1. If you are given a quantity of one thing in a given ratio, set up the boxes.
Apples and oranges in the ratio 4:3.
Abraham has 20 apples. How many pieces of fruit in total?
20 Apples so 1 “box” = 20 ÷ 4
There must be 15 oranges, so = 35 in total.
Conversion questions:
Remember to find the exchange rate by working out what the scale factor is
7 ÷ 5 = 1.4
So in this case
from £ to € I have to x 1.4
from € to £ I have to ÷ 1.4
Comparing prices = compare 1 item or 1ml/1g of each thing is the easiest.
6 cans of coke = £ cans of coke = £9.95
1can = can =
1 can – 51.6p 1 can = 49.8p
20 cans is cheaper.
Converting speeds:
200m in 15 seconds
x4 x4
800m in 60seconds
x60 [800m in 1min] x60
48000m in 1 hour
[48km in 1hour]
Conversions in square brackets, proportion with arrows
So speed is 48km/hour 5 € 1 3 5 7 20 ÷6 ÷6
÷20
÷20

2. A farmer has sheep and cows in the ratio 4:3.
The farmer has 160 sheep. How many animals does he have altogether?
Work out the exchange
rate and use it to
complete the table.
iPad costs £250 in UK.
iPad costs $320 in USA.
Which is cheaper? By how much?
Shampoo comes in two sizes. A 200ml bottle costs £2.19 or a 300ml bottle costs £2.99. Which is cheaper?
A runner sprints 100m in 12 seconds. What is their speed in km per hour? $ 1 5 6 9 20
Recap: Standard form
1.8 x 104 =
1500 = __ x 10__
Recap: BIDMAS
3a2 when a = -6
2a3 when a = -4

3. Recursive Sequences Tuesday, 27 November 2018
Understand the parts of a recursive formula
Generate a sequence of numbers from a recursive formula
Use a recursive formula to describe a sequence

4. T(n+1) = T(n) + 6 , T(1) = 7

5. T(n+1) = T(n) + 6, T(1) = 7
T(n+1) = T(n) -4 ,
T(1) = 0.5
T(n+1) = 3T(n) +2 ,
T(1) = 2

6. c)Will the number of lily pads overtake the population of frogs?
If so, when?

7. Describe the following sequence using a recursive formula 5, 12, 19, 26

8. c)Will the number of lily pads overtake the population of frogs?
If so, when?

9. How would you describe a recursive sequence to yourself 1 hour ago?
Dave says the sequence 6, 14, 22, 30 is given by the recursive formula T(n+1) = T(n + 6), T(1) = 8 What has he done wrong?
How would you describe a recursive sequence to yourself 1 hour ago?

11. Show that 𝑥 3 −6𝑥+3=0 can be written in the form 𝑥 = 3 6𝑥 −3
Use the iteration formula 𝑥 𝑛+1 = 3 6 𝑥 𝑛 −3 to find an approximate solution to 2 decimal places. Start with 𝑥 0 =2.
𝑥 𝑛+1 = 3 6 (𝑥 𝑛 ) −3
𝑥 5 =2.1427…
𝑥 1 = 3 6(2) −3 =2.080
𝑥 6 =2.1440…
𝑥 2 = 3 6(2.080…) −3 =2.116
𝑥 7 =2.1446…
𝑥 3 = 3 6(𝑎𝑛𝑠) −3 = …
𝑥 8 =2.1449…
𝑥 9 =2.1450…
𝑥 4 =2.1396…
𝐶𝑜𝑛𝑡𝑖𝑛𝑢𝑖𝑛𝑔 𝑡𝑜 𝑝𝑟𝑒𝑠𝑠 𝑒𝑞𝑢𝑎𝑙𝑠 𝑙𝑒𝑎𝑑𝑠 𝑡𝑜 which rounds to 2.15 to 2dp

12. Worksheet
Concentrate on Part 1b, 2b and 3b (Substitution) 15minutes Extension – Iterate until 4 decimals remain constant Q4) Xn+1 = 9+ 4𝑥 n start x0 = 2 Q5) Xn+1 = 26 −4𝑥 n start x0 = 1

13. Q1b)
X1 =2.6684…
X2= …
X3 = 2.793…
X4 =2.793
Answer = 2.79 to 2 dp
Q2b)
X1 =6.333…
X2= 6.223…
X3 = 6.225…
X4 =6.225
Answer = 6.2 to 2 dp
Q3b)
X1 = 2.213
X2= 1.908
X3 =
X4 =
X5 = 1.818
X6 = 1.817
Answer = 1.82 to 2 dp
Q4b)
X1 = 4.123…
X2= 5.049…
X3 = 5.40
X4 =
X5 = 5.57
X6 = 5.596
X7 = 5.60
X8 = 5.60
Answer = 5.60 to 2 dp
Q5b)
X1 = 5
X2= 3
X3 =
X8 =
X11 = 3.747
X12 = 3.745
X13= 3.744
Answer = 3.74 to 2 dp