Download New Curriculum Revision List higher

New Curriculum Revision List - Higher
Number
Order positive/negative intergers, decimals, fractions and use inequality symbols.
Apply the four operations (including formal written methods) to integers, decimals, fractions
and mixed numbers, positive or negative. Understand and use place value e.g. in
multiplication of decimals and divide decimals by another decimal.
Recognise number families/relationships, and use inverse operations. Use BIDMAS.
Identify prime numbers, factors (divisors), multiples, common factors, common multiples, HCF,
LCM, prime factorisation - use this to identify HCF/LCM.
Apply systematic listing strategies e.g. for combinations.
Use powers and roots, estimate powers and roots of any given positive number.
Use index laws including negative and fractional indices.
Calculate exactly with fractions, surds and multiples of pi.
Write in standard form and perform calculations in standard form.
Convert between terminating decimals and their fractions; change recurring decimals into
fractions and vice versa.
Change a ratio into a fraction.
Find fractions and percentages of amounts; express one quantity as a fraction of another;
increase or decrease by a percentage (and use decimal multipliers); reverse percentages.
Use standard units of mass, length, time, money and other measures, including compound
measures such as speed, and be able to give a proportion of an amount.
Approximation and estimation.
Rounding to decimal places, significant figures and identify upper/lower bounds.
Ratio, proportion and rates of change
Convert between different units and use compound measures e.g. speed, rates of pay, unit
prices, density and pressure.
Use scale factors, scale diagrams and maps.
Express one quantity as a fraction of another, or a percentage of another.
Use ratio notation, including reduction to simplest form; divide a quantity by a ratio.
Express a multiplicative relationship between two quantities as a ratio or fraction.
Understand and use proportion as equality of ratios, use 1:n.
Relate ratios to fractions and to linear functions.
Define percentages as per 100; interpret percentages/percentage changes as a fraction or
decimal; compare two quantities using percentages; percentages greater than 100; problems
involving percentage change, increase/decrease, original value, simple interest.
Solve problems involving direct and inverse proportion, graphically/algebraically.
Compare lengths, areas and volumes using ration, link to similarity (including trigonometric
ratios) and scale factors.
Understand that y is inversely proportional to x is equivalent to y=1/x and construct/interpret
equations that describe direct and inverse proportion.
Interpret the gradient of a straight line as a rate of change; the gradient at a point on a curve
is the instantaneous rate of change; apply the concepts of average and instantaneous rate of
change (gradients of chords and tangents) in numerical, algebraic and graphical contexts.
Growth/decay problems, e.g. compound interest, work with general iterative processes.
Algebra
Use correct notation and vocabulary such as equation, formula, identity, expression, inequality.
Substitution into formulae and expressions, including powers, roots, decimals and negatives.
Simplify expressions, including surds and algebraic fractions, by collecting like terms; expanding
brackets and factorising; index laws.
Recall and use mathematical formulae, including circumference and area of a circle,
Pythagoras theorem, SOHCAHTOA.
Rearrange formulae to change the subject.
Argue mathematically that algebraic expressions are equal; algebraic proof.
Interpret simple expressions as functions with input and output e.g. write a simple two step
equation out using a function machine. Interpret the reverse process as the "inverse function";
interpret the succession of two functions as a "composite function".
Use coordinates in all four quadrants, use a table of values to generate coordinates.
Plot linear graphs in the form y=mx+c; identify gradients and y-intercepts; find the equation of a
line through two points or through one point and a given gradient; identify parallel and
perpendicular lines.
Identify and interpret roots, intercepts, turning points of quadratic functions graphically and
deduce roots algebraically (completing the square).
Recognise, sketch and interpret graphs of linear functions, quadratics, simple cubic graphs
and reciprocals. Also exponential functions and trigonometric functions. Sketch translations
and reflections of a given function.
Calculate or estimate gradients of graphs and areas under graphs (including quadratic and
other non-linear graphs) and interpret results of real life graphs.
Recognise and use the equation of a circle with centre at the origin; find the equation of a
tangent to a circle at a given point.
Solve linear equations algebraically and graphically.
Solve quadratic equations (including those that require rearrangement) by factorising, by
completing the square, by using the quadratic formula; find approximate solutions using a
graph.
Solve two simultaneous equations in two variables, either two linear equations or one linear one
quadratic, algebraically and find approximate solutions using a graph.
Find approximate solutions to equations numerically using iteration.
Derive equations/expressions/formulae from a worded sentence.
Solve linear inequalities with one or two variables and quadratic inequalities with one variable;
represent inequalities on a number line, using set notation and on a graph.
Generate a sequence from a term to term or position to term rule.
Recognise and use triangular numbers, squares and cubes, simple linear sequences, Fibonacci
type sequences, quadratic sequences and simple geometic progressions.
Find the nth term of a linear sequence.
Geometry and measures
Use correct notation e.g. to show angles, parallel lines, perpendicular lines, right angles, sides
equal in length and draw diagrams fro a written description.
Be able to accurately construct perpendicular bisectors, a perpendicular line at any point,
angle bisector and use construction to solve loci problems.
Know and apply angle rules including angles at a point, angles on a straight line, vertically
opposite angles, alternate and corresponding angles, angles in a triangle, base angles in an
isosceles triangles. Also demonstrate proofs/deduction.
Explain the properties of a given quadrilateral, including squares, rectangles, parallelograms,
trapezium, kites, rhombuses, by breaking down angle characteristics and side characteristics.
Explain the properties of different triangles, by breaking down angle characteristics and side
characteristics.
Use congruence for triangles (SSS, SAS, ASA, RHS)
Identify and describe congruent and similar shapes, including on a set of axes.
Use rotation, reflection, translation and enlargement (including fractionaland negative scale
factors).
Describe the changes and invariance achieved by combinations of rotations, reflections and
translations.
Identify and apply circle definitions and properties including centre, radius, chord, diameter,
circumference, tangent, arc, sector and segment.
Circle theorem, including angles, radii, tangents and chords.
Solve geometrical problems on coordinate axes.
Identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms,
cylinders, pyramids, cones and spheres.
Construct and interpret plans and elevations of 3D shapes.
Use standard units of measure.
Measure line segments and angles in geometric figures, including interpreting maps and scale
drawings and use of bearings.
Know and apply formulae to calculate area of triangles, parallelograms, trapezium, volume of
coboids and other prisms (including cylinders).
Know the formulae for circumference and area of a circle, be able to find perimeters of 2D
shapes involving circles; find surface area and volume of spheres, pyramids, cones and
composite solids.
Calculate arc lengths, angles, and areas of circle sectors.
Apply the concepts of congruence and similarity.
Know Pythagoras theorem, SOHCAHTOA, exact values of sin/cos for 0, 30, 45, 60 and 90
degrees and for tan at 0, 30, 45 and 60 degrees.
Know and apply the sine and cosine rules to find unknown lengths and angles. Also be able to
find the area of a triangle using trigonometry.
Describe translations as 2D vectors.
Addition and subtraction of vectors, multiplication of vectors, diagrammatic and column
representations of vectors. Use vectors to construct geometric arguments and proof.
Statistics
Use sampling and descibe limitations of samples.
Construct and interpret tables, charts and diagrams, including frequency tables; bar charts,
pie charts and pictograms; vertical line charts; tables and line graphs for time series data.
Construct and interpret diagrams including histograms and cumulative frequency graphs.
Interpret, analyse and compare data sets through graphical representations e.g. box plots and
appropriate measures e.g. median, mean, mode, modal class, range, quartiles, IQR.
Apply statistics to describe a population.
Use and interpret scatter graphs for two variables; recognise correlation and know it does not
indicate causation; draw lines of best fit and make predictions.
Probability
Record, describe and analyse the frequency of outcomes of probability experiments using
tables and frequency trees.
Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes
of future experiments.
Relate relative expected frequencies to theoretical probability, using appropriate language
and the 0-1 probability scale.
Probabilities in a situation add to 1.
Understand larger samples tend to be more accurate.
Set out information systematically e.g. tables, grids, Venn diagrams, tree diagrams, sample
space diagrams, two way tables and use these to solve problems.
Calculate the probability of independent and independent combined events.