**Table of Contents**

** Unit 1 | Algebra**

Page 1 | Expressions and Formulae

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

** Unit 2 |Graphs**

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

** Unit 3 |Geometry and Measure **

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

**Unit 4 | Numbers**

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

** Unit 5 | Statistics and Probability **

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

**Unit 4 | Calculus **

*Estimating*

L.O – To be able estimate the answer to complex sums including those involving square roots

In order to estimate the answer to a problem, round all the numbers in the problem to **1 s.f. **This leaves ‘easier’ numbers to deal with which you can use to work out the answer.

**Example 1:**

Estimate the answer for

Rounding all the numbers to 1 s.f. gives

Now, work out the answer

**Example 2:**

Estimate the value of 65234 x 0.73523

- Rounding all the numbers to 1 s.f. gives 70000 x 0.7
- Now work out the answer

70000 x 0.7 = 49000

**Example 3:**

Estimate the value of

Rounding all the numbers to 1 s.f. gives

Now work out the answer

**Steps:**

- Round all the numbers in the problem to 1 s.f.
- Next, simply work out the answer

- Show all your working
- Remember no calculators!

__Estimating with square roots__

**Example 1:**

Estimate √83

- The square numbers either side of 83 are 81 and 100
- The square root of 81 = 9

100 =10

- 83 is closer to 81, therefore √83 must be closer to 9 than 10

Since 83 is quite close to 81, I have chosen a value quite close to 9 – 9.2

**Example 2:**

Estimate √12

- The square numbers either side of 12 are 9 and 16
- The square root of 9 = 3

16 = 4

- Since 12 is closer to 9, but not too close, 9.4 seems sensible

**Steps:**

- Find the 2 square numbers either side of the number in question

Writing out the square numbers may help you

**1, 4, 9, 16, 25, 36, 47, 64, 81, 100 etc**

- Find the square roots of the square numbers in step 1
- Pick a sensible number in between these square roots

There won’t just be one right answer! Markschemes will allow for a range of answers as long as they are sensible!