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
Powers and Roots
L.O – To learn and be able to apply the rules regarding powers and roots
Powers
Powers are the mini numbers on top of ‘normal’ numbers. They are a very useful shorthand e.g. 34 is just a shorter way of writing 3x3x3x3 – the power tells us how many times to multiply 3 by itself.
1. When multiplying, add the powers
Example 1:
42 + 46 = 42+6 = 48
303 + 307 = 303+7 = 3010
2. When dividing, subtract the powers
Example 1:
65 62 = 65-2 = 63
158 – 155 = 158-5 = 153
3. When raising one power to another, multiply the powers
Example 1:
(72)4 = 72×4 = 78
(25)3 = 25×3 = 215
4. Anything to the power 1 is just itself
Example 1:
X1 = X
51 = 5
121 = 12
5. Anything to the power 0 is always 1
Example 1:
X0 = 1
30 = 1
290 = 1
6. 1 to any power is always 1
Example 1:
12 = 1
124 = 1
10 = 1
7. With fractions, apply power to top and bottom
Example 1:
The numerator(1) and the denominator(3) of the fractions have been squared
Negative powers
If a number/fraction is raised to a negative power;
- Turn the number/fraction upside down
- Then make the power positive
Example 1:
Fractional powers
The power means square root – √
The power means cubed root – 3√
The power means fourth root – 4√ etc.
Example 1:
251/2 = √25 = 5
91/3 = 3√9 = 9
811/4 = 4√81 = 3
Two stage fractional powers
Some powers can be fractions like etc
These fractions represent a root and and a power
- The trick is to split the fraction into its root and power
- Once you have split the fraction, apply the root first, then the power
Example 1:
94/3
– 94/3 = (9)1/3 x 4 = (91/3)4 = 34 = 81
1253/2
– 1253/2 = (125)1/2 x 3 = (1251/2)3 = 253 = 15625
Square roots
The square root of a number can be positive or negative. There is the possibility of a negative answer as when you square a negative number, the answer is positive.
Example 1:
√ 4 = +2 or -2
√64 = +8 or -8
Questions: