GCSE Mathematics (Foundation) AQA
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113 topics in 9 modules
☑️ Foundation 29 topics
- Types of Number
- BODMAS
- Multiplying by 10, 100, 1000
- Multiplying/ Dividing Whole Numbers
- Multiplying/ Dividing with Decimals
- Negative Numbers
- Prime Numbers
- Factors, Multiples, Prime Factors
- HCF and LCM
- Fractions without a Calculator
- Fraction Problems
- Decimals, Fractions, Percentages
- Rounding Numbers
- Estimating
- Rounding Errors
- Powers
- Roots
- Multiplying
- Dividing
- Multiplying Double Brackets
- Factorising
- Solving Equations
- Expressions, Formulas, Functions
- Rearranging Formulas
- Sequences
- Inequalities
- Quadratic Equations
- Simultaneous Equations
- Proof
☑️ Indices 12 topics
- Understanding of Power
- Multiplication Laws of Indices
- Division Laws of Indices
- Zero Power Rule
- Negative Power Rule
- Fractional Indices
- Power of a Power
- Multiplying and Dividing Indices with the Same Base
- Standard Form and Indices
- Application of Indices in Real Life Context
- Evaluating Expressions with Indices
- Simplifying Expressions with Indices
☑️ Algebra 1 topic
- Simplifying
☑️ Graphs 8 topics
- Coordinates and Midpoints
- Straight-Line Graphs
- Straight-Line Graphs: Gradients
- y= mx + c
- Quadratic Graphs
- Solving Equations with graphs
- Distance-Time Graphs
- Real-life Graphs
☑️ Ratio, Proportion and Rates of Change 9 topics
- Ratios
- Direct Proportion problems
- Inverse Proportion problems
- Percentages
- Compound Growth and Decay
- Unit Conversions
- Area and Volume Conversions
- Time Intervals
- Speed, Density and Pressure
☑️ Shapes and Area 10 topics
- Properties of 2D Shapes
- Congruent Shapes
- Similar Shapes
- The Four Transformations
- Perimeter and Area
- Perimeter and Area- Circles
- 3D Shapes
- 3D Shapes- Surface area
- 3D Shapes- Volume
- Projections
☑️ Angles and Geometry 13 topics
- Angle Basics
- Angle Rules
- Parallel Lines
- Geometry Problems
- Angles in Polygons
- Triangle Construction
- Loci and Construction
- Bearings
- Maps
- Scale Drawings
- Pythagoras' Theorem
- Trigonometry- Cos, Sin, Tan
- Vectors
☑️ Probability and Statistics 16 topics
- Probability
- AND/ OR Rules
- Tree Diagrams
- Sets
- Venn Diagrams
- Sampling
- Bias
- Collecting Data
- Median, Mean, Mode, Range
- Pie Charts
- Bar Graphs
- Scatter Graphs
- Frequency Tables
- Grouped Frequency Tables
- Interpreting Data
- Comparing Data Sets
☑️ Trigonometry 15 topics
- Introduction to Trigonometry
- Understanding Right-Angled Triangles
- The Sine Function (sin)
- The Cosine Function (cos)
- The Tangent Function (tan)
- SOHCAHTOA: Using Trigonometric Ratios
- Finding Missing Sides in Right-Angled Triangles
- Finding Missing Angles in Right-Angled Triangles
- Solving Problems Involving Right-Angled Triangles
- Real-Life Applications of Trigonometry
- Trigonometric Ratios in Different Sized Triangles
- Angle of Elevation and Depression
- Using Trigonometry with Bearings
- Simple Trigonometric Equations
- Understanding and Using Inverse Trigonometric Functions
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GCSE Mathematics (Foundation) AQA Revision Content
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GCSE Mathematics (Foundation) AQA - Foundation - Types of Number Content Preview
Foundation
Types of Number
Natural (Counting) Numbers
- Simply termed as the counting numbers, these start from 1 and go up to infinity (1, 2, 3, 4, 5, …). They exclude zero and negative numbers.
Whole Numbers
- This is a set that begins from 0, followed by all the positive integers (0, 1, 2, 3, 4, …). They are simply the natural numbers with the addition of zero.
Integers
- These include all positive and negative whole numbers, as well as zero (…, -3, -2, -1, 0, 1, 2, 3, …).
Rational Numbers
- These are any numbers that can be written as a fraction or ratio of two integers. Remember, this includes whole numbers and fractions, as well as decimals that terminate or recur.
Irrational Numbers
- These are numbers that cannot be written as a fraction or ratio of two integers. This includes decimals that never terminate or recur. Examples of these are √2 or π.
Real Numbers
- These are all the numbers on the number line including rational and irrational numbers. They also include all the integers, fractions and decimal numbers, except for imaginary numbers.
Prime Numbers
- These are numbers that have only two distinct positive divisors: 1 and the number itself. For example, the number 2 is the first prime number as it can only be divided evenly by 1 and 2.
Composite Numbers
- These are numbers that have more than two distinct positive divisors. For example, the number 4 is a composite number because it can be divided evenly by 1, 2 and 4.
Even Numbers
- These are any integer divisible by 2. If the last digit ends with 0, 2, 4, 6, or 8 it's an even number.
Odd Numbers
- These are any integer not divisible by 2. If the last digit ends with 1, 3, 5, 7, or 9, it's an odd number.
Remember, understanding these types of numbers is the first step in getting to grips with the fundamental concepts of mathematics.
Question: State whether √50 is rational or irrational.
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