Advanced Indices

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Advanced Powers and Roots

Powers and roots can be expressed (written) in more than one way.

Negative powers

Negative powers are equivalent (the same as) to 1 ÷ the number.

Half powers

Half powers are the same as a square root.

Third powers

Third powers are the same as cube roots.

Fraction powers

Deal with one part of the fraction at a time.

Calculating Fractional Powers

Fractions can be powers.

$Step 1 with a positive fractional power$

Step 1 with a positive fractional power

The denominator of the fractional power becomes the root of the number.
The numerator of the fractional power becomes the power of the number.

$Step 2 with a positive fractional power$

Step 2 with a positive fractional power

Calculate the root of the number first.

$Step 3 with a positive fractional power$

Step 3 with a positive fractional power

Calculate the power of the answer to the previous step.

$Step 1 with a negative fractional power$

Step 1 with a negative fractional power

Go through the same process as with a positive fractional power.
But, it is now equivalent (the same as) to 1 ÷ the number.

$Step 2 with a negative fractional power$

Step 2 with a negative fractional power

Calculate the answer to the positive fractional power.
Insert the answer as the denominator to a fraction. The numerator is 1.
The answer can either remain as a fraction or you can convert it into a decimal.

Numbers

1.1

Integers

1.1.1Integers 1.1.2Ordering Numbers 1.1.3The Four Rules of Operations 1.1.4Hierarchy of Operations 1.1.5Definitions & Terms 1.1.6HCF & LCM 1.1.7Standard Form 1.1.8Standard Form 2 1.1.9Prime Numbers 1.1.10End of Topic Test - Standard Form

1.2

Fractions

1.2.1Fractions 1.2.2Using Fractions 1.2.3Conversion 1.2.4Reciprocals

1.3

Decimals

1.3.1Decimals 1.3.2Decimals 2 1.3.3Exam-Style Questions - Recurring Decimals 1.3.4Comparing & Converting Decimals 1.3.5End of Topic Test - Fractions & Decimals

1.4

Powers & Roots

1.4.1Square Numbers 1.4.2Index Notation 1.4.3Exam-Style Questions - Index Notation 1.4.4Advanced Indices 1.4.5Surds 1.4.6End of Topic Test - Powers & Roots

1.5

Set Language & Notation

1.5.1Sets

1.6

Percentages

1.6.1Percentages 1.6.2Percentage Change 1.6.3Percentages in Finance 1.6.4Compound Interest

1.7

Ratio & Proportion

1.7.1Manipulating Ratios 1.7.2Proportion

1.8

Degree of Accuracy

1.8.1Rounding & Significant Figures 1.8.2Estimation 1.8.3Upper & Lower Bounds 1.8.4Limits of Accuracy 1.8.5Limits of Accuracy 2 1.8.6End of Topic Test - Rounding & Estimation

Equations, Formulae & Identities

2.1

Algebraic Manipulation

2.1.1Algebra Basics 2.1.2Power Rules & Collecting Terms 2.1.3Expanding Brackets 2.1.4Expanding Brackets 2 2.1.5Factorising Quadratics 2.1.6Algebraic Fractions 2.1.7Proofs 2.1.8End of Topic Test - Algebra & Proofs 2.1.9Exam-Style Questions - Algebraic Proof

2.2

Expressions & Formulae

2.2.1Rearranging Formulae 2.2.2Simple Formulae 2.2.3End of Topic Test - Algebra Manipulation & Formula

2.3

Linear Equations

2.3.1Solving Linear Equations 2.3.2Simultaneous Linear Equations

2.4

Quadratic Equations

2.4.1Solving Quadratics 2.4.2Solving Quadratics 2 2.4.3End of Topic Test - Solving Equations 2.4.4Simulateous Quadratic Equations 2.4.5Exam-Style Questions - Simultaneous Equations 2.4.6Graphs of Simultaneous Equations 2.4.7End of Topic Test - Simultaneous Equations

2.5

Proportion

2.5.1Graphs & Proportion

2.6

Inequalities

2.6.1Solving Inequalities 2.6.2Graphs of Inequalities 2.6.3Exam-Style Questions - Inequalities 2.6.4End of Topic Test - Inequalities

Sequences, Functions & Graphs

3.1

Sequences

3.1.1Sequence Rules 3.1.2Finding Terms 3.1.3Exam-Style Questions - Sequences 3.1.4End of Topic Test - Sequences

3.2

Functions

3.2.1Functions 3.2.2Composite & Inverse 3.2.3End of Topic Test - Functions

3.3

Graphs

3.3.1Plotting Graphs 3.3.2Straight Line Graphs 3.3.3Properties of Graphs 3.3.4Quadratic Graphs 3.3.5Practical Graphs 3.3.6Graphs of Polynomials 3.3.7End of Topic Test Graphs

3.4

Common Graphs

3.4.1Graphs of Common Functions 3.4.2Transformations of Graphs 3.4.3End of Topic Test - Transformations and Graph

3.5

Calculus

3.5.1Derivatives of Functions 3.5.2Maxima & Minima

Geometry

4.1

Angles, Lines & Triangles

4.1.1Angles & Lines 4.1.2Angle Rules 4.1.3Angles in Triangles 4.1.4Exam-Style Questions - Angles

4.2

Polygons

4.2.1Polygons 4.2.2Quadrilaterals 4.2.3Congruence 4.2.4Scale Factor 4.2.5Exam-Style Questions - Enlargements 4.2.6End of Topic Test - Geometry

4.3

Symmetry

4.3.1Symmetry 4.3.2Exam-Style Questions - Reflection

4.4

Measures

4.4.1Measurements 4.4.2Time 4.4.3Bearings 4.4.4Speed

4.5

Circle Properties

4.5.1Properties of a Circle 4.5.2Circle Theorems 4.5.3Circle Theorems 2 4.5.4Circle Theorems 3 4.5.5Exam-Style Questions - Circle Theorems

4.6

Trigonometry & Pythagoras’ theorem

4.6.1Pythagoras' Theorem 4.6.2Trigonometry 4.6.3Sine & Cosine for Obtuse Angles 4.6.4Triangle Formulae 4.6.5Exam-Style Questions - Trigonometry & Area

4.7

Mensuration of 2D Shapes

4.7.1Standard Units 4.7.2Perimeter of 2D Shapes 4.7.3Area of 2D Shapes 4.7.4Area & Circumference of Circle 4.7.5End of Topic Test - Trigonometry & Shapes

4.8

3D Shapes & Volume

4.8.13D Shapes 4.8.2Surface Area 4.8.3Volume 4.8.4Exam-Style Questions - Volume

Vectors & Transformation Geometry

5.1

Vectors

5.1.1Vectors 5.1.2Vectors 2 5.1.3Exam-Style Questions - Vectors

5.2

Transformation Geometry

5.2.1Transformations 5.2.2Rotations 5.2.3Translations & Reflections 5.2.4Enlargements 5.2.5Effects of Transformations

Statistics & Probability

6.1

Statistical Measures

6.1.1Basic Statistics 6.1.2Frequency Table

6.2

Graphical Representation of Data

6.2.1Pictograms, Bar Charts & Pie Charts 6.2.2Histograms 6.2.3Cumulative Frequency 6.2.4Cumulative Frequency 2 6.2.5Exam-Style Questions - Cumulative Frequency 6.2.6End of Topic - Datasets

6.3

Probability

6.3.1Probability 6.3.2Theoretical Probability 6.3.3Experimental Probability 6.3.4Venn Diagrams 6.3.5Sample Space Diagrams 6.3.6Tree Diagrams 6.3.7Independent Events 6.3.8Conditional Probability 6.3.9End of Topic Test - Probability 6.3.10Exam-Style Questions - Probability

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