HYC GCSE Foundation
Y9F Unit 1a – Integers and place value - Mathswatch
Use and order positive and negative numbers. - 2
Order integers and decimals using the symbols < and >. - 5
Add and subtract positive and negative integers. - 17, 18
Recall all multiplication facts to 10×10 and derive corresponding division facts. - 18
Multiply or divide any number by powers of 10. - 30
Multiply and divide negative numbers. - 68b
Recall and apply BIDMAS (not including powers). - 75
Round numbers to a given power of 10. - 31
Y9F Unit 1b – Decimals
Use decimal notation and place value. - 1
Identify the value of digits in a decimal or whole number. - 1
Compare and order decimals using the < and > symbols. Understand the ≠ symbol. - 5
Add, subtract, multiply and divide decimals, including calculations involving money. - 17, 18, 66, 67
Multiply or divide by any number between 0 and 1. - 66
Round to the nearest integer, decimal places and significant figures. - 31, 32, 90
Estimate answers to calculations by rounding to 1SF. - 91
Use one calculation to find the answer to another. - 92
Y9F Unit 1c – Indices, powers and roots
Find and recall the square numbers up to 10×10 and their corresponding roots. - 81
Understand the difference between positive and negative square roots. - 81
Recall the cubes of 1, 2, 3, 4, 5 and 10. - 81
Evaluate expressions involving squares, cubes and roots (and know how to do this on a calculator). - 81
Use index notation for powers of 10 including negative powers. - 82
Use the laws of indices to multiply and divide numbers written in index form. - 131
Use BIDMAS including with powers. - 131
Y9F Unit 1d – Factors, multiples and primes
List all three-digit integers than can be made from three given integers. - 1
Recognise odd and even numbers. - 1
Identify factors, multiples and prime numbers. - 28
List factors and multiples systematically. - 28
Express a number as a product of prime factors in index form. - 78
Find common factors and multiples of two numbers. - 79, 80
Find the HCF and LCM of two numbers by listing, using Venn diagrams and using prime factors. - 79, 80, 127a
Solve simple problems using HCF, LCM and prime numbers. - 79, 80
Y9F Unit 2a - Algebra: the basics
Use notation and symbols correctly and write expressions. - 7
Identify different types of algebra. - 7
Simplify expressions by collecting like terms. - 33
Multiply two simple algebraic expressions. - 34
Simplify expressions by cancelling. - 34
Use index notation when multiplying or dividing algebraic terms - 82
Use index laws in algebra. - 131
Y9F Unit 2b – Expanding and factorising single brackets
Multiply a single number term over a bracket. - 93
Write and simplify expressions using squares and cubes - 33,34,35
Expand and simplify expressions involving brackets. - 93
Argue mathematically to show two expressions are equivalent.
Recognise factors of algebraic terms involving single brackets. - 94
Factorise algebraic expressions by taking out common factors. - 94
Y9F Unit 2c - Expressions and substitution into formulae
Write expressions to solve problems representing a situation. - 137
Substitute numbers into simple algebraic expressions - 95
Substitute numbers into expressions involving brackets and powers. - 95
Substitute positive and negative numbers into expressions. - 95
Derive a simple formula. - 137
Substitute numbers into a worded formula. - 95
Substitute numbers into a formula. - 95
Y9F Unit 3a – Tables
Design and use data-collection sheets for grouped, discrete and continuous data, use inequalities for grouped data, and introduce ≤ and ≥ signs. - 63
Sort, classify and tabulate data, both discrete and continuous quantitative data, and qualitative data. - 63
Construct tables for time–series data. - 153
Extract data from lists and tables.
Use correct notation for time, 12- and 24-hour clock. Work out time taken for a journey from a timetable. - 6a/b
Design and use two-way tables for discrete and grouped data. - 61
Construct and read frequency tables, including identifying the mode/modal class. - 65a,62
Y9F Unit 3b – Charts and graphs
Plot coordinates in the first quadrant and read graph scales in multiples. - 8
Draw and interpret pictograms and bar charts. - 16,15
Draw and interpret dual bar charts and vertical line charts. - 64
Draw and interpret line graphs including for time series data. - 153
Draw and interpret histograms with equal class intervals. - 205
Draw and interpret stem and leaf diagrams, including back-to-back. - 128b
Y9F Unit 3c – Pie charts
Know how many degrees there are in a full turn, half turn and quarter turn.
Measure and draw angles, to the nearest degree. - 46a
Interpret simple pie charts using simple fractions and percentages. - 128a
Construct pie charts for categorical data and discrete/ continuous numerical data. - 128a
Use a pie chart to find the mode and total frequency. - 128a,62
Understand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie charts. - 128a
Y9F Unit 3d – Scatter graphs
Draw scatter graphs. - 129
Interpret points on a scatter graph and identify outliers. - 129
Draw the line of best fit on a scatter diagram by eye, and understand what it represents. - 129
Use the line of best fit make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing. - 129
Distinguish between positive, negative and no correlation using lines of best fit. Interpret correlation in terms of the problem. - 129
Understand that correlation does not imply causality. State how reliable their predictions are, i.e. not reliable if extrapolated. - 129
Y9F Unit 4a - Fractions
Use diagrams to find equivalent fractions or compare fractions and write fractions to describe shaded parts of diagrams. - 25
Express a given number as a fraction of another.
Write a fraction in its simplest form and find equivalent fractions. Order fractions. - 25.26
Convert between mixed numbers and improper fractions.(KS3) - N35
Add and subtract fractions, writing the answer as a mixed number where appropriate - .71
Multiply and divide a fraction by an integer and vice versa. - 73,74
Multiply and divide fractions. - 73,74
Y9F Unit 4b – Fractions, decimals and percentages
Convert between fractions and decimals. - 84
Recognise recurring decimals and convert fractions into recurring decimals, using correct notation. - 177
Compare and order fractions, decimals and integers, using inequality signs. - 3,73
Express a given number as a percentage of another number. - 89
Convert between fractions, decimals and percentages. - 85
Order fractions, decimals and percentages, including use of inequality signs. - 85
Y9F Unit 4c – Percentages
Find a percentage of a quantity using non-calculator methods. - 87
Find a percentage of a quantity using calculator methods. - 88
Calculate percentage change. - 109
Increase and decrease amounts by percentages using non-calculator methods. - 108
Use multipliers to increase and decrease amounts by percentages. - 108
Y9F Unit 5a – Equations
Write expressions and set up simple equations. - 137
Use function machines.
Solve simple equations.
Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation. - 135
Solve linear equations which contain brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution - .135
Rearrange simple equations. - 136
Substitute into a formula, and solve the resulting equation. - 95
Solve problems by setting up and solving equations, including involving angle or perimeter problems. - 137
Y9F Unit 5b – Inequalities
Show inequalities on number lines. - 138
Construct inequalities to represent a set shown on a number line. - 138
Write down whole number values that satisfy an inequality. - 138
Solve an inequality and show the solution set on a number line. - 139
Solve two inequalities in x, find the solution sets and compare them to see which value of x satisfies both. - 139
Y9F Unit 5c – Sequences
Recognise sequences of odd and even numbers, and other sequences including Fibonacci sequences. - 104,141
Write the term-to-term definition of a sequence in words.
Generate arithmetic sequences of numbers, triangular number, square and cube integers and sequences derived from diagrams. - 37
Find the next term in a sequence, including negative values. - 37
Find the nth term of a linear sequence. - 103
Use the nth term of an arithmetic sequence to generate terms. - 103
Use the nth term of an arithmetic sequence to decide if a given number is a term in the sequence or to find the first term that is less than/greater than a certain value. - 102
Continue a geometric progression and find the term-to-term rule, including negatives, fraction and decimal terms. - 163
Continue a quadratic sequence and use the nth term to generate terms. - 213
Y10F Unit 6a – Properties of shapes, parallel lines and angle factsMathswatch
Measure angles using a protractor. - 46a
Use correct notation to identify sides and angles. - 9, 122
Identify types of lines and special types of triangle and quadrilateral.
Recall and use the angle sum of triangles and quadrilaterals. - 121, 123
Solve angle problems involving intersecting lines.
Understand and use the angle properties of parallel lines. - 120
Calculate interior and exterior angles of triangles. - 120
Y10F Unit 6b – Interior and exterior angles of polygons
Recognise and name the polygons up to 10 sides. - 10
Identify regular and irregular polygons. - 10
Calculate and use the interior angle sum of polygons. - 123
Calculate and use the angles of regular polygons. - 123
Use the sum of exterior angles of a polygon. - 123
Use the sum of the interior and exterior angle. - 123
Identify shapes which are congruent. - 12b
Explain why some polygons fit together and some do not - .12a
Y10F Unit 7a – Statistics and sampling
Plan an investigation, deciding what data to collect and how to analyse it. Understand how sources of data may be biased.
Recognise types of data: primary secondary, quantitative and qualitative. - 63
Identify which primary data they need to collect and in what format, including grouped data.
Explain why a sample may not be representative of a whole population. - 152
Y10F Unit 7b – The averages
Calculate the mean, mode, median and range for discrete data. - 62
Interpret and find the median, mean and range from a (discrete) frequency table. - 130a
Interpret and find the range, modal class, interval containing the median, and estimate of the mean from a grouped data frequency table. - 130b
Interpret and find the mode, mean and range from a bar chart, the median, mode and range from stem and leaf diagrams. - 62, 128b
Compare the mean, median, mode and range. - 62
Recognise the advantages and disadvantages between measures of average.
Y10F Unit 8a – Perimeter and area
Convert between units of measure within one system, including time. - 112
Make sensible estimates of a range of measures in everyday settings.
Measure shapes to find perimeters and areas using a range of scales.
Find the perimeter of rectangles, triangles, parallelograms, trapezia and compound shapes. - 52
Recall and use the formula for the area of rectangles and triangles. - 53, 54
Recall and use the formula for the area of a trapezium and parallelogram. - 55, 56
Find the surface area of a prism. - 114
Convert between metric area measures. - 112
Y10F Unit 8b – 3D forms and volume
Identify and name common solids. - 43
Sketch nets of cuboids and prisms. - 44
Recall and use the formula for the volume of a prism. - 115, 119
Convert between metric units of volume (and capacity). - 112
Y10F Unit 9a – Real-life graphs
Use input/output diagrams. - 36
Use co-ordinates in all four quadrants. - 8
Find the co-ordinates of the midpoint of a line segment. - 133
Draw and interpret straight line graphs representing real-life situations. - 96
Draw distance-time graphs and velocity-time graphs. - 143
Calculate speed for a section of a distance-time graph. - 142, 143
Y10F Unit 9b – Straight line graphs
Draw and recognise graphs of y=a, x=a, y=x and y=-x. - 96
Use a table of values to plot graphs of the form y=mx+c. - 96
Sketch the graph of a linear function directly from the gradient and y-intercept. - 97
Identify parallel lines from their equations. - 97
Draw graphs of the form ax+by=c. - 96
Find the equation of a straight line. - 159a
Find the equation of the line through one point with a given gradient. - 159b
Y10F Unit 10a – Transformations 1: rotations and translations
Describe rotations. Accurately rotate shapes - 49
Accurately rotate shapes. - 49
Understand how vectors work. Translate a given shape by a vector. - 50
Describe translations. - 50
Y10F Unit 10b – Transformations 2: reflections and enlargements
Describe reflections including stating the equation of the line of reflection. - 48
Reflect shapes in horizontal and vertical lines. - 48
Reflect shapes in diagonal lines. - 48
Describe and perform enlargements using a positive integer scale factor. - 148
Describe and perform enlargements using a positive fractional scale factor. - 148
Y10F Unit 11a – Ratio
Write ratios in their simplest form. - 38
Share a quantity in a given ratio. - 106
Solve ratio problems in context. - 106
Compare ratios, including writing them in the form 1:n and n:1. - 38
Write a ratio as a fraction or linear function. - 107
Write lengths, areas and volumes of two shapes as ratios in simplest form. - 200
Y10F Unit 11b – Proportion
Solve word problems involving direct and inverse proportion. - 42
Work out which product is best value. - 41
Solve proportion problems involving recipes. - 39
Convert between currencies. - 105
Solve proportion problems using the unitary method. - 106
Identify values that are in direct and inverse proportion including from graphs. - 107
Y10F Unit 12 – Pythagoras and trigonometry
Recall and apply Pythagoras’ Theorem to calculate the length of the hypotenuse, including in applied problems. - 150
Recall and apply Pythagoras’ Theorem to calculate the length a shorter side, including in applied problems. - 150
Use Pythagoras’ Theorem to justify if a triangle is right angled or not. - 150
Recall the trigonometric ratios sin, cos and tan and apply them to calculate sides in right angled triangles. - 168
Recall the trigonometric ratios sin, cos and tan and apply them to calculate angles in right angled triangles. - 168
Use trigonometry to solve applied problems in 2D. - 168
Know exact trigonometric values. - 173
Y10F Unit 13a – Probability 1
Use the language of probability and position events on the probability scale. - 14
Find theoretical probabilities and express them as fractions, decimals or percentages. - 59
Work out probabilities from frequency tables and two-way tables. - 61
Identify mutually exclusive events and know that the sum of the probabilities of all outcomes is 1. - 60
Use 1 – p as the probability of an event not occurring where p is the probability of the event occurring. - 60
Y10F Unit 13b – Probability 2
Find the probability of an event happening using relative frequency. - 125
Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities.
List all outcomes for combined events systematically. - 58, 126
Work out probabilities from Venn diagrams including using union and intersection. - 127, 185
Use tree diagrams to calculate the probability of two independent events. - 151
Use tree diagrams to calculate the probability of two dependent events. - 151
Y10F Unit 14 – Multiplicative reasoning
Understand and use speed. - 142
Understand and use density. - 142
Understand and use pressure. - 142
Calculate percentage profit or loss. - 87, 109
Make calculations involving repeated percentage change. - 109
Calculate compound interest. - 164
Solve reverse percentage problems. - 110
Y11F Unit 15a – Plans and elevationsMathswatch
Measure and draw lines, to the nearest mm and measure and draw angles to the nearest degree. - 46a/b
Know and use compass directions.
Draw sketches of 3D solids. - 43
Know and use the terms face, edge and vertex (vertices). - 43
Identify and sketch planes of symmetry of 3D solids. - 11
Draw plans and elevations of 3D shapes. - 51
Given the plans and elevations, sketch the 3D solid. - 51
Y11F Unit 15b – Construction, loci and bearings
Visually identify shapes which are congruent. - 12b
Use bearings to specify direction. - 124
Use a ruler and compass to construct perpendicular bisectors (including from a point), angle bisectors and angles of 90° and 45°.146a/b, - 145
Draw and construct diagrams from given instructions to show a region bounded by a circle and a line, a given distance from a point/line, equal distances from 2 points/lines. - 165
Use constructions to solve loci problems. - 165
Draw and use accurate scale diagrams. - 38
Solve problems involving bearings. - 124
Y11F Unit 16a – Quadratic equations: expanding and factorising
Define a quadratic expression.
Expand double brackets. - 134b
Square a linear expression. - 134b
Factorise quadratics of the form x2+bx+c. - 157
Factorise quadratics of the form x2-a2 using the difference of two squares. - 158
Solve quadratic equations by factorising. - 157
Y11F Unit 16b – Quadratic equations: graphs
Generate points and plot graphs of simple quadratic functions. - 98
Generate points and plot graphs of more general quadratic functions. - 98
Identify the line of symmetry of a quadratic graph. - 96
Find approximate solutions to quadratic equations using a graph. - 160
Interpret graphs of quadratic functions from real-life problems - .160
Identify and interpret roots, intercepts and turning points of quadratic graphs. - 160
Y11F Unit 17 – Perimeter, area and volume 2
Identify and name parts of a circle. - 116
Recall and use the formulae for area and circumference of circles. Give answers in terms of π - 117, 118
Find the radius or diameter when given the area or circumference of a circle. - 117, 118
Calculate the perimeter or area of composite shapes made from parts of circles. - 17, 118
Calculate arc length and sector area - 149
Calculate the volume and surface area of a cylinder. - 119, 114b
Calculate the surface area and volume of spheres, cones and pyramids. - 169, 170, 171
Y11F Unit 18a – Fractions
Add and subtract mixed number fractions. - 71a
Multiply mixed number fractions. - 73
Divide mixed numbers by whole numbers and vice versa.7 - 4
Find the reciprocal of an integer, decimal or fraction. Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number multiplied by its reciprocal is 1. - 76
Y11F Unit 18b – Indices and standard form
Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, fractions and powers of a power. - 82
Use numbers raised to the power of zero. - 82
Convert large and small numbers into standard form. - 83
Convert large and small numbers out of standard form. - 83
Add and subtract numbers in standard form. - 83
Multiply and divide numbers in standard form. - 83
Y11F Unit 19a – Similarity and congruence in 2D
Use the basic congruence criteria for triangles (SSS, SAS, ASA and RHS). - 166
Solve angle problems involving congruence. - 166
Identify shapes which are similar; including all circles or all regular polygons with equal number of sides. - 144
Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides. - 144, 48
Solve problems to find missing lengths in similar shapes. - 144
Know that scale diagrams, including bearings and maps are ‘similar’ to the real-life examples. - 38, 144
Y11F Unit 19b – Vectors
Understand and use column notation in relation to vectors. - 174
Be able to represent information graphically given column vectors. - 174
Identify two column vectors which are parallel. - 174
Calculate using column vectors, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector. - 219
Y11F Unit 20 – Rearranging equations, graphs and simultaneous equations
Change the subject of a formula involving the use of square roots and squares. - 136
Answer ‘show that’ questions using consecutive integers (n, n + 1), squares a2, b2, even numbers 2n, and odd numbers 2n +1.
Find the equation of the line through two given points. - 159b
Recognise, sketch and interpret graphs of simple cubic and reciprocal functions. - 161, 99
Write simultaneous equations to represent a situation. - 162
Solve simultaneous equations (linear/linear) algebraically and graphically - .162