GCSE ExamSolutions Maths All exams boards
Full course content, a smart revision plan and instant past paper feedback for GCSE ExamSolutions Maths All exams boards.
Start revising this course →Content Overview
155 topics in 6 modules
☑️ Number 12 topics
- Standard Form
- Prime Factorisation
- How to find the HCF and LCM
- Using 2 or 3 Venn diagrams
- HCF and LCM exam questions
- Significant Figures
- Significant Figures Challenge
- Calculating upper and lower bounds
- Bounds with decimal places and significant figures
- Calculating the maximum and minimum
- How to use bounds to solve real world problems
- The Aeroplane problem
☑️ Algebra 79 topics
- Expanding a single bracket
- Expanding two or more brackets
- Squaring brackets
- Terms in expressions and equations
- Linear Equations with a positive x term
- Linear Equations with a negative x term
- Linear Equations with a two x terms
- Linear Equations with brackets
- Linear Equations that are fractions
- Solve by elimination
- Same x terms
- Same y terms but opposite signs
- Same y terms but both signs are negative
- Same y terms but both signs are positive
- Neither x term nor y term are the same
- Substitution methods (Quadratic SImultaneous)
- Introduction to indices (exponents)
- Multiplication rules for indices
- Division rule for indices
- Negative indices
- Fractions raised to a negative index
- Rational (fractional) indices
- Simplifying terms with negative powers
- Expressing terms in the form axn
- Equations in which the power has to be found
- Summary of indices
- Surds- Introduction & simplifying
- Addition and subtraction of surds
- Multiplying surds
- Dividing Surds
- Rationalising surds
- Exam Questions
- f(x) notation
- Composite functions
- The inverse of a function
- Introduction to factorising
- Highest common factor (HCF)
- Factorising by grouping
- Factorising quadratic expressions
- Mixed Exercise – Factorising
- Completing the square
- Applications of completing the square
- Exam Questions – Completing the square
- Solve by factorising
- Solve by completing the square
- Solve by the quadratic formula
- Exam Questions – Solved by the quadratic formula
- Line segment
- Parallel lines
- Perpendicular lines
- Equation of a straight line: y=mx+c
- Equation of a line given the gradient and point
- Distance between two points
- Mid-point of a line segment
- Equation of a parallel line
- Equation of a perpendicular bisector
- Intersection of two straight lines
- Intersection of a straight line and a parabola
- Intersection of a straight line and a hyperbola
- Sketching quadratic graphs
- Rules for reversing the inequality sign
- Solving a linear type
- Quadratic inequalities
- Basic graphs used in transformations
- Translations of graphs
- Reflections of graphs
- Equation of a circle
- Finding the centre and radius
- Simplifying algebraic fractions
- Exam Questions – Simplifying a rational expression
- Addition and subtraction of algebraic fractions
- Exam Questions – Addition & subtraction
- Multiplication of algebraic fractions
- Further simplifying of ‘stacked fractions’
- Definition and finding the nth term
- Recurrence relationships
- Quadratic sequences
- Exam Questions – Recurrence relationships
- Iteration
☑️ Geometry 35 topics
- Angles in Parallel lines
- Interior angles
- Exterior angles
- Similar shapes
- Exam question (HARD)
- Scale factor of length, surface area and volume
- Scale factor length, surface area and volume (4 worded problems)
- Pythagoras’ Theorem
- Area and Arc length
- Circle theorems - Part 1
- Circle theorems - Part 2
- Circle theorems - Part 3
- Circle theorems - Exam questions
- Volumes of Prisms
- Trigonometry – Right-Angled Triangles - Introduction to trigonometry
- Trigonometry – Right-Angled Triangles - Finding the length of a side
- Trigonometry – Right-Angled Triangles - Finding an angle
- Trigonometric ratios for 30°, 45° and 60°
- Trig ratios for multiples of 30°, 45° and 60°
- Area of a triangle – Given two sides and an included angle
- Sine rule
- Cosine rule
- Bearings – Applications of the sine and cosine rules
- Trigonometric graphs
- Translations of trig graphs
- Reflections of trig graphs
- What is a vector and a scalar quantity?
- Vector notation 2d
- Position vectors 2d
- Equal and negative vectors
- Multiplying a vector by a scalar 2d
- Addition and subtraction of vectors 2d
- Magnitude of a 2 dimensional vector
- How to solve vector geometry problems(Hard)
- Exam Question (Hard)
☑️ Ratios 12 topics
- Ratios
- Writing ratios in the form 1:N
- Ratio sharing amounts
- What is a percentage?
- Finding a percentage of a quantity
- Converting a fraction to a percentage
- Calculating a percentage change
- Increasing / decreasing a quantity by a percentage
- Multipliers
- Simple interest
- Compound interest
- Reverse percentages
☑️ Probability 8 topics
- Sample space diagrams
- Tree Diagrams
- Probability Tree Diagrams for Independent Events
- And Rule (multiplication) / Or Rule (addition for mutually exclusive events)
- Probability Tree Diagrams for Dependent Events
- Venn Diagrams - Algebra of sets
- Venn Diagrams - Venn diagrams
- Venn Diagrams - Notation and defining regions
☑️ Statistics 9 topics
- Mean for discrete data
- Calculating the mean from a frequency table
- Exam Questions – Discrete data / mean
- Cumulative frequency curves
- Box Plots
- Drawing histograms and calculating frequency density
- Class width and height of intervals
- Finding the mean in a histogram (exam question)
- Estimating the Median of a histogram
GCSE ExamSolutions Maths All exams boards Revision Content
Take a look at the written content available for this course. Practice-question availability may vary.
GCSE ExamSolutions Maths All exams boards - Number - Standard Form Content Preview
Number
Standard Form
Understanding Standard Form
- Standard form, also known as scientific notation or exponential notation, is a way of writing or displaying large or small numbers compactly.
- It is represented as a × 10^n, where 1 ≤ a <10 and 'n' is an integer.
- The value 'a' is called the mantissa and 'n' is called the exponent or power.
- Positive 'n' means the decimal point moves to the right, indicating a large number.
- Negative 'n' means the decimal point moves to the left, indicating a small number.
Converting to Standard Form
- If the number is already in decimal form, place the decimal point such that the number becomes between 1 and 10. This number becomes the mantissa.
- Count the number of places you moved the decimal point. This will be your exponent.
- If you moved the decimal to the left, the exponent is positive. If to the right, the exponent is negative.
Converting from Standard Form
- Look at the exponent. If it's positive, move the decimal point in the mantissa to the right. If it's negative, move the point to the left.
- Make sure to add zeros as placeholders if needed.
Calculations in Standard Form
- When adding or subtracting numbers in standard form, they should have the same exponent. If not, convert them so they do before performing the operation.
- To multiply or divide numbers in standard form, multiply or divide the mantissas and add or subtract the exponents, respectively.
Application of Standard Form
- Standard form is often used to represent very large quantities such as distances in space or very small sizes such as the size of atoms.
- It's also used to simplify calculations and make them more manageable.
Common Mistakes to Avoid
- Forgetting that the decimal point in the mantissa should be after the first digit.
- Miscounting the number of places moved when finding the exponent.
- When adding or subtracting, forgetting to make sure the exponents are the same.
- Not considering the direction of the decimal point movement when determining the sign of the exponent.
Question: Convert the number 0.0000432 into standard form.
Unlock instant, personalised feedback
Sign up to Adapt to practise the exam questions available for this course with instant, personalised feedback.
Start revising this course →Try Adapt now
Add this exact course and build your personalised revision plan.