Higher GCSE Maths (all numbers in brackets are MyMaths lessons from GCSE exams 2017)
Calculations
Order positive and negative integers and decimals. (1068, 1072)
Round to a given number of decimal places or significant figures.(1001, 1005)
Use mental and written methods to add, subtract, multiply and divide with positive and
negative integers and decimals.(1007, 1011, 1013, 1916, 1917)
Use BIDMAS to complete calculations in the correct order.
Expressions
Use algebraic notation and simplify expressions by collecting like terms. (1178, 1179)
Substitute numbers into formulae and expressions. (1186)
Use the laws of indices. (1033, 1045, 1301, 1951)
Multiply a single term over a bracket. (1247)
Take out common factors in an expression. (1155)
Simplify algebraic fractions and carry out arithmetic operations with algebraic fractions. (1149, 1151, 1164)
Angles and polygons
Use angle facts including at a point, on a line, at an intersection and for parallel lines.(1082, 1109)
Use bearings to specify directions.(1086)
Identify types of triangle and quadrilateral and use their properties. (1080, 1102, 1130, 1141)
Identify congruent shapes and use congruence to prove geometric results.(1148)
Identify similar shapes and use similarity to find lengths and areas. (1119)
Calculate the properties of polygons including interior and exterior angles for regular
polygons. (1100, 1320)
Handling data
Identify when a sample may be biased.(1212, 1248, 1249)
Construct and interpret frequency tables, bar charts and pie charts. (1214, 1215, 1205, 1206, 1207)
Calculate the mean, median and mode of a data set.(1192, 1202, 1254)
Calculate the range and interquartile range of a data set. (1203)
Use averages and measures of spread to compare data sets. (1192)
Use frequency tables to represent discrete or continuous grouped data. (1196)
Construct bar charts and construct histograms with equal or unequal class widths. (1197)
Calculate summary statistics from a grouped frequency table. (1201, 1202, 1254, 1255)
Construct and interpret cumulative frequency curves and box plots. (1194, 1195, 1333)
Plot scatter graphs and recognise correlation. (1213, 1250)
Use tables and line graphs to represent time series data. (1198, 1939)
Fractions, decimals and percentages
Find fractions and percentages of amounts. (1030, 1031, 1046)
Add, subtract, multiply and divide with fractions and mixed numbers. (1017, 1040, 1047, 1074)
Convert between fractions, decimals (including recurring decimals) and percentages. (1015, 1016, 1063,
1066)
Order fractions, decimals and percentages.
Formulae and functions
Substitute values into formulae and rearrange formulae to change their subject. (1170, 1171, 1186)
Write an equation to represent a function and find inputs and outputs.(1159)
Find the inverse of a function and construct and use composite functions. (1940, 1941)
Use the terms expression, equation, formula, identity, inequality, term and factor. (1942)
Construct proofs of simple statements using algebra. (1150, 1247, 1938)
Expand brackets to get a quadratic expression and factorise quadratics into brackets. (1150, 1151, 1156,
1157)
Working in 2D
Measure line segments and angles accurately.
Use scale drawings and bearings. (1086, 1103, 1117)
Calculate the areas of triangles, parallelograms, trapezia and composite shapes. (1108, 1128, 1129)
Describe and transform shapes using reflections, rotations, translations (described as 2D vectors) and
enlargements (including fractional and negative scale factors). (1099, 1113, 1115, 1125, 1127)
Identify what changes and what is invariant under a combination of transformations.
Probability
Use experimental data to estimate probabilities and expected frequencies.(1211, 1264)
Use tables to represent the outcomes of probability experiments. (1211)
Calculate theoretical probabilities and expected frequencies using the idea of equally likely events.(1263)
Recognise mutually exclusive events and exhaustive events and know that the probabilities of mutually
exclusive exhaustive events sum to 1. (1262, 1263)
Compare theoretical probabilities with experimental probabilities. (1264)
Measures and accuracy
Use approximate values obtained by rounding to estimate calculations.(1005, 1043, 1969)
Use an estimate to check an answer obtained using a calculator. (1043, 1932, 1933, 1969)
Use, and convert between, standard units of length, mass, capacity and other measures including compound
measures. (1121, 1246)
Solve problems involving compound measure such as speed and density. (1121, 1246 )
Find upper and lower bounds on the value of a quantity that has been rounded. (1006, 1067, 1968)
Find upper and lower bounds on expressions that involve quantities that have been rounded.(1006, 1067)
Equations and inequalities
Solve linear equations including when the unknown appears on both sides. (1182, 1319, 1928, 1929)
Solve quadratic equations using factorisation, completing the square and the quadratic
formula. (1160, 1169, 1181, 1185, 1950)
Solve a pair of linear or linear plus quadratic simultaneous equations. (1174, 1177, 1236, 1319)
Use iterative processes to find approximate solutions to equations. (1956)
Solve inequalities and display your solution on a number line or a graph. (1161, 1162, 1163, 1189)
Circles and constructions
Find the area and circumference of a circle and composite shapes involving circles. (1083, 1088)
Calculate arc lengths, angles and areas of sectors. (1952)
Prove and apply circle theorems. (1087, 1142, 1321)
Use standard ruler and compass constructions and solve problems
involving loci. (1089, 1090, 1147)
Ratio and proportion
Find fractions and percentages of amounts and express one number as a fraction or percentage of another.
(1015, 1037)
Divide a quantity in a given ratio and reduce a ratio to its simplest form. (1036, 1038, 1039)
Use scale factors, scale diagrams and maps. (1103)
Solve problems involving percentage change. (1060, 1237, 1302, 1934)
Factors, powers and roots
Know and use the language of prime numbers, factors and multiples. (1032 )
Write a number as a product of its prime factors. (1044)
Find the HCF and LCM of a pair of integers. (1032, 1034, 1044)
Estimate the square or cube root of an integer. (1033, 1053)
Find square and cube roots of numbers and apply the laws of indices. (1033, 1053, 1301, 1924)
Simplify expressions involving surds including rationalising fractions. (1064, 1065)
Graphs
Find and interpret the gradient and y-intercept of a line and relate these to the equation of the line in the
form y = mx + c. (1153, 1311, 1314, 1957)
Identify parallel and perpendicular lines using their equations. (1314, 1957)
Draw line graphs and quadratic curves. (1153, 1180, 1312, 1959)
Identify roots, intercepts and turning points of quadratic curves using graphical and
algebraic methods. (1180, 1185, 1959, 1960)
Use graphs to solve problems involving distance, speed and acceleration. (1322, 1323)
Recognise and draw graphs of cubic and reciprocal functions. (1071, 1172, 1958)
Recognise and draw the graphs of exponential functions. (1070, 1126, 1188)
Recognise and sketch the graphs of trigonometric functions. (1126)
Recognise and sketch translations and reflections of graphs. (1172, 1126, 1188, 1955)
Draw and interpret graphs of non-standard functions and use them in real-life problems. (1184, 1322)
Approximate the gradient of a curve at a given point and the area under a graph. Interpret these values in
real-life problems including kinematic graphs. (1128, 1312, 1944, 1953)
Recognise and use simple equations of circles and find the tangent to a circle at a point. (1152)
Working in 3D
Draw and interpret plans and elevations of 3D shapes.(1078, 1098, 1106)
Calculate the volume of cuboids and right prisms.(1137, 1138, 1139)
Calculate the surface area and volume of spheres, pyramids, cones and composite shapes. (1107, 1122,
1136)
Know and apply the relationship between lengths, areas and volumes of similar shapes.(1085, 1119, 1140)
Calculations
Perform calculations involving roots and indices, including negative and fractional indices. (1033, 1045,
1301, 1951)
Perform exact calculations involving fractions, surds and π. (1065, 1074)
Work with numbers in standard form.( 1049, 1050, 1051)
Pythagoras and trigonometry
Use Pythagoras’ theorem to find a missing side in a right-angled triangle or the length of a line segment on a
coordinate grid. (1064, 1112)
Use trigonometric ratios to find missing lengths and angles in triangles. (1131, 1133)
Find the exact values of sin θ and cos θ for key angles. (1943)
Use the sine and cosine rules to find missing lengths and angles. (1094, 1095, 1120)
Use the sine formula for the area of a triangle. (1144)
Calculate with vectors and use them in geometric proofs. (1134, 1135)
The probability of combined events
Use tables and Venn diagrams to represent sets. (1262, 1921, 1922)
Use a possibility space to represent the outcomes of two experiments and to calculate probabilities. (1199,
1263)
Use a tree diagram to show the outcomes of one or more experiments and to calculate probabilities. (1208,
1935, 1966)
Calculate conditional probabilities. (1334, 1967)
Sequences
Generate a sequence using a term-to-term or position-to-term rule. (1173)
Recognise a linear sequence and find a formula for its nth term. (1165)
Recognise a quadratic sequence and find a formula for its nth term. (1166)
Recognise and use special sequences. (1920, 1946, 1947)
Units and proportionality
Use compound measures. (1121, 1246)
Convert between standard units of measure and compound units. (1121, 1246, 1970, 1971)
Compare lengths, areas and volumes of similar shapes. (1061, 1329)
Solve direct and inverse proportion problems. (1048, 1948, 1949)
Describe direct and inverse proportion relationships using an equation. (1048, 1948, 1949)
Recognise graphs showing direct and inverse proportion and interpret the gradient of a straight line graph.
(1048, 1948, 1949)
Find the instantaneous and average rate of change from a graph. (1312)
Solve repeated proportional change problems (1070, 1238)