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Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

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 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

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 6 | Decimals

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:

  1. Round all the numbers in the problem to 1 s.f.
  2. Next, simply work out the answer
  • Show all your working
  • Remember no calculators!

Estimating with square roots

Example 1:

Estimate √83

  1. The square numbers either side of 83 are 81 and 100
  2. The square root of 81 = 9

100  =10

  1. 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

  1. The square numbers either side of 12 are 9 and 16
  2. The square root of 9 = 3

16 = 4

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

 

Steps:

  1. 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

  1. Find the square roots of the square numbers in step 1
  2. 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!

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