G3N
WASSCE · 18 topics

Mathematics

G3N tutors you through the full WASSCE Mathematics syllabus offline — from Number Sets, Fractions and Percentages, Algebraic Expressions and Factorisation and more — with adaptive lessons, instant quizzes and exam-ready summaries.

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Syllabus

What you’ll cover in Mathematics.

The complete topic outline G3N teaches, mapped to the WASSCE curriculum.

Year 1

3 topics
Number Sets
  • Develop the real number system using the closure property
    • Identify natural numbers as counting numbers starting from 1 to infinity
    • Identify whole numbers as numbers starting from 0 to infinity
    • Identify integers as the set of positive and negative whole numbers including zero
    • Define rational numbers as numbers expressible as a/b where a and b are integers and b ≠ 0
    • Recognise irrational numbers as numbers that cannot be expressed as a/b (e.g. √2, π)
    • Define real numbers as the combination of rational and irrational numbers
    • Distinguish terminating decimals (finite digits) from non-terminating decimals (endless digits)
    • Identify recurring (repeating) decimals as non-terminating decimals with a repeating pattern
  • Distinguish between rational and irrational numbers and solve related problems
    • Convert recurring decimals to common fractions using algebraic method (multiply by 10^n)
    • Convert terminating decimals to fractions by placing over a power of 10
    • Convert fractions to decimals by dividing the numerator by the denominator
    • Apply the Pythagorean Spiral (Wheel of Theodorus) to generate irrational numbers
    • Compare and order rational and irrational numbers on a number line
    • Apply rational numbers in real-life contexts such as banking, sharing, and calculating scores
    • Apply irrational numbers in contexts involving circles, trigonometry, and engineering
  • Establish the properties of real numbers: Commutative, Associative, Distributive, Identity, and Inverse
    • State the commutative property for addition: a + b = b + a
    • State the commutative property for multiplication: a × b = b × a
    • State the associative property for addition: (a + b) + c = a + (b + c)
    • State the associative property for multiplication: (a × b) × c = a × (b × c)
    • State the distributive property: a × (b + c) = a × b + a × c
    • Identify additive identity (0) and multiplicative identity (1)
    • Identify additive inverse (opposite) and multiplicative inverse (reciprocal) of real numbers
    • Apply properties of real numbers to simplify arithmetic expressions
  • Apply properties of subsets (two and three sets) to solve real-life problems
    • Define sets, subsets, and proper subsets
    • Distinguish between subsets and proper subsets using set notation
    • Perform union and intersection operations on two sets
    • Find the complement of a set within a universal set
    • Represent two-set relationships using Venn diagrams
    • Solve two-set word problems using Venn diagrams and set formulas
    • Represent three-set relationships using Venn diagrams
    • Apply the formula n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C)
Fractions and Percentages
  • Establish the concept of fractions and perform operations on fractions
    • Define a fraction as a numerical value representing parts of a whole, group, or ratio
    • Identify the numerator (number of selected parts) and denominator (total equal parts) of a fraction
    • Classify fractions as proper, improper, mixed, like, unlike, equivalent, or unit fractions
    • Generate equivalent fractions by multiplying or dividing numerator and denominator by the same factor
    • Identify benchmark fractions (0, 1/4, 1/2, 3/4, 1) and use them as reference points
    • Represent fractions on a number line, with paper strips, and using Cuisenaire rods
    • Add and subtract fractions and mixed numbers with like and unlike denominators
    • Multiply fractions using the rule: numerators multiply numerators, denominators multiply denominators
  • Investigate connections between fractions, decimals, and percentages
    • Convert fractions to decimals by dividing numerator by denominator or finding an equivalent fraction over a power of 10
    • Convert decimals to fractions by placing the decimal over the appropriate power of 10 and simplifying
    • Convert percentages to fractions by writing the percentage as a fraction out of 100
    • Convert fractions to percentages by multiplying the fraction by 100
    • Convert decimals to percentages by multiplying the decimal by 100
    • Convert percentages to decimals by dividing by 100
    • Recognise that fractions, decimals, and percentages are equivalent representations of the same value
    • Apply conversions between fractions, decimals, and percentages in real-life contexts
  • Establish additive and multiplicative inverses of fractions using multi-purpose model charts
    • Define additive inverse: the number that when added to a fraction gives zero (opposite sign)
    • Find the additive inverse of proper, improper, and mixed fractions
    • Define multiplicative inverse (reciprocal): the number that when multiplied by a fraction gives 1
    • Find the multiplicative inverse of fractions by swapping numerator and denominator
    • Use multi-purpose model charts (fraction strips, grids, number lines) to visualise inverses
    • Verify additive inverse: a/b + (−a/b) = 0
    • Verify multiplicative inverse: a/b × b/a = 1
  • Apply percentages to solve real-life problems involving finance and commerce
    • Calculate percentage increase using the formula: (increase ÷ original price) × 100%
    • Calculate percentage decrease using the formula: (decrease ÷ original price) × 100%
    • Define commission as a percentage fee paid to an agent for facilitating a sale
    • Calculate commission using: Commission = commission rate × selling price
    • Define discount as a reduction in the original price expressed as a percentage
    • Calculate selling price after discount and find the marked price given the selling price and discount
    • Define profit as the gain when selling price exceeds cost price
    • Calculate profit and percentage profit: (profit ÷ cost price) × 100%
  • Solve problems involving simple and compound interest
    • Define principal (P), rate (R), time (T), and simple interest (S.I.)
    • Apply the simple interest formula: S.I. = (P × R × T) / 100
    • Calculate the amount at the end of a period using A = P + S.I. = P(1 + TR/100)
    • Rearrange the simple interest formula to find P, R, or T given the other quantities
    • Distinguish between simple interest (calculated on original principal only) and compound interest (calculated on accumulated amount)
    • Apply the compound interest formula: A = P(1 + R/100)^n
    • Calculate compound interest for annual, semi-annual, quarterly, and monthly compounding periods
    • Solve real-life problems involving savings accounts, loans, and investments using simple and compound interest
Algebraic Expressions and Factorisation
  • Use number patterns and variables to formulate and simplify algebraic expressions
    • Identify number patterns and determine the rule or nth term of a sequence
    • Write algebraic expressions for the nth term of a pattern
    • Define key algebraic terms: variable, constant, term, coefficient, monomial, binomial, trinomial
    • Formulate algebraic expressions to model real-life situations
    • Add and subtract like terms to simplify algebraic expressions
    • Multiply algebraic expressions using the distributive property
    • Divide algebraic expressions by finding and cancelling common factors
    • Apply the algebraic order of operations (BODMAS/PEDMAS) to evaluate and simplify expressions
  • Factorise algebraic expressions using various methods
    • Factorise expressions by identifying and extracting the highest common factor (HCF)
    • Factorise four-term expressions by grouping (regrouping of terms)
    • Use algebraic tiles to model and solve factorisation problems
    • Apply standard algebraic identities: (a+b)² ≡ a² + 2ab + b² and (a−b)² ≡ a² − 2ab + b²
    • Factorise quadratic trinomials of the form x² + bx + c by splitting the middle term
    • Verify factorisation by expanding the factors back to the original expression
    • Apply factorisation to solve simple equations and real-life problems
  • Recognise perfect squares and apply the difference of two squares
    • Identify perfect square numbers (4, 9, 16, 25, ...) and perfect square expressions
    • Recognise expressions in the form a² as perfect squares
    • State the difference of two squares identity: a² − b² = (a + b)(a − b)
    • Factorise expressions of the form a² − b² using the identity
    • Apply the difference of two squares to evaluate numerical expressions without a calculator
    • Solve equations and real-life problems involving the difference of two squares
    • Distinguish between a perfect square and a difference of two squares
  • Perform operations on algebraic fractions and determine conditions for zero or undefined
    • Define an algebraic fraction as a fraction containing at least one variable
    • Simplify algebraic fractions by cancelling common factors in numerator and denominator
    • Add and subtract algebraic fractions with monomial denominators using LCM
    • Add and subtract algebraic fractions with binomial denominators using LCM
    • Multiply algebraic fractions by multiplying numerators together and denominators together
    • Divide algebraic fractions by multiplying by the reciprocal of the divisor
    • Determine values of the variable that make an algebraic fraction undefined (denominator = 0)
    • Determine values of the variable that make an algebraic fraction equal to zero (numerator = 0)

Year 2

9 topics
Number Sets
  • Simplify surds and perform operations on surds
    • Define a surd as an irrational number that cannot be simplified to remove the root symbol
    • Identify pure surds (entire expression is a surd) and mixed surds (rational × surd, e.g. 3√2)
    • Identify compound surds as the sum or difference of two or more surds
    • Simplify surds by extracting perfect square factors (e.g. √12 = 2√3)
    • Add and subtract like surds by collecting like terms
    • Multiply surds using √a × √b = √(ab)
    • Divide surds using √a ÷ √b = √(a/b)
    • Rationalise the denominator of a fraction with a surd by multiplying by the conjugate
  • Apply laws of indices and solve exponential equations
    • Define a positive index as repeated multiplication (m^a = m × m × ... × a times)
    • Define zero index: any non-zero base raised to the power 0 equals 1 (m^0 = 1)
    • Define negative index: m^(−a) = 1/m^a
    • Apply the product rule for indices: m^a × m^b = m^(a+b)
    • Apply the quotient rule for indices: m^a ÷ m^b = m^(a−b)
    • Apply the power of a power rule: (m^a)^b = m^(ab)
    • Interpret and evaluate fractional indices: m^(1/n) = nth root of m; m^(p/q) = (m^(1/q))^p
    • Solve exponential equations by expressing both sides with the same base and equating exponents
  • Apply laws of logarithms to simplify expressions and solve equations
    • Define logarithm as the inverse of an index: if a^x = N then log_a(N) = x
    • Apply the product law of logarithms: log_a(MN) = log_a(M) + log_a(N)
    • Apply the quotient law of logarithms: log_a(M/N) = log_a(M) − log_a(N)
    • Apply the exponent law of logarithms: log_a(M^n) = n × log_a(M)
    • Apply the change of base law: log_a(N) = log_b(N) / log_b(a)
    • Evaluate log_a(a) = 1 and log_a(1) = 0
    • Use logarithm tables and calculators to evaluate logarithms and antilogarithms
    • Solve logarithmic equations using the laws of logarithms
  • Perform operations in modular arithmetic and solve congruence problems
    • Define modular arithmetic as remainder arithmetic (mod n means finding the remainder after dividing by n)
    • Perform addition in modular arithmetic: (a + b) mod n
    • Perform subtraction in modular arithmetic: (a − b) mod n
    • Perform multiplication in modular arithmetic: (a × b) mod n
    • Perform division in modular arithmetic using modular inverse
    • State properties of modular arithmetic: commutative, associative, identity, and inverse properties
    • Find the modulo of negative numbers by adding multiples of the modulus until positive
    • Define congruence: a ≡ b (mod n) means n divides (a − b)
Equations and Inequalities
  • Solve simultaneous linear equations using elimination, substitution, and graphical methods
    • Define simultaneous equations as a system of two or more equations with the same unknowns
    • Solve simultaneous linear equations using the elimination method by manipulating coefficients to eliminate one variable
    • Solve simultaneous linear equations using the substitution method by rearranging one equation and substituting into the other
    • Solve simultaneous linear equations using the graphical method by plotting both equations and finding the point of intersection
    • Translate real-life word problems into simultaneous equations
    • Interpret solutions of simultaneous equations in the context of the problem
    • Verify solutions by substituting back into both original equations
Rigid Motion
  • Perform and describe geometric transformations including translation, reflection, rotation, and enlargement
    • Define translation as a transformation that moves every point of a shape by the same vector v = (a, b)
    • Apply the translation rule: (x, y) → (x + a, y + b) to find image coordinates
    • Recognise that translation produces a congruent image with the same orientation
    • Define reflection as a transformation that flips a shape across a mirror line
    • Apply reflection rules: across x-axis (x, y) → (x, −y); across y-axis (x, y) → (−x, y)
    • Apply reflection rules: across y = x: (x, y) → (y, x); across y = −x: (x, y) → (−y, −x)
    • Define rotation as a transformation that turns a shape about a fixed centre of rotation by a given angle
    • Perform clockwise and counterclockwise rotations of 90°, 180°, and 270° about the origin
Data Collection, Organisation and Representation
  • Design and use data collection instruments for statistical investigations
    • Identify types of data collection instruments: questionnaire, interview guide, observation guide, and survey
    • Distinguish between quantitative and qualitative data collection instruments
    • Design a questionnaire following a 9-step process: define objectives, identify population, choose type, draft questions, review, pilot, refine, distribute, collect
    • Formulate clear, unbiased, and relevant questions for a questionnaire
    • Design an interview guide with structured or semi-structured questions
    • Design an observation guide with specific observable criteria
    • Select the most appropriate data collection instrument for a given statistical investigation
  • Organise and represent data using cumulative frequency tables, ogives, waffle charts, and box-and-whisker plots
    • Construct cumulative frequency tables from raw data or frequency distributions
    • Draw less-than ogives by plotting cumulative frequency against upper class boundaries
    • Draw more-than ogives by plotting cumulative frequency against lower class boundaries
    • Use ogives to estimate the median, quartiles, and percentiles
    • Construct a waffle chart using a 10×10 grid where each cell represents 1% of the data
    • Interpret waffle charts to compare proportions visually
    • Identify the five-number summary: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum
    • Draw a box-and-whisker plot using the five-number summary
  • Conduct a real-life data collection project and present findings using appropriate charts
    • Design a data collection instrument for a real-life mini-project
    • Distribute the instrument, collect responses, and tally the data
    • Organise collected data into a frequency distribution table
    • Present data using a bar chart, pie chart, and histogram
    • Interpret the charts and draw conclusions from the collected data
  • Calculate and interpret measures of dispersion: range, mean absolute deviation, variance, standard deviation, and interquartile range
    • Calculate the range as the difference between the maximum and minimum values
    • Calculate mean absolute deviation (MAD) as the mean of the absolute deviations from the mean
    • Define variance as the mean of the squared deviations from the mean: v = Σ(x − x̄)² / n
    • Calculate variance for ungrouped and grouped data
    • Calculate standard deviation as the square root of the variance
    • Interpret standard deviation as a measure of how spread out values are from the mean
    • Calculate the interquartile range (IQR) as Q3 − Q1
    • Calculate quartile deviation as IQR / 2
Ratios, Rates and Proportions
  • Distinguish between ratios and rates and apply them to solve problems
    • Define ratio as a comparison of two or more quantities of the same type
    • Distinguish between part-to-part ratios and part-to-whole ratios
    • Define rate as a comparison of two quantities with different units (e.g. km/h, GHS/kg)
    • Calculate unit rate by dividing the quantity by the number of units
    • Scale ratios up or down to find equivalent ratios
    • Set up proportions from equivalent ratios and solve for unknown quantities
  • Apply direct proportion and proportional reasoning to solve problems
    • Define direct proportion: as one quantity increases, the other increases at a constant rate
    • Recognise the constant of proportionality k in y = kx
    • Solve proportion problems using the cross-multiplication method
    • Apply proportional reasoning to scale drawings, maps, and models
    • Solve word problems involving direct proportion in everyday contexts
  • Interpret and analyse distance-time graphs
    • Identify distance on the y-axis and time on the x-axis in a distance-time graph
    • Calculate speed from a distance-time graph as the gradient of the line: speed = distance / time
    • Interpret a steeper line as a faster speed
    • Interpret a horizontal line segment as the object being at rest
    • Interpret a straight line as constant speed (uniform motion)
    • Interpret a curved line as acceleration or deceleration
    • Sketch a distance-time graph from a description of a journey
    • Solve problems using the formula: distance = speed × time
  • Apply ratios and proportions to financial mathematics and health calculations
    • Calculate Body Mass Index (BMI) using the formula: BMI = weight (kg) / height² (m²)
    • Interpret BMI values against standard health categories (underweight, normal, overweight, obese)
    • Calculate drug dosage for patients using proportional reasoning (mg per kg of body weight)
    • Apply percentage calculations to tax, discount, and salary problems
    • Solve real-life problems combining ratios, rates, and percentages
Patterns and Relations Involving Sequences and Series
  • Analyse and extend arithmetic sequences and find their sums
    • Define an arithmetic (linear) sequence as a sequence with a constant common difference d
    • Find the common difference d = U_(n+1) − U_n for any arithmetic sequence
    • Apply the general term formula: U_n = a + (n − 1)d to find the nth term
    • Use the general term formula to find the number of terms n given the last term
    • Apply the sum formula for arithmetic sequences: S_n = n/2 × [2a + (n − 1)d]
    • Apply the alternative sum formula: S_n = n/2 × (first term + last term)
    • Identify and extend the Fibonacci sequence (each term is the sum of the two preceding terms)
    • Solve real-life problems modelled by arithmetic sequences (salary increments, stacking objects)
  • Analyse and extend geometric sequences and find their sums
    • Define a geometric (exponential) sequence as a sequence with a constant common ratio r
    • Find the common ratio r = U_(n+1) / U_n for any geometric sequence
    • Apply the general term formula: U_n = ar^(n−1) to find the nth term
    • Apply the sum formula for geometric sequences: S_n = a(r^n − 1) / (r − 1) for r ≠ 1
    • Distinguish between arithmetic and geometric sequences given a pattern
    • Solve real-life problems modelled by geometric sequences (compound interest, population growth, depreciation)
  • Apply sequences and series to financial and real-life problem solving
    • Calculate compound interest using the geometric sequence formula A_n = P × r^n
    • Calculate depreciation of assets using geometric decay: U_n = a × (1 − rate)^(n−1)
    • Model population growth using geometric sequences
    • Model salary increments and bonus schemes using arithmetic sequences
    • Solve multi-step real-life problems identifying whether arithmetic or geometric sequences apply
Surface Areas and Volumes
  • Calculate surface areas of three-dimensional shapes and convert between units
    • Distinguish between SI units of area (m², cm²) and Imperial units (ft², in²)
    • Convert between SI and Imperial area units
    • Calculate the surface area of a cuboid: 2(lw + lh + wh)
    • Calculate the total surface area of a cylinder: 2πr² + 2πrh
    • Calculate the surface area of a sphere: 4πr²
    • Calculate the surface area of a cone: πr² + πrl where l is the slant height
    • Calculate the surface area of a square-based pyramid: base area + 4 × triangular face area
    • Calculate the surface area of a triangular-based pyramid (tetrahedron)
  • Calculate volumes and capacities of three-dimensional shapes and apply to real-life problems
    • Distinguish between SI units of volume (m³, cm³, litres) and Imperial units (ft³, gallons)
    • Convert between volume units: 1 litre = 1000 cm³; 1 m³ = 1000 litres
    • Calculate the volume of a cube: s³
    • Calculate the volume of a cuboid: length × width × height
    • Calculate the volume of a cylinder: πr²h
    • Calculate the volume of a sphere: (4/3)πr³
    • Calculate the volume of a cone: (1/3)πr²h
    • Solve real-life problems involving container capacity, material quantities, and storage space
Working with Data and Probability Experiments
  • Conduct a statistical mini-project on data collection and analysis
    • Design a data collection instrument (questionnaire or survey) for a class project
    • Collect data from at least 50 students covering topics such as height, weight, or test scores
    • Tally responses and construct a frequency distribution table
    • Calculate measures of central tendency: mean, median, and mode
    • Calculate measures of dispersion: range, variance, and standard deviation
    • Present data using charts and graphs (bar chart, pie chart, histogram, ogive)
    • Interpret the results and draw conclusions from the analysis
  • Calculate and interpret simple probability
    • Define an experiment, sample space, event, and outcome in probability
    • List the sample space of a probability experiment using a table or tree diagram
    • Calculate the probability of an event: P(A) = number of favourable outcomes / total outcomes
    • Calculate the probability of the complement of an event: P(A') = 1 − P(A)
    • Distinguish between equally likely and non-equally likely outcomes
    • Apply probability to real-life situations (weather forecasting, games, quality control)
  • Calculate compound probabilities for mutually exclusive and independent events
    • Define mutually exclusive events as events that cannot occur at the same time
    • Apply the addition rule for mutually exclusive events: P(A ∪ B) = P(A) + P(B)
    • Define independent events as events where the occurrence of one does not affect the other
    • Apply the multiplication rule for independent events: P(A ∩ B) = P(A) × P(B)
    • Define dependent events as events where the occurrence of one affects the probability of the other
    • Calculate conditional probability for dependent events
    • Use tree diagrams to calculate compound probabilities for with-replacement and without-replacement scenarios
    • Solve real-life probability problems involving cards, dice, marbles, and surveys
Vectors and Trigonometry
  • Perform operations on vectors and apply vector properties in two dimensions
    • Distinguish between scalar quantities (magnitude only) and vector quantities (magnitude and direction)
    • Represent a position vector OM = (x, y) using column vector notation
    • Express vector AB as the difference of position vectors: AB = OB − OA = (x₂ − x₁, y₂ − y₁)
    • Add vectors graphically (head-to-tail rule) and algebraically
    • Subtract vectors: A − B = A + (−B)
    • Calculate the resultant vector as the vector sum of two or more vectors
    • Apply the commutative law for vector addition: a + b = b + a
    • Apply the associative law for vector addition: (a + b) + c = a + (b + c)
  • Apply trigonometric ratios to solve problems involving right-angled triangles, angles of elevation and depression, and bearings
    • State the three primary trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
    • Use the mnemonic SOH-CAH-TOA to recall trigonometric ratios
    • Apply Pythagoras' theorem: a² + b² = c² to find missing sides in right-angled triangles
    • Use trigonometric ratios to find a missing side given an angle and one side
    • Use inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) to find missing angles
    • Define angle of elevation as the angle measured upward from the horizontal
    • Define angle of depression as the angle measured downward from the horizontal
    • Solve problems involving angles of elevation and depression using trigonometric ratios

Year 3

6 topics
Logical Reasoning and Variations
  • Establish the validity of logical arguments and use them to make relevant decisions in solving problems
    • Define a logical statement (proposition) and determine whether it is true or false
    • Identify positive and negative statements and distinguish them from non-statements
    • Use logical connectives: 'and' (conjunction, ∧), 'or' (disjunction, ∨), 'not' (negation, ¬), and 'if…then' (conditional)
    • Construct compound statements using conjunction and disjunction with everyday examples
    • Build truth tables for conjunction (p ∧ q) and disjunction (p ∨ q)
    • Evaluate the truth value of compound statements using truth tables
    • Use Venn diagrams to represent and analyse logical arguments (e.g. 'All my brothers are farmers')
    • Make intelligent guesses to establish valid arguments and draw logical conclusions
  • Analyse the impact of variations and conduct simple investigations to solve day-to-day problems
    • Define direct variation: one variable increases as another increases at a constant rate (y = kx)
    • Identify the constant of proportionality k in a direct variation relationship
    • Apply direct variation to real-life examples such as area of a circle varying with the square of the radius
    • Define inverse variation: one variable increases as another decreases (y = k/x)
    • Apply inverse variation to examples such as subscription length and cost per year
    • Define joint variation: a variable varies directly with two or more other variables simultaneously
    • Apply joint variation to examples such as gravitational force (F = Gm₁m₂/d²)
    • Define partial variation: a variable is partly constant and partly varies with another (y = ax + c)
Quadratic Functions and Equations
  • Solve problems on quadratic functions and equations, including real-life problems
    • Distinguish between a quadratic expression (ax² + bx + c, a ≠ 0) and a quadratic equation (ax² + bx + c = 0)
    • Solve quadratic equations by the factorisation method, including splitting the middle term
    • Explain why the leading coefficient a cannot equal zero in a quadratic equation
    • Solve quadratic word problems by setting up and solving quadratic equations (e.g. dimensions of a rectangle given area and perimeter)
    • Draw graphs of quadratic functions by constructing a table of values
    • Identify the vertex (turning point), axis of symmetry, x-intercepts (roots), and y-intercept of a parabola
    • Determine the maximum or minimum value of a quadratic function from its graph
    • Solve quadratic equations graphically by reading the x-intercepts of the parabola
Circles, Geometric Construction, and Loci
  • Draw circles for given radii, apply circle theorems, and verify properties of tangents
    • Identify and label the parts of a circle: centre, radius, diameter, circumference, arc (major and minor), chord, secant, tangent, sector (major and minor), segment (major and minor), semi-circle, and quadrant
    • Draw a circle of a given radius using a compass and ruler by measuring the radius from the initial point
    • Construct a circle passing through three non-collinear points using perpendicular bisectors
    • State and apply the circle theorem: the angle subtended by a chord at the centre is twice the angle at the circumference
    • State and apply the circle theorem: the angle subtended by a diameter at the circumference is 90°
    • State and apply the circle theorem: angles subtended at the circumference by the same arc are equal
    • State and apply the circle theorem: two equal chords subtend equal angles at the centre
    • State and apply the circle theorem: opposite angles in a cyclic quadrilateral are supplementary (add to 180°)
  • Perform geometric construction of quadrilaterals and determine loci under given conditions
    • Recall and construct angles of 75°, 105°, 135°, and 150° using compass and straight edge
    • Construct a triangle given two sides and the included angle (SAS condition)
    • Construct a triangle given two angles and the included side (ASA condition)
    • Construct a triangle given all three angles and a side length
    • Construct a quadrilateral given sufficient information (sides and diagonal lengths)
    • State Locus Theorem 1: the locus of points at a fixed distance d from a point P is a circle with centre P and radius d
    • State Locus Theorem 2: the locus of points at a fixed distance d from a line l is a pair of parallel lines
    • State Locus Theorem 3: the locus of points equidistant from two fixed points P and Q is the perpendicular bisector of PQ
Trigonometric Graphs
  • Draw graphs of trigonometric functions and use them to determine equations and solve related problems
    • Identify the shape and key features of the sine graph: period 360°, amplitude 1, starting at (0°, 0), reaching maximum 1 at 90° and minimum −1 at 270°
    • Identify the shape and key features of the cosine graph: period 360°, amplitude 1, starting at (0°, 1), reaching minimum −1 at 180°
    • Identify the shape and key features of the tangent graph: period 180°, undefined at 90° and 270° (vertical asymptotes), crossing zero at 0°, 180°, and 360°
    • Construct a table of values and plot the sine function on the interval [0°, 360°]
    • Construct a table of values and plot the cosine function on the interval [0°, 360°]
    • Construct a table of values and plot the tangent function on the interval [0°, 360°]
    • Plot transformed trigonometric functions such as f(θ) = 2 sin θ + 3 and identify changes in amplitude and vertical shift
    • Relate the tangent function to the ratio sin θ / cos θ and explain why it is undefined where cos θ = 0
Bivariate Data and Statistical Reasoning
  • Establish simple mathematical relationships between two variables using scatter graphs and solve related problems
    • Define bivariate data as data involving two variables measured on the same individual or unit
    • Distinguish between univariate data (one variable) and bivariate data (two variables)
    • Identify the independent variable (x-axis) and the dependent variable (y-axis) in bivariate data
    • Collect bivariate data from observational studies (e.g. height vs weight, hours studied vs test score)
    • Plot bivariate data as a scatter graph by representing each observation as an ordered pair
    • Describe the relationship (correlation) shown by a scatter graph: positive, negative, or no correlation
    • Draw conclusions and justify them based on patterns observed in a scatter plot
    • Collect data from an experimental study with treatment and control groups and represent on a scatter graph
  • Compare different datasets and use appropriate mathematical vocabulary to make inferences and justify conclusions
    • Evaluate the quality of a dataset by considering precision, units, and suitability for the stated purpose
    • Compare two datasets representing the same information at different levels of precision (e.g. heights in cm vs metres)
    • Select the dataset that is most appropriate for analysis and explain the reasoning
    • Make inferences from data presented in charts, tables, or graphs and provide reasoned justifications
    • Interpret trends in data published in local and international media (newspapers, TV, journals)
    • Use appropriate statistical vocabulary (trend, range, mean, correlation) in oral and written discussions
    • Design and execute a mini data collection project on a contemporary community issue
    • Present findings using charts and tables and make conclusions with recommendations
Probability of Dependent and Independent Events
  • Apply probability reasoning to analyse dependent and independent events and solve real-life problems
    • Identify examples from print and electronic media where probability is used to influence decisions
    • Interpret a stated probability (e.g. 60% chance of rain) by explaining its meaning, assumptions, and limitations
    • Explain how weather forecasts, medical statistics, and sports outcomes use probability
    • Define independent events as events where the outcome of one does not affect the probability of the other
    • Apply the multiplication rule for independent events: P(A and B) = P(A) × P(B)
    • Define dependent events as events where the outcome of one affects the probability of the other
    • Apply the multiplication rule for dependent events: P(A and B) = P(A) × P(B | A)
    • Apply the addition law to find the probability that at least one of two events occurs
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