Mathematics

Starter block (Until October break)

• Long multiplication
• Time
• Integers
• Order of operations
• Algebraic substitution
• Simplifying algebraic expressions (adding, subtracting and multiplying)
• Powers

Fractions and Percentages

• Equivalence of any fraction
• Simplify any fraction
• Find a fraction of a whole number
• Convert a mixed number  improper fraction
• Change percentages  fractions
• Calculate percentages of numbers using the fractional equivalent
• Calculate various percentages of quantities
• Switch between fractions, decimals and percentages e.g. == 0∙15 = 15%
• Add and subtract simple fractions, where one denominator is a multiple of the other, simplifying the answer e.g. +=  +  =
• Express one quantity as a percentage of another e.g. 25 out of 40 in a test
• Convert fractions  recurring decimals
• Solve problems involving fractions, decimal fractions and percentages in a real life context e.g. two for the price of one, three for the price of two or 30% discount, time and a half

Angles

• Name angles using three letter notation e.g. ABC
• Calculate angles whose sum is 90º, 180º, 360º
• Calculate the complement and supplement of an angle
• Use the fact that the sum of the angles of a triangle is 180º to find missing angles (including isosceles and equilateral triangles)
• Identify vertically opposite angles
• Identify corresponding and alternate angles
• Identify arms and vertex of an angle using letter notation e.g. arms AB and BC and vertex B
• Identify parallel and perpendicular lines
• Prove that lines are parallel using angle properties
• Calculate interior angles of regular polygons with four or more sides

Decimals

• Read, write, record, order and sequence decimal notation to tenths, hundredths and thousandths
• Understand the equivalence between tenths, hundredths, thousandths and decimal notation
• Add and subtract decimals with one or more decimal places
• Multiply and divide decimals by whole numbers
• Use rules to multiply and divide decimals by 10, 100 and 1000
• Round decimal numbers to one or more decimal places
• Multiply and divide any whole number or decimal by 10, 100, 1000
• Multiply and divide any whole number or decimal by a multiple of 10, 100, 1000
• Add, subtract, multiply and divide numbers with up to three decimal places, including times in seconds, money, length, weight, volume
• Apply knowledge of decimal place to length, weight and volume, e.g. 0∙001km = 1m,
  0∙275kg = 275g, 0∙35l = 350ml
• Round decimals to estimate answers to calculations

Coordinates and Symmetry

• Draw and label a Cartesian (coordinate) diagram accurately, including arrows in positive direction, x and y axes labelled and scale on grid lines at regular intervals
• Read and plot points in four quadrants of a Cartesian diagram  (+4^th level)
• Identify transformation by reflection and translation of a point or shape on a grid   (+4^th level)
• Identify all lines of symmetry in a 2D shape
• Create symmetrical patterns and pictures

Unit Conversion and Scale

• Change centimetres to millimetres, centimetres to metres, etc
• Recognise the impact that premature rounding can have on a calculation   (+4^th level)
• Measure lengths to the nearest millimetre
• Understand and use scale in ratio form
• Calculate true lengths from scaled plans e.g. 1cm to 10cm, 1cm to 20m, 1:200
• Produce an accurate drawing from a sketch
• Identify true measurements using scales such as 1cm to 10cm or 1cm to 8m
• Use the fact that 1 litre of water weighs 1kg and 1 tonne = 1000kg when solving problems in a real life context

Area & Perimeter

• Properties of triangles and quadrilaterals
• Calculate the perimeter of composite shapes composed of squares, rectangles and triangles
• Use formulae A =lb to calculate the area of rectangles and squares
• Find the area of right-angled triangles from the area of the surrounding rectangle
• Use the formula A =bh to calculate the area of right-angled triangles
• Find the area of composite shapes composed of squares, rectangles and right-angled triangles

Volume

• Use the formula V = lbh to find the volume of a cube and a cuboid in cubic centimetres (cm³)  
• Calculate the volume of composite 3D objects
• Use the fact that 1 litre = 1000ml = 1000cm³ and that 1ml = 1cm³ when solving problems in a real life context
• Use the fact that 1 litre of water weighs 1kg and 1 tonne = 1000kg when solving problems in a real life context.

Equations 1

• Understand the concept of an equation as a balance
• Solve equations including those with negative and fractional answers
• Solve equations with unknown terms on either side of the equation
• Check answer by substitution

Patterns & Sequences

• Continue a given sequence
• Find a rule for a sequence and express in algebraic notation  (+4^th level)
• Generate terms of a sequence using a given formula or rule  (+4^th level)
• Working both ways with the formula  (+4^th level)
• Find a specific term in a sequence using the rule e.g. 100th term (+4^th level)

Ratio

• Understand the concept and notation of ratio
• Express quantities as a ratio e.g. boys : girls 12 : 18
• Simplify ratio e.g. 12 : 18 = 2 : 3
• Calculate a quantity given the ratio
• Understand the relationship between simple proportion and ratio
• Understand how to share an amount in a given ratio
• Convert ratio to same units before simplifying e.g. 10p : £2 = 10 : 200 = 1 : 20
• Solve problems in context using ratios

Multiples, Factors and Primes

• Calculate the factors and multiples of a number
• Calculate the highest common factor and lowest common multiple
• Identify prime numbers
• Calculate the prime factors of a number and write numbers as a product of prime factors in index form e.g. 30 = 2 x 3 x 5
• Identify square and cubic numbers
• Use concepts of multiples and factors to solve problems
• Record square and cubic numbers using index notation e.g. 5 x 5 x 5 = 5³

Expanding Brackets

• Expand and simplify a single bracket  (4^th level)
• Expand and simplify a single bracket with a negative coefficient  (4^th level)
• Work with more complex expressions involving more than one single bracket   (4^th level)

Factorisation

• Factorise an expression using the HCF  (4^th level)

Significant Figures

• Understand the concept of a significant figure  (4^th level)
• Understand the uses of rounding to a significant figure
• Demonstrate knowledge of rounding to a set number of significant figures   (4^th level)

 

Bearings

• Understand and calculate 3-figure bearings
• Use angle properties to calculate bearings including calculating B from A, given A from B
• Calculate true lengths from scale drawing including 3-figure bearings
• Produce accurate scale drawings from a sketch including 3-figure bearings
• Investigate navigation in the world

Fraction Operations

• Add and subtract fractions mentally
• Add and subtract fractions and mixed numbers with different denominators without a calculator
• Add and subtract fractions in context
• Add and subtract mixed numbers, simplifying the answer
• Multiply and divide fractions mentally, with or without a calculator as appropriate
• Add, subtract, multiply and divide fractions in context  (+4^th level)
• Add and subtract fractions and mixed numbers with a calculator

Equations 2

• Construct algebraic equations from oral and written information  (4^th level)
• Solve equations involving brackets

Inequations

• Solve inequations  (+4^th level)
• Construct and solve inequations that include reverse of sign and brackets   (4^th level)

Statistics 1

• Display & Retrieve information in tables, pie charts, bar and line graphs
• Use the most appropriate graphical representations for data  (4^th level)
• Calculate the mean, median, mode (modal) and range from non-grouped data   (4^th level)
• Calculate the median and range from an ordered stem and leaf diagram  (4^th level)
• Draw & interpret ordered stem-and-leaf diagrams including back-to-back  (4^th level)
• Use a spreadsheet to organise & display data & produce graphs
• Knowledge of qualitative/quantitative & continuous/discrete data
• Knowledge of bias in samples and be able to conduct surveys which avoid bias
• Make predictions based on data sourced
• Work with others to plan & conduct a suitable survey/investigation

Probability

• Describe & calculate a probability  (+4^th level)
• Write a probability as a fraction/decimal/percentage
• Understand the probabilities 0 (impossible) and 1 (certain)
• Be able to list possible outcomes for simple random events
• Understand the probability of an event not happening is ‘1 minus the probability of it occurring’
• Explain why the consequences of the event should be considered when making choices.

Standard Form

• Convert Numbers  Scientific Notation  (4^th level)
• Perform scientific notation calculations with calculator

Enlargement and Reduction

• Enlarge & reduce shapes using scale factor
• Enlarge & reduce a shape given the coordinates of its vertices
• Find missing lengths given similar shapes and a scale factor
• Calculate a scale factor from similar shapes
• Use the linear scale factor to calculate the length of missing sides
• Find the image of a point or a shape on a coordinate diagram
• Recognise similar shapes

Powers & Roots

• Understand the link between a power and root (4^th level)
• Evaluate square and cube roots (4^th level)
• Introduce the concept of rational and irrational numbers

Percentages

• Express one number as a percentage of another, including increase and decrease
• Calculate the initial value by reversing the change
• Perform calculations involving appreciation and depreciation  (4^th level)
• Calculate compound interest  +4^th level)

Pythagoras

• Use Pythagoras’ Theorem to calculate side lengths  (4^th level)
• Perform calculations within real life context
• Understand and apply the Converse of Pythagoras’ Theorem
• Understand how to calculate the distance between 2 points

Statistics 2

• Select and justify the most appropriate average to represent a data set  (4^th level)
• Select the most appropriate statistical diagram to represent a given data set   (4^th Level)
• Determine the five figure summary from an ordered set of data
• Draw a box plot
• Find the range and interquartile, semi-interquartile range
• Construct a cumulative frequency table
• Calculate the mean, median, mode and range from a frequency table
• Construct a histogram
• Group and order data (discrete or continuous) using equal class intervals and construct grouped frequency tables
• Interpret and compare statistical data from box plots, back to back stem and leaf diagrams and histograms
• Describe the correlation in a scattergraph in qualitative terms e.g. strong positive correlation

Circle

• Recognise and describe radius, diameter and circumference and connect that circumference of a circle is about 3.14 times the length of the diameter  (4^th level)
• Understand how to calculate the circumference of a circle  (4^th level)
• Understand how to calculate the area of a circle  (4^th level)
• Find the radius and/or diameter given the circumference  (4^th level)
• Find the radius and/or diameter given the area  (4^th level)
• Understand how to calculate the arc length of a sector
• Understand how to calculate the area of a sector
• Calculate area and perimeter of composite shapes including circles, semi-circles and quarter circles

Algebraic Operations

• Expanding Brackets
  • (ax + b)(cx + d)
  • (ax + b)(cx² + dx + e)
• Factorising
  • Common factor
  • Difference of two squares
  • Trinomials with unitary and non-unitary coefficients of x²
• Write quadratic expressions with unitary coefficient of x² in completed square form

Linear Relationships

• Find the equation of a straight line using y – b = m(x – a)
• Find the coordinates of points where straight lines intersect both axes

Statistics

• Calculate the standard deviation of a data sample
• Median and semi-interquartile revision
• Compare the consistency of data referencing standard deviation and SIQR
• Scatter graphs and equation of line of best fit

Changing the Subject of a Formula

• Change the subject of a linear equation
• Change the subject of an equation involving a square or square root term

Simultaneous Equations

• Construct linear equations from text involving two variables
• Solve simultaneous equations graphically
• Solve simultaneous equations algebraically

Triangle Trigonometry

• Use the sine rule to find missing sides and angles
• Use the cosine rule to find missing sides and angles
• Find the area of a triangle using A_tri = ½ a b sin C
• Solve trigonometry problems in context including problems involving bearings

Surds

• Simplify surds by identifying squared term factors
• Perform calculations involving surds (all four operations)
• Rationalise the denominator

Indices

• Multiply and divide terms of the form ax^b where a and b are rational numbers
• Understand and apply the rule that (a^m)ⁿ = a^mn
• Express terms of the form ax^-b in the form
• Understand that  and apply this knowledge to calculations

Algebraic Fractions

• Reduce an algebraic fraction to its simplest form
• Apply one of the four operations to algebraic fractions

Vectors

• Adding or subtracting two-dimensional vectors using directed line segments
• Determining coordinates of a point from a diagram representing a 3D object
• Adding or subtracting two-dimensional or three-dimensional vectors using components
• Express a journey as a difference of position vectors i.e. = b – a
• Magnitude of a vector (link to Pythagoras)

Function Notation

• Understand and use functional notation in the following ways
  • Evaluate f(2) for various functions
  • Solve f(a) = b where a and b are rational numbers

Shape Properties

• Use shape properties to find interior and exterior angles in polygons

Equations and Inequations with Fractions

• Solve equations and inequations with fractions

Quadratic Equations

• Factorise to solve quadratic equations
• Apply quadratic formula to solve quadratic equations
• Understand relationship between discriminant and roots
• Apply knowledge graphically

Quadratic Relationships

• Recognise and determine the equation of a quadratic function from its graph
  • y = kx²
  • y = (x + p)² + q
• Sketch a quadratic function
  • y = (x – m)(x – n)
  • y = (x + p)² + q
• Identify features of a quadratic function
  • Nature
  • Turning point
  • Equation of axis of symmetry

Trigonometric Graphs

• Know how to sketch basic graphs
  • y = sin x
  • y = cos x
  • y = tan x
• Understand features of trigonometric graphs including
  • Amplitude
  • Vertical translation
  • Multiple angles
  • Phase angles

Trigonometric equations

• Work with trigonometric relationships in degrees
  • Evaluate sine, cosine and tangent of angles 0 – 360
  • Understand the concept of related angles
  • Solve basic equations
  • Apply trigonometric identities to simplify expressions

Higher Mathematics Course Content

June

1. Straight Line
2. Functions and Graphs

August

1. Recurrence Relations
2. Differentiation
3. Trigonometry
4. Polynomials

Assessment

1. Quadratic Theory
2. Integration
3. Addition/Double Angle Formulae
4. Circle
5. Vectors

Prelim

1. Wave Function
2. Further Calculus
3. Logarithmic/Exponential Functions

Prelim 2