High School Math Year 2

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Unit 1 · Quadratic Expressions: Expand, Factorise and Simplify Like an Expert
Unit overview By the end of this unit, students can expand products of two and three brackets, including squared brackets, factorise quadratics of the form x² + bx + c and ax² + bx + c, use the difference of two squares and perfect squares (including for quick arithmetic), factorise completely, and simplify, multiply, divide, add and subtract algebraic fractions with quadratic tops and bottoms. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Algebraic processes: expansion of brackets, factorisation of quadratic expressions, the difference of two squares, and simplification of algebraic fractions (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Algebraic manipulation: expanding products of brackets (including three brackets), factorising quadratics ax² + bx + c, the difference of two squares, and simplifying, adding, subtracting, multiplying and dividing algebraic fractions • GCSE Mathematics (UK, Higher): Algebra: expanding products of two or more binomials, factorising quadratics including ax² + bx + c and the difference of two squares, and simplifying and manipulating algebraic fractions • US Algebra I/II and the SAT: Seeing structure in expressions (A-SSE.2, for example x⁴ − y⁴ as a difference of squares), arithmetic with polynomials and rational expressions (A-APR.1, A-APR.7); SAT Passport to Advanced Math Students will be able to: • expand and simplify products of two or three brackets, including (a + b)² and (a − b)² • factorise quadratics x² + bx + c in all four sign cases, taking out a common factor first • factorise quadratics ax² + bx + c by splitting the middle term and grouping • factorise using the difference of two squares and perfect squares, factorise completely, and use a² − b² for quick arithmetic • simplify algebraic fractions with quadratics by cancelling factors, and multiply, divide, add and subtract them Calculator use: all five lessons and the whole unit test are non-calculator, matching the non-calculator papers of IGCSE and GCSE, where these algebra skills are mostly tested. All questions are original and written for this course. British spelling is used.

  • Lesson 1 · Expanding Double Brackets: Why (x + 3)² Is Not x² + 9
  • Lesson 1 Exit Quiz: Expanding Double Brackets
  • Lesson 2 · Factorising x² + bx + c: Find the Two Secret Numbers
  • Lesson 2 Exit Quiz: Factorising x² + bx + c
  • Lesson 3 · Factorising ax² + bx + c: Split the Middle Term
  • Lesson 3 Exit Quiz: Factorising ax² + bx + c
  • Lesson 4 · Difference of Two Squares and Perfect Squares: Work Out 51² − 49² in Your Head
  • Lesson 4 Exit Quiz: Difference of Two Squares
  • Lesson 5 · Algebraic Fractions with Quadratics: Factorise First, Then Cancel
  • Lesson 5 Exit Quiz: Quadratic Fractions
  • Unit 1 Test: Quadratic Expressions (Section A)

Unit 2 · Quadratic Equations: Every Way to Find x When It Is Squared
Unit overview By the end of this unit, students can solve quadratic equations by factorising, by completing the square and with the quadratic formula, use the discriminant to decide how many roots there are, form quadratic equations from areas, numbers, journeys and heights and reject impossible roots, and solve equations that become quadratic, including fractions with x in the denominator, using the sum and product of the roots. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Quadratic equations by factorisation, completing the square and the formula; word problems leading to quadratics; sum and product of roots and forming an equation from its roots (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Solving quadratic equations by factorisation, completing the square and the quadratic formula (answers to a given accuracy), forming quadratics from problems, and algebraic fractions leading to quadratics • GCSE Mathematics (UK, Higher): Solving quadratics by factorising (including a ≠ 1), completing the square and turning points, the quadratic formula, and setting up and solving quadratic equations in context • US Algebra I/II and the SAT: Solving quadratics by inspection, completing the square, the quadratic formula and factoring (A-REI.4), the discriminant and number of solutions, and the SAT Advanced Math questions on quadratics Students will be able to: • solve quadratic equations by factorising, including a ≠ 1 and the difference of two squares, after rearranging to = 0, without losing a root of x = 0 • complete the square, solve with exact surd answers and find the minimum point and line of symmetry of a quadratic curve • use the quadratic formula for exact and 2-decimal-place answers, and use the discriminant to find the number of roots or an unknown coefficient • form quadratic equations from areas, consecutive numbers, journeys, Pythagoras and heights, rejecting impossible roots and answering in context • solve equations with x in the denominator, reject roots that make a denominator zero, and use the sum and product of roots to form equations Calculator use: Lesson 3 (the quadratic formula) is calculator allowed, because answers correct to 2 decimal places are set on calculator papers. The other four lessons and Section A of the test are non-calculator, matching the non-calculator papers of IGCSE and GCSE, where factorising, completing the square and exact surd answers are tested. Section B of the test is calculator allowed. All questions are original and written for this course. British spelling is used.

Unit 3 · Sequences and Series: Spot the Pattern, Predict the Future
Unit overview By the end of this unit, students can use term-to-term and position-to-term rules, find the nth term of a linear sequence and decide whether a number belongs to it, work with arithmetic progressions (finding any term, the number of terms, and a and d from two terms), find the sum of an arithmetic series in real problems such as savings and seating, work with geometric progressions including growth and decay, and find the sum of a geometric series and, as a challenge, the sum to infinity, choosing an AP or a GP to model a situation. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Sequences and series: the nth term, arithmetic and geometric progressions, the sums of APs and GPs, and word problems (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Continuing sequences, the nth term of linear sequences, geometric sequences, and exponential growth and decay. The sums of series go beyond 0580 and are covered in Cambridge IGCSE Additional Mathematics (0606) • GCSE Mathematics (UK, Higher): Term-to-term and position-to-term rules, the nth term of linear sequences, deciding whether a number is in a sequence, and geometric progressions; arithmetic and geometric series lead on to A level • US Algebra I/II and the SAT: Arithmetic and geometric sequences with explicit formulas (F-BF.2, F-LE.2), the sum of a finite geometric series (A-SSE.4, Algebra II), and exponential growth and decay (SAT Advanced Math) Students will be able to: • find and use the nth term of a linear sequence, decide whether a number is a term, and find the first term above or below a value • use a + (n − 1)d to find any term of an AP, the number of terms, and the first term and common difference from two given terms • find the sum of an arithmetic series with either sum formula, and solve problems on savings, seating and stacking, including finding n or d from a sum • find terms, positions and the common ratio of a GP, and model growth and decay with a GP • find the sum of a geometric series and the sum to infinity when r is between −1 and 1, and choose an AP or a GP to model a situation Calculator use: all five lessons and the whole unit test are non-calculator. The ratios, percentages and differences are chosen so that every term and sum can be worked out by hand; real exams often allow a calculator for growth and decay with awkward numbers. The sum formulas are given in the questions, as on many exam formula lists, while the nth-term formulas are expected to be known. All questions are original and written for this course. British spelling is used.

Unit 4 · Logarithms: Turn Giant Powers into Simple Sums
Unit overview By the end of this unit, students can move between index form and log form, evaluate logarithms (including fractional and negative values), use the product, quotient and power laws to simplify and evaluate expressions, write logs in terms of log 2 and log 3, solve logarithmic equations and reject roots that are not allowed, and solve exponential equations, including growth and decay problems, with a calculator. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Indices and logarithms: the relationship between indices and logarithms, the laws of logarithms, simplifying and evaluating log expressions, using given values of logs, and simple logarithmic and exponential equations (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Indices and exponential growth and decay, including compound interest and depreciation (Extended); logarithms, the laws of logarithms and solving equations of the form aˣ = b are taught in Cambridge IGCSE Additional Mathematics (0606), which this unit also prepares for • GCSE Mathematics (UK, Higher): Laws of indices and exponential growth and decay (Higher); logarithms themselves first appear in A level Mathematics, so Lessons 1–4 extend strong Higher students • US Algebra II and the SAT: Logarithms as solutions of exponential equations (F-LE.4), the inverse relationship between exponents and logarithms (F-BF.5) and exponential models (F-LE.1, F-LE.2); SAT Advanced Math: exponential growth and decay (logarithms themselves are not tested on the SAT) Students will be able to: • convert between index form and log form, and evaluate logs of whole numbers, fractions, decimals and roots • use the product, quotient and power laws to combine logs into a single log and to expand a log • simplify log expressions to exact values and write logs in terms of log 2 and log 3, using given values where needed • solve logarithmic equations, including those that lead to quadratics, and reject roots that make a log undefined • solve exponential equations by matching bases or by taking logs, and solve growth and decay problems to a stated accuracy Calculator use: Lessons 1–4, Section A and Questions 1–3 of Section B are non-calculator, as the laws of logarithms are tested with exact answers. Lesson 5 and Questions 4 and 5 of Section B allow a calculator, as for exponential equations and growth problems on the IGCSE, GCSE and WASSCE calculator papers; every rounded answer states its accuracy (3 significant figures, or a whole number of years). All questions are original and written for this course. British spelling is used. Bases of logs are written as subscripts (log₂ 8), and log with no base means log₁₀.

Unit 5 · Inequalities and Linear Programming: Find the Best Possible Answer
Unit overview By the end of this unit, students can solve linear, double and simultaneous inequalities and list their integer solutions, solve quadratic inequalities using a sketch of the curve, show and describe regions defined by inequalities in two variables, form inequalities from problems written in words, and use linear programming to find the best plan by testing the vertices of a feasible region (including whole-number solutions). The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Linear inequalities in one and two variables, graphical representation of inequalities, and linear programming: forming constraints, the feasible region and the objective function (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Linear inequalities, quadratic inequalities, representing inequalities graphically and finding regions; linear programming problems with a feasible region and an objective function (Extended) • GCSE Mathematics (UK, Higher): Solving linear inequalities, including double inequalities, solving quadratic inequalities, and representing inequalities in two variables as regions on a graph (Higher); optimisation with an objective function extends strong Higher students towards A level Further Mathematics (Decision) • US Algebra I/II and the SAT: Solving linear inequalities (A-REI.3), graphing systems of linear inequalities as half-planes (A-REI.12), creating inequalities to represent constraints (A-CED.1, A-CED.3); SAT Algebra: linear inequalities in one or two variables and systems of inequalities Students will be able to: • solve linear inequalities with brackets and fractions, double inequalities and simultaneous inequalities, and list their integer solutions • solve quadratic inequalities by finding critical values and using a sketch of the curve • show a region defined by inequalities on a graph, with solid and dashed lines, and describe a given region with inequalities • form inequalities in one or two variables from problems written in words, including hidden rules and rounding the right way • solve linear programming problems: write the constraints and the objective function, find the vertices of the feasible region and choose the best plan, including whole-number solutions Calculator use: all five lessons and the whole unit test are non-calculator. The numbers are chosen so that every vertex and every critical value can be found by hand, as in the inequality and linear programming questions on the WASSCE, IGCSE and GCSE papers. All questions are original and written for this course. British spelling is used. In this course the region that IS wanted is shaded; some exams shade the part that is NOT wanted, so students should read each question carefully.

Unit 6 · Graphs of Functions: See the Shape Behind Every Equation
Unit overview By the end of this unit, students can draw and interpret quadratic graphs, using the roots, the y-intercept, the line of symmetry and the turning point; solve equations by reading graphs and by choosing the right straight line to draw; plot cubic and reciprocal graphs and use their asymptotes; recognise and sketch linear, quadratic, cubic, reciprocal and exponential graphs from their key features; and find rates of change from tangents and distances from the area under a speed–time graph. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Graphs of quadratic functions from tables of values; reading roots, the maximum or minimum and the line of symmetry; solving related equations graphically; the gradient of a curve by drawing a tangent (Paper 2 graph questions) • Cambridge IGCSE Mathematics (0580, Extended): Graphs of functions: linear, quadratic, cubic, reciprocal and exponential; asymptotes; solving equations graphically, including the line to draw; estimating gradients with tangents; distance from the area under a speed–time graph • GCSE Mathematics (UK, Higher): Recognising, sketching and interpreting graphs of quadratic, cubic, reciprocal and exponential functions; roots, intercepts and turning points; approximate solutions from graphs; gradients of curves and areas under graphs in real contexts • US Algebra I/II and the SAT: Graphing functions and their key features (F-IF.7), intersections of graphs as solutions (A-REI.11), exponential models (F-LE), interpreting rates of change, and SAT Advanced Math questions on graphs Students will be able to: • plot quadratic graphs from tables of values and find their roots, y-intercept, line of symmetry and turning point • solve equations from a graph, using horizontal lines and the straight line found by rearranging, and decide how many solutions there are • plot and sketch cubic and reciprocal graphs, find the roots of a factorised cubic and state the asymptotes of y = k/x • recognise linear, quadratic, cubic, reciprocal and exponential graphs and match equations to sketches by their key features • estimate a rate of change from a tangent, interpret it with units, and estimate distance under a speed–time graph with trapezia Calculator use: all five lessons and the whole unit test are non-calculator. Graph questions in IGCSE and GCSE often appear on both papers, and every value here is chosen to work out by hand; in the tangent questions the two points on the tangent are given, so every gradient is exact. All questions are original and written for this course. British spelling is used.

Unit 7 · Functions and Mappings: The Machines That Turn x into y
Unit overview By the end of this unit, students can read and use function notation, including inputs such as f(−3), f(2a) and f(x + 1), and solve f(x) = k; classify relations as one-to-one, many-to-one, one-to-many or many-to-many, decide which are functions, and state domains and ranges, excluding values that make a denominator zero; form and simplify composite functions fg(x), gf(x) and ff(x); find and check inverse functions of linear and simple rational functions; and solve exam-style problems such as fg(x) = k and f(x) = f⁻¹(x), or find an unknown constant. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Relations and functions: mappings and arrow diagrams, one-to-one and many-to-one mappings, domain and range, composite and inverse functions (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Functions: function notation, domain and range, inverse functions f⁻¹(x), composite functions fg(x) = f(g(x)), and solving equations involving functions • GCSE Mathematics (UK, Higher): Functions: interpreting f(x) notation, finding composite functions and inverse functions, and solving equations such as fg(x) = k • US Algebra I/II and the SAT: Function notation and evaluation (F-IF.1, F-IF.2), domain and range, composition of functions (F-BF.1c), inverse functions (F-BF.4), and the SAT Advanced Math questions on functions Students will be able to: • use function notation to evaluate f(−3), f(2a) and f(x + 1), and solve f(x) = k or find an unknown constant • classify relations from arrow diagrams and pairs, decide which are functions, and find a domain and range, excluding values that make a denominator zero or a square root negative • find and simplify composite functions fg(x), gf(x) and ff(x), and evaluate them in the correct order • find inverse functions of linear and simple rational functions by rearranging, and check them with ff⁻¹(x) = x • solve exam problems such as fg(x) = k, f(x) = f⁻¹(x) and fg(x) = gf(x), including ones that lead to quadratics, and reject values that are not allowed Calculator use: all five lessons and the whole unit test are non-calculator, matching the non-calculator papers of IGCSE and GCSE, where function notation, composite and inverse functions are tested with exact algebra. All questions are original and written for this course. British spelling is used.

Unit 8 · Circle Theorems: Unlock the Hidden Angles in Every Circle
Unit overview By the end of this unit, students can use the angle at the centre, the angle in a semicircle, angles in the same segment, cyclic quadrilaterals, tangents, the alternate segment theorem and the perpendicular from the centre to a chord to find unknown angles and lengths, and can write each step with the full theorem as its reason, as examiners require. Every diagram is drawn to scale from computed coordinates. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme that includes marks for reasons (45 marks, 75 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Geometry: circle theorems (angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilaterals, tangents and the alternate segment theorem) and chord properties, in Paper 1 objectives and Paper 2 structured questions that ask for reasons • Cambridge IGCSE Mathematics (0580, Extended): Geometry: circle theorems (angle in a semicircle, tangent and radius, angle at the centre, angles in the same segment, cyclic quadrilaterals, alternate segment) and the symmetry properties of chords and tangents • GCSE Mathematics (UK, Higher): Geometry and measures: apply and prove the standard circle theorems (G10), combined with angle facts and Pythagoras in reasoned, multi-step problems • US Geometry and the SAT: Circles: inscribed angles, the tangent–radius relationship and inscribed quadrilaterals (G-C.2, G-C.3), and chord lengths with the Pythagorean theorem (G-SRT.8); SAT Geometry and Trigonometry (circles) Students will be able to: • use the angle at the centre (including reflex angles) and the angle in a semicircle, with isosceles triangles made by radii • use angles in the same segment and the angle properties of cyclic quadrilaterals, including the exterior angle, to form and solve equations • use the facts that a tangent meets a radius at 90° and that two tangents from a point are equal, with Pythagoras • use the alternate segment theorem with isosceles triangles, parallel lines and cyclic quadrilaterals, and prove it • use the perpendicular from the centre to a chord with Pythagoras to find chords, distances and radii, and solve multi-step problems giving full reasons Calculator use: all five lessons and the whole unit test are non-calculator, matching how circle theorems are tested on the non-calculator papers of IGCSE and GCSE: every angle is a whole number or an exact decimal, and every length is a whole number or a simplified surd. All questions are original and written for this course. British spelling is used.

Unit 9 · Similarity and Congruence: Same Shape, Different Size
Unit overview By the end of this unit, students can prove that two triangles are congruent using SSS, SAS, ASA (or AAS) and RHS, find scale factors and missing lengths in similar shapes, spot similar triangles in nested and bow-tie diagrams, and use the area factor k² and the volume factor k³ for areas, surface areas, volumes, masses and capacities. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (44 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Congruent and similar triangles, scale factors and enlargement, and the ratios of lengths, areas and volumes of similar figures (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Congruence and similarity: calculating lengths of similar shapes, and using the relationships between lengths, areas and volumes of similar shapes and solids • GCSE Mathematics (UK, Higher): Congruence criteria SSS, SAS, ASA and RHS and simple proofs (G5, G6); similarity and scale factors for lengths, areas and volumes (G19) • US Geometry and the SAT: Triangle congruence and similarity criteria used to solve problems and prove relationships (HSG-CO.B.8, HSG-SRT.B.5); SAT Geometry and Trigonometry questions on similar triangles Students will be able to: • choose the correct test (SSS, SAS, ASA/AAS or RHS) and write a short congruence proof with a reason for each step • find the scale factor between similar shapes and use it to find a missing length, or show that two shapes are not similar • find lengths in similar triangles, including nested and bow-tie triangles and part of a side • use the area factor k² to find areas, and find k from two areas • use the volume factor k³ for volumes, masses and capacities, find k from two volumes, and move between length, area and volume factors Calculator use: all five lessons and the whole unit test are non-calculator, matching the non-calculator papers of IGCSE and GCSE, where these skills are often tested. Scale factors are friendly numbers and every cube root is the root of a perfect cube. All questions are original and written for this course. British spelling is used (US: "dilation" for "enlargement").

Unit 10 · Statistics II: Read the Shape of Any Data Set
Unit overview By the end of this unit, students can build and read cumulative frequency tables and curves, find the median, quartiles, interquartile range and percentiles from them, draw and compare box plots, draw and read histograms with unequal class widths using frequency density, and calculate the mean deviation, variance and standard deviation, choosing the most suitable average and measure of spread for a data set. The unit has five lessons of about 15 minutes, each ending with a five-question exit quiz, and an exam-style unit test: Section A has 18 multiple-choice questions and Section B has five structured problems with marks shown on every part, a model solution and an M/A/B mark scheme (45 marks, 70 minutes). Every practice and quiz question comes with a full step-by-step solution, and the practice set in each lesson rises from warm-up questions to exam-standard and challenge questions. These skills map to the main upper-secondary courses and exams: • WASSCE Core Mathematics (WAEC): Statistics: cumulative frequency tables and curves (ogives), the median, quartiles, interquartile range and percentiles, histograms, and the mean deviation, variance and standard deviation of ungrouped and grouped data (Paper 1 objectives and Paper 2 structured questions) • Cambridge IGCSE Mathematics (0580, Extended): Statistics: cumulative frequency diagrams, the median, quartiles, interquartile range and percentiles, box-and-whisker plots, histograms with unequal class widths (frequency density), and comparing distributions • GCSE Mathematics (UK, Higher): Statistics: cumulative frequency graphs, box plots, histograms with unequal class widths, quartiles and the interquartile range, and comparing distributions using an average and a measure of spread (S3, S4) • US Algebra I and the SAT: Summarising, representing and interpreting data (S-ID.1–3): box plots and histograms, comparing centre (median, mean) and spread (interquartile range, standard deviation), and the effect of extreme values; SAT Problem-Solving and Data Analysis Students will be able to: • make a cumulative frequency table, plot the points at the upper class boundaries, and read "at most", "more than" and "between" values from the curve • find the median, quartiles, interquartile range and percentiles from a cumulative frequency curve, and work backwards from a percentage to a value • find the five-number summary of a list, draw and read box plots, test for outliers, and compare two distributions using an average and a spread in context • draw histograms with unequal class widths using frequency density, and read frequencies, totals and estimates within part of a class from a histogram • calculate the mean deviation, variance and standard deviation of a list or a frequency table (dividing by n), and choose a suitable average and measure of spread Calculator use: Lessons 1–4 and Section A of the unit test are non-calculator. Every reading from a cumulative frequency curve falls on a plotted point, and the class widths and frequencies are chosen so that the divisions are short. Lesson 5 and Section B allow a calculator, as in the IGCSE and GCSE calculator papers and WASSCE Paper 2, where standard deviations usually appear; every rounded answer states its accuracy. The variance is always the population variance (divide by n), so students should use σx (or σn) on a calculator, not sx. All questions and data sets are original and written for this course. British spelling is used.