x + 2 C : 8x + 2 = C D : 8x + 2 = 2(4x + 1)

Indices What does the word “reciprocal” mean? The reciprocal of a number is 1 divided by the number, so: The reciprocal of 2 is ½ The reciprocal of 10 is 1/10 0 does not have a reciprocal When we multiply a number by its reciprocal, we always get 1: 3 x 1/3 = 1 Reciprocals of fractions are just upside down: Reciprocal of 2/5 is 5/2

Write down the value of 52

Which is bigger 32 or 23?

 

 

 

 

Write down the value of 33

Write down the reciprocal of 4.