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

4. 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

5. 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

6. 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

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

8. 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

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

10. 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

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

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

13. 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)

14. 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) + ( )
50 = (19) + (31)

15. 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)

16. 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.

17. 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

18. 6x
A : Identity
B : Equation
C : Expression
D : Formula

19. 4x = 18
A : Identity
B : Equation
C : Expression
D : Formula

20. 6x + 12 = 3(2x + 4) A : Identity B : Equation C : Expression
D : Formula

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

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

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

24. 9b - l0
A : Identity
B : Equation
C : Expression
D : Formula

25. 2x² + 3x – 7 = 0
A : Identity
B : Equation
C : Expression
D : Formula

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

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

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

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

30. 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

31. Write down the value of 52

32. Which is bigger 32 or 23?

37. Write down the value of 33

38. Write down the reciprocal of 4.