GCSE Mathematics (Higher) OCR
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99 topics in 8 modules
☑️ Number 10 topics
- BODMAS and types of number
- Multiples, prime factors and factors
- HCF and LCM
- Fractions
- Fractions, percentages and decimals
- Fractions and recurring decimals
- Rounding numbers
- Estimating
- Bounds
- Standard form
☑️ Surds 12 topics
- Understanding surds: definition and examples
- Simplifying surds
- Rationalising the denominator
- Adding and subtracting surds
- Multiplying and dividing surds
- Surd form to decimal conversion
- Solving equations involving surds
- Expanding brackets with surds
- Conjugate of a surd
- Real life applications of surds
- Surds in quadratic equations
- Simplifying expressions with surds
☑️ Algebra 16 topics
- Powers and roots
- Multiplying out brackets
- Factorising
- Manipulating surds
- Solving equations
- Rearranging formulas
- Factorising quadratics
- The Quadratic Formula
- Completing the square
- Algebraic fractions
- Sequences
- Inequalities
- Graphical inequalities
- Iterative methods
- Simultaneous Equations
- Proof
☑️ Graphs 13 topics
- Straight Lines and Gradients
- y = mx + c
- Drawing straight line graphs
- Coordinates and ratios
- Parallel and Perpendicular Lines
- Quadratic Graphs
- Harder Graphs
- Solving Equations using graphs
- Graph Transformations
- Real-Life Graphs
- Distance-Time Graphs
- Velocity-Time graphs
- Gradients of Real-Life Graphs
☑️ Ratio, Proportions and Rates of Change 6 topics
- Ratios
- Direct and Inverse Proportion
- Percentages
- Compound Growth and Decay
- Unit Conversions
- Speed, Pressure and Density
☑️ Geometry and Measures 17 topics
- Geometry
- Parallel Lines
- Geometry Problems
- Polygons
- Triangles and Quadrilaterals
- Circle Geometry
- Congruent Shapes
- Similar Shapes
- The Four Transformations
- Areas- Triangles and Quadrilaterals
- Areas- Circles
- 3D shapes - Surface Area
- 3D shapes- Volume
- Enlargements and Projections
- Triangle Constructions
- Loci and Constructions
- Bearings
☑️ Pythagoras and Trigonometry 7 topics
- Pythagoras' Theorem
- Trigonometry- Sin, Cos and Tan
- Trigonometry- Common Values
- The Sine and Cosine Rules
- 3D Pythagoras
- 3D Trigonometry
- Vectors
☑️ Probability and Statisitcs 18 topics
- Probability basics
- Counting Outcomes
- Probability Experiments
- The AND/OR Rules
- Tree Diagrams
- Conditional Probability
- Sets and Venn Diagrams
- Sampling and Bias
- Collecting Data
- Mean, Median, Mode and Range
- Frequency Tables- Finding Averages
- Grouped Frequency Tables
- Box Plots
- Cumulative Frequency
- Histograms and Frequency Density
- Time Series
- Scatter Graphs
- Comparing Data Sets
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GCSE Mathematics (Higher) OCR Revision Content
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GCSE Mathematics (Higher) OCR - Number - BODMAS and types of number Content Preview
Number
BODMAS and types of number
BODMAS Rule
- BODMAS stands for Brackets, Orders (i.e., Powers and Square Roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- This rule dictates the order in which operations should be carried out to solve an expression.
- Brackets always come first in this hierarchy. Compute everything inside brackets first.
- Orders or indices come next: any calculations involving powers or square roots are done at this stage.
- Division and Multiplication come next and are equal in the hierarchy. These operations are performed from left to right.
- Finally, Addition and Subtraction are also equal in hierarchy. These operations are performed from left to right.
Types of Number
Prime Numbers
- A prime number is any number that has only two distinct natural number divisors: 1 and itself.
- Examples are 2, 3, 5, 7, 11, 13. Note, 1 is not a prime number.
Composite Numbers
- A composite number is any number that is greater than one and is not a prime number.
- In other words, a composite number has more than two distinct natural number divisors.
- Examples include 4, 6, 8, 9, 10.
Rational Numbers
- A rational number can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
- Examples are -7, 0, 1/2, -4/9.
Irrational Numbers
- An irrational number cannot be expressed as a fraction or quotient of two integers. Their decimal expansion is non-repeating and non-terminating.
- Notable examples include the square root of 2 and π.
Real Numbers
- Real numbers include all the counting numbers, fractions, terminating and recurring decimals, and irrational numbers.
- In other words, if a number is either rational or irrational, it is a real number.
Square Numbers and Cube Numbers
- A square number is the result when a number has been multiplied by itself, while a cube number is a number multiplied by itself twice.
- For instance, 4 (2x2) and 9 (3x3) are examples of square numbers, while 8 (2x2x2) and 27 (3x3x3) are examples of cube numbers
Question: Given the expression 2 + 3 x (2^2 - 1), using the BODMAS rule, what would be the calculated result?
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