  # Maths GCSE Online Course

Our SMART Diagnostic Tool maximises revision time by focusing strictly on lessons that need more work.

★ No long term contracts
★ Unlimited support from UK-qualified teachers
★ Over 290 lessons and tutorials
★ Live Parent Report Dashboard
★ Only £45 per month, cancel any time
★ First month FREE!

#### The Smart Diagnostic Tool

The SDT is an advanced dynamic diagnostic tool for analysing student assessments and creating individualised study plans, based specifically around each student’s current learning requirements for their GCSE maths revision.

Parents and students have direct and unlimited access to our online tutors. Simply call or send a question through our ‘ask a tutor’ email system and one of our qualified teachers will send you a reply.

#### Study anywhere and anytime

Access your personalised online GCSE from any device that has an internet connection. Students work at their own pace and set their own schedule. Parents can monitors progress through easy-to-read reports.

#### Fully aligned to major exam boards

GCSE content is tailored to each individual exam board. Choose your personalised course that is aligned to the OCR, AQA, EdExcel or WJEC exam Boards, ensuring consistency for your child.

## Live Parent Report Dashboard

The GCSE Maths course gives parents powerful tools to help their children with their GCSE Maths revision.

We don’t just support your kids’ GCSE maths revision, you will be regularly informed about their progress, to help you keep them motivated. ### Numbers

• Multiplying 4-digit numbers by 3-digit numbers
• Multiplying 4-digit numbers by 4-digit number
• Multiplying decimals by 10, 100 and 1000
• Repeated subtraction with divisors greater than 20 with remainders as fractions
• Repeated subtraction with divisors less than 35 with some remainders
• Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders
• Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders
• Using divide, multiply and subtraction in the bring down method
• Dividing decimals by 10, 100 and 1000
• Directed numbers: addition and subtraction
• Directed numbers: multiplication and division
• Using Order of Operation procedures (BIDMAS) with Fractions
• Multiples and Factors of Whole Numbers
• Highest common factor
• Factors by grouping
• Rounding decimals
• Decimals to three decimal places
• Adding decimals with a different number of decimal places
• Subtracting decimals with a different number of places
• Multiplying decimals by whole numbers
• Multiplication of decimals by decimals to two decimal places
• Dividing decimal fractions by whole numbers
• Dividing numbers by a decimal fraction
• Adding and subtracting fractions with different denominators
• Multiplying fractions by whole numbers
• Fractions of whole numbers
• Multiplying fractions
• Multiplying mixed numbers (mixed numerals)
• Finding reciprocals of fractions and mixed numbers (mixed numerals)
• Dividing fractions
• Dividing mixed numbers (mixed numerals)
• Adding indices when multiplying terms with the same base
• Subtracting indices when multiplying terms with the same base
• Multiplying indices when raising a power to a power
• Multiplying indices when raising to more than one term
• Terms raised to the power of zero
• Negative Indices
• Fractional indices
• Complex fractions as indices
• Calculating Percentages and Fractions of Quantities
• Introduction to percentages, including relating common fractions to percentages
• Changing fractions and decimals to percentages using tenths and hundredths
• Changing percentages to fractions and decimals
• One quantity as a percentage of another
• Compound interest
• Significant figures
• Average speed
• Scientific notation with larger numbers
• Scientific notation with small numbers
• Changing scientific notation to numerals
• Number sets and their members
• Properties of real numbers using addition and multiplication
• Introducing surds
• Some rules for the operations with surds
• Simplifying surds
• Creating entire surds
• Adding and subtracting like surds
• Expanding surds
• Conjugate binomials with surds
• Rationalising the denominator
• Rationalising binomial denominators

### Measurement

• Compare and convert formal units of measurement
• Estimate, measure and compare the capacity of containers
• Introducing the rules for finding the area of a rectangle and a parallelogram
• Finding the area of a triangle and other composite shapes
• Area of a trapezium
• Area of a rhombus
• Area of a circle
• Area of regular polygons and composite figures
• Surface area of a cube/rectangular prism
• Surface area of a triangular/trapezoidal prism
• Surface area of a cylinder and sphere
• Surface area of pyramids
• Surface area of cones
• Surface area of composite solids
• Introducing the formula for volume
• Using the cubic metre to measure volume
• Solving Problems about Volume - Part 1
• Solving Problems about Volume - Part 2
• Finding the volume of prisms
• Volume of a cylinder and sphere
• Volume of pyramids and cones
• Composite solids
• Problems with length
• Problems with mass
• Problems with area
• Problems with volume/capacity

### Geometry

• Using the prefix to determine polygons
• Recognise and name prisms according to spatial properties
• Recognise and name pyramids according to spatial properties
• Recognise nets for prisms, pyramids, cubes and cones
• Viewing 3-D shapes
• Constructing models
• Complementary and supplementary angles
• Vertically opposite angles
• Angles at a Point
• Parallel Lines
• Additional questions involving parallel lines
• Angle sum of a triangle
• Exterior angle theorem
• To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra
• More difficult exercises involving parallel lines
• Further difficult exercises involving formal reasoning
• Angles of regular polygons
• Complementary angle results
• Bearings - the compass
• Theorem - Equal arcs on circles of equal radii subtend equal angles at the centre
• Theorem - Equal angles at the centre of a circle on equal arcs
• Theorem - The perpendicular from the centre of a circle to a chord bisects the chord
• Theorem - The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord
• Theorem - Equal chords in equal circles are equidistant from the centres
• Theorem - Chords in a circle which are equidistant from the centre are equal
• Theorem - The angle at the centre of a circle is double the angle at the circumference standing on the same arc
• Theorem - Angles in the same segment of a circle are equal
• Theorem - The angle of a semi-circle is a right-angle
• Theorem - The opposite angles of a cyclic quadrilateral are supplementary
• Theorem - The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle
• Theorem - The tangent to a circle is perpendicular to the radius drawn to it at the point of contact
• Theorem - Tangents to a circle from an external point are equal
• Theorem - The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment
• Theorem - The products of the intercepts of two intersecting chords are equal
• Theorem - The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof]
• Theorem - If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic
• Theorem - If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic
• Theorem - When circles touch, the line of the centres passes through the point of contact
• Theorem - Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points
• Geometric constructions
• To identify collinear points, coplanar lines and points in 2 and 3 dimensions
• Angle bisector construction and its properties (Stage 2)
• Circumcenter and incenter (Stage 2)
• Orthocentre and centroids (Stage 2)
• Constructions and loci - single condition
• Constructions and loci - multiple conditions
• Similar triangles
• Using similar triangles to calculate lengths
• Special triangles
• Use grids to enlarge/reduce 2D shapes
• Special transformations - reflections, rotations and enlargements
• Transformations - reflections
• Geometry transformations without matrices: reflection (Stage 2)
• Geometry transformations without matrices: translation (Stage 2)
• Geometry transformations without matrices: rotation (Stage 2)
• Geometry transformations without matrices: dilation or enlargement (Stage 2)
• The definition and concept of combined transformations resulting in an equivalent single transformation
• Recognise and name triangles
• Midsegments of Triangles
• Congruent triangles, Test 1 and 2
• Congruent triangles, Test 3 and 4
• Proofs and congruent triangles.
• Examples involving overlapping triangles
• Find the hypotenuse
• Pythagorean triples
• Find the hypotenuse Part 2
• Calculating a shorter length of a right-angled triangle
• Proofs of Pythagoras theorem
• Graphing the trigonometric ratios - I Sine curve
• Graphing the trigonometric ratios - II Cosine curve
• Graphing the trigonometric ratios - III Tangent curve
• Graphing the trigonometric ratios - IV Reciprocal ratios
• Trigonometric ratios
• Using the calculator
• Using the trigonometric ratios to find unknown length. [Case 1 Sine]
• Using the trigonometric ratios to find unknown length. [Case 2 Cosine]
• Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]
• Unknown in the denominator. [Case 4]
• Angles of elevation and depression
• Trigonometric ratios in practical situations
• Using the calculator to find an angle given a trigonometric ratio
• Using the trigonometric ratios to find an angle in a right-angled triangle
• Trigonometric ratios of 30°, 45° & 60° - exact ratios
• The cosine rule to find an unknown side. [Case 1 SAS]
• The cosine rule to find an unknown angle. [Case 2 SSS]
• The sine rule to find an unknown side. Case 1.
• The sine rule to find an unknown angle. Case 2.
• The area formula
• Reciprocal ratios
• Angles of any magnitude
• Trigonometric ratios of 0°, 90°, 180°, 270° and 360°
• Distance formula
• Mid-point formula
• The straight line
• Lines through the origin
• General form of a line and the x and y Intercepts

### Sequences

• General sequences
• Finding Tn given Sn

### Algebra

• Algebraic expressions
• Simplifying Algebraic expressions: combining addition and subtraction
• Simplifying algebraic expressions: multiplication
• Simplifying algebraic expressions: division
• Expanding algebraic expressions: multiplication
• Expanding algebraic expressions: negative multiplier
• Expanding and simplifying algebraic expressions
• Simplifying algebraic fractions using the index laws
• Algebraic fractions resulting in negative indices
• Cancelling binomial factors in algebraic fractions
• Products in simplification of algebraic expressions
• Algebraic Expressions - Larger expansions
• Simplifying algebraic fractions
• Simplifying absolute values
• Quadratic polynomials of the form y = ax² + bx + c
• Graphing perfect squares: y=(a-x) squared
• Solve by graphing
• Graphing cubic curves
• Solving equations containing addition and subtraction
• Solving equations containing multiplication and division
• Solving two step equations
• Solving equations containing binomial expressions
• Equations involving grouping symbols
• Equations involving fractions
• Solving for the variable
• Simultaneous equations
• Simultaneous equations- Elimination method
• Simultaneous equations- Elimination method part 2
• Applications of simultaneous equations
• Expansions leading to the difference of two squares
• Common factor and the difference of two squares
• Factorising quadratic trinomials [monic] - Case 2
• Factorising quadratic trinomials [monic] - Case 3
• Factorising quadratic trinomials [monic] - Case 4
• Factorisation of non-monic quadratic trinomials
• Factorisation of non-monic quadratic trinomials - moon method
• Substitution into algebraic expressions
• Equations resulting from substitution into formulae
• Changing the subject of the formula
• Simplifying easy algebraic fractions
• Factorisation of algebraic fractions including binomials
• Solving Inequalities.
• Solving and graphing inequalities
• Inequalities on the number plane
• Difference of two squares
• Quadratic trinomials [monic] - Case 1
• Problem solving with quadratic equations
• Solving simultaneous quadratic equations graphically
• Vectors

### Statistics

• The range
• The mode
• The mean
• The median
• Calculating the median from a frequency distribution
• Calculating mean, mode and median from grouped data
• Range as a measure of dispersion
• Measures of spread: the interquartile range
• Pie and bar graphs
• Scatter Diagrams
• Stem and Leaf Plots along with Box and Whisker Plots
• Cumulative frequency
• Frequency histograms and polygons
• Line graphs

### Probability

• Frequency distribution table
• Relative frequency
• Probability of Simple Events
• Rolling a pair of dice
• Experimental probability
• Tree diagrams - not depending on previous outcomes
• Tree diagrams - depending on previous outcomes