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!