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WASSCE · 22 topics

Additional Mathematics

G3N tutors you through the full WASSCE Additional Mathematics syllabus offline — from Number and Algebraic Patterns, Applications of Algebra, Spatial Sense and more — with adaptive lessons, instant quizzes and exam-ready summaries.

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Syllabus

What you’ll cover in Additional Mathematics.

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

Year 1

8 topics
Number and Algebraic Patterns
  • Solve problems involving properties of binary operations
    • Describe and interpret the characteristics of commutative, associative, distributive and closure properties of binary operations
    • Determine the identity element of a binary operation and use it to find the inverse of a given element
    • Establish the properties of operations on sets, including commutative, associative, and distributive properties, sets algebra, and apply them to solve problems
    • Expand binomial expressions for positive integer indices using Pascal's triangle
    • Use the combination approach and other approaches to determine the coefficient and exponent of a given term in a binomial expansion
  • Perform basic operations on surds and solve simple indicial and logarithmic equations
    • Rationalise surds with binomial denominators
    • Recollect the initial laws of indices and establish other laws for negative powers and roots
    • Recognise the relationship between surds and indices and apply laws of indices to simplify expressions
    • Pose and solve simple equations involving indices
Applications of Algebra
  • Examine, analyse, determine and predict other terms in a pattern or sequence
    • Recognise sequences as an enumerated collection of objects in which repetitions are allowed and classify sequences into linear or exponential
    • Find the nth term of linear and exponential sequences
  • Distinguish among various types of relations, find the domain and range, and evaluate functions
    • Identify relations and functions and describe their differences
    • Use function notation to evaluate functions for inputs in their domain and outputs in the co-domain
    • Establish, describe and determine bijective functions and composite functions
    • Find the inverse of simple functions
    • Determine the composite of two given functions
    • Recognise and use appropriate algebraic notation for properties of linear and non-linear functions and solve them simultaneously
    • Recognise linear equations in two variables, draw their graphs, and find the area enclosed by two graphs
    • Solve up to three systems of linear equations simultaneously by algebraic manipulations
  • Perform operations on matrices and apply them to solve problems
    • Recognise a matrix (including types of matrices) and state its order
    • Add and subtract 2×2 matrices and multiply a matrix by a scalar and a matrix by a matrix (2×2 matrices)
Spatial Sense
  • Describe the properties of lines, including parallel, perpendicular and midpoints
    • Describe the properties of parallel and perpendicular lines and midpoints of line segments
    • Predict the midpoint of a line segment given two points and find the generalisation of the midpoint formula
    • Recall the formula for finding the gradient of a line and apply it to find the equation of a straight line in various forms
    • Use standard algebraic manipulations to find the equation of parallel and perpendicular lines, including the equation of the perpendicular bisector of a line
    • Determine the acute angles between two intersecting lines with the aid of technological tools such as GeoGebra
    • Apply knowledge of gradient and the tangent function to find the acute angle between two intersecting lines
  • Perform algebraic manipulations of vectors and resolve vectors using the triangle, parallelogram and polygon laws of addition
    • Perform algebraic and graphical operations on vectors (addition, subtraction, scalar multiplication) and interpret their geometrical meaning
    • Determine the resultant of vectors using the triangle and parallelogram laws of addition
Measurement of Triangles
  • Describe diagrammatically and algebraically ways of representing problems involving angles of elevation and depression and solve related word problems
    • Recall basic trigonometric ratios and use the knowledge to solve problems relating to triangles
    • Use special triangles and the unit circle to determine the geometrical and functional values of trigonometric ratios, including special angles
  • Identify values of the special angles in degrees and radians and solve problems relating to the coordinates of the unit circle
    • Determine radian measure and apply the knowledge to solve practical problems of arc length
    • Identify the coordinates of the quadrantal angles in a unit circle and use them to find the trigonometric values of quadrantal angles
Principles of Calculus
  • Describe graphically and algebraically the behaviour of a function about an input value and determine its derivative
    • Describe and interpret the meaning of the limit of a function through graphical and algebraic approaches
    • Classify left-hand and right-hand limits algebraically and with the aid of technology
    • Distinguish between continuous and discontinuous functions near an input value on its domain
    • Use the limits of a function to find its derivative
    • Investigate the rate of change of a function with respect to a variable using technology or innovative approaches
    • Generalise the behaviour of a moving object along a path or curve
Applications of Calculus
  • Determine the equation of tangents and normal to a curve at a given point
    • Use knowledge of differentiation to determine the equation of tangents and normal to curves at a given point
    • Apply differentiation to find the rate of change
Organising, Representing and Interpreting Data
  • Collect quantitative and qualitative data, and organise and present data using graphs
    • Identify and present appropriate ways of collecting and representing data
    • Categorise data and determine which scale of measurement describes the data
    • Organise data into appropriate frequency distribution tables manually and with Microsoft Excel
    • Present data using appropriate graphs by hand and/or by technology and justify why a particular representation is more suitable than others for a given situation
    • Compare various statistical representations and justify why a particular representation is more suitable than others for a given situation
  • Calculate the measures of central tendency and measures of dispersion and interpret the results
    • Calculate measures of central tendency (mode, mean and median) for a given data by formulas or other techniques and establish which is appropriate to report on a given data
    • Work out simple measures of dispersion (range, quartile and inter-quartile range) for raw data and interpret them in context
Making Predictions with Data
  • Explain combination and permutation, state their difference, and solve basic problems related to permutation and combination
    • Use the fundamental counting principle to identify and determine the number of ways an event can occur
    • Discuss the concepts of permutation and combination and use them to solve real life problems
    • Distinguish between the concepts of permutation and combination and establish the relationship between them
    • Simplify permutation and combination expressions and solve related problems
  • Explain the terminologies in probability and find the relative frequency in a given experiment
    • Conduct an experiment (e.g. tossing coins or dice) to determine the relative frequencies of events and interpret them

Year 2

7 topics
Application of Algebra
  • Investigate De Morgan's law on sets algebraically and graphically, formulate and solve real life problems up to three sets
    • Describe set theory as a foundation for many subfields of mathematics and create and model set problems in areas pertaining to industry, commerce, and sports
    • Use the expansion for (1-x)^n or (1+x)^n to approximate exponential numbers
  • Examine sequences, generate terms of recurrence sequences and apply arithmetic and geometric sequences to real life problems
    • Generate the terms of a recurrence sequence and find an explicit formula for the sum of the sequence
    • Use recursive and explicit formulae of sequences to model situations and translate between the two forms
    • Determine the arithmetic and geometric means of linear and exponential sequences and apply linear and exponential sequences to solve real life problems
  • Apply indices and logarithms to solve real life problems, sketch and interpret logarithmic functions, and solve quadratic inequalities and linear programming problems
    • Review indices and apply the idea to create and solve real life problems involving indices
    • Use the properties of logarithms and indices to solve equations involving logarithms, including changing the base
    • Draw graphs of logarithmic functions using appropriate technology and by hand, and interpret them
    • Describe the processes of solving quadratic equations by graphical method, factorisation, and inspection for quadratic functions
    • Solve quadratic inequalities involving real life problems
    • Use a graphical approach (by hand and technology) to solve simultaneous linear inequalities
    • Predict and identify the region representing the solution to systems of linear inequality
    • Determine the maximum and minimum values within given constraints
  • Multiply matrices, determine the inverse of a 2×2 matrix, find the determinant up to a 3×3 matrix and represent matrices in linear transformations
    • Distinguish between singular and non-singular square matrices (2×2 and 3×3) and evaluate determinants
    • Multiply an m×n matrix by an n×1 matrix
    • Transform systems of linear equations into matrix form and state the matrix representing a linear transformation
    • Find the inverse of a matrix using linear transformation
    • Model and solve problems based on real life situations using matrices
Spatial Sense
  • Deduce the equation of a circle and find its centre and radius
    • Explore the equation of a circle and its properties using technological tools such as GeoGebra and Geometer's Sketchpad
    • Apply knowledge of the distance between two points and the Pythagoras theorem to describe a circle in algebraic form
    • Apply knowledge of properties of lines to derive the equations of a circle, a tangent and normal to a circle
    • Deduce relations of various loci under given conditions
  • Apply knowledge of vectors to solve geometric problems including the dot product and applications to triangles
    • Apply the knowledge of vector operations to solve simple geometric problems, including the position vector of a point that divides a vector internally and externally in a given ratio
    • Derive the rule for scalar (dot) product and use it to solve problems relating to angles between two vectors
    • Use vectors to establish the sine and cosine rules and solve problems involving areas of polygons
Measurement of Triangles
  • Find trigonometric values using compound, multiple and half angles and prove the sine and cosine rules
    • Prove and apply compound angles to derive the identities for multiple angles and half angles
    • Derive the sine and cosine rules and apply them to solve problems
    • Use correct algebraic techniques to isolate trigonometric functions and find the values of angles that make a trigonometric equation true
Principles of Calculus
  • Determine the appropriate rule and use it to find the derivative of a function
    • Identify the rules of differentiation (power rule, product rule, quotient rule, chain rule)
    • Apply the product and quotient rules to differentiate functions
    • Identify and apply techniques of differentiation to solve problems involving transcendental functions
    • Generalise the behaviour with respect to the slope of a moving object along a curve
  • Estimate the area under a curve using the trapezoid rule
    • Distinguish between partitioning an interval for a given step size and the number of subintervals
    • Identify and write a definite integral notation and its connection to the limits of the partial sum of areas; identify integration as a reverse process of differentiation
    • Compare and judge the effect of reduction in step size and increase in the number of subintervals in an interval for a given function on the area under a curve
Applications of Calculus
  • Investigate the turning point of a function
    • Find the maximum and minimum values and points of a function, sketch the functions and solve some real life problems
    • Use the second derivative of a function to classify the maximum, minimum and saddle point of that function and perform curve sketching
Organising, Representing and Interpreting Data
  • Conduct research on a given situation, collect, organise, and represent the data graphically and explain the findings using the graphs
    • Undertake research to gather data using appropriate tools and present graphical representations of findings
Making Predictions with Data
  • Solve problems using the axioms and the laws of probability
    • Use De Morgan's law in set theory to establish the addition and multiplication laws of probability and apply them to solve real life problems
  • Solve real life problems using combination and permutation
    • Describe the number of ways objects can be arranged using fundamental counting principles
    • Solve real life problems involving permutations
    • Model and solve real life problems involving combinations

Year 3

7 topics
Applications of Algebra
  • Construct compound statements and truth tables using logical connectives
    • Form statements including negation statements and comment on them
    • Draw implications from given statements and their converses
    • Identify and construct compound statements and form simple statements using the connectives
    • Use conjunction, disjunction, implication and negation to construct truth tables of compound statements
  • Apply linear transformation in finding images of points and object points, reflections, rotations and compositions of transformations
    • Find the equation of the image of a line under a linear transformation
    • Use linear transformation to determine image and object points
    • Find the composition of linear transformations
    • Apply linear transformation in finding translations, reflections, rotations and enlargements of points and plane figures
Spatial Reasoning
  • Construct a parabola of a given quadratic equation and explain its key features
    • Describe the shape of the graphs of quadratic functions
    • Explore the graphs of quadratic functions with different parameters using technological tools such as GeoGebra and Geometer's Sketchpad, or by hand
    • Explore and describe the features of a parabola (focus, directrix, axis of symmetry and vertex) using a technological tool and relate it to real life
  • Sketch a parabola given the directrix and focus
    • Describe a given locus as a parabola
    • Deduce the directrix and focus from a parabolic equation and vice versa
    • Describe the appropriate orientation of a parabola given its equation
    • Use the directrix and focus to sketch a parabola
  • Deduce the equation of the tangent and normal to a parabola
    • Describe the equation of lines and derivatives of functions in the context of parabolas
    • Determine the equations of the tangent and normal to a parabola at a given point
    • Find the point of intersection for a line and a parabola
Measuring Triangles
  • Draw and analyse basic trigonometric graphs using values of the unit circle, maximum values and minimum values
    • Sketch basic trigonometric graphs by hand and/or by technological tools and analyse their properties in the unit circle
    • Identify the maximum and minimum values of trigonometric graphs and the turning points of trigonometric functions
    • Review compound angle identities and use them to derive harmonic identities
    • Find the maximum and minimum values of a trigonometric function expressed in the form a sin x + b cos x
Principle of Calculus
  • Identify and apply the integration rules to evaluate integrals
    • Identify and apply the basic rules of integration (power rule, sum rule, difference rule, multiplication by a constant) to evaluate integrals
    • Identify and apply appropriate techniques for integration of a function, including the method of substitution for definite and indefinite integrals
    • Identify and apply appropriate techniques of integration to solve problems involving transcendental functions (exponential and natural logarithm functions)
Application of Calculus
  • Determine distance, area under a curve and volumes of solids of revolution
    • Find the area under a constant function or curve and distinguish between total area, net area and signed area
    • Find the area between two curves
    • Find the volume of a solid formed after rotation about a horizontal or vertical axis
Organising and Representing and Interpreting Data
  • Describe the nature and strength of relationship between two given variables using scatter diagrams and correlation coefficient
    • Distinguish between univariate and bivariate data and give examples and explain the concept of correlation
    • Construct a scatter plot using given data sets and use it to describe the relationship between two variables
    • Analyse and describe visual data in a scatter plot by interpreting the relationship between given bivariate data sets
    • Describe the Spearman's Rank correlation coefficient and interpret the results within a given situation
  • Model and solve problems using regression analysis
    • Describe the concept of regression and distinguish between correlation and regression, and describe situations that call for the use of regression
    • Fit a linear function to given data and use the line of best fit to solve problems in the context of the data
Making Predictions with Data
  • Solve problems involving conditional probability using permutations and combinations
    • Explain the concepts that give rise to conditional probabilities
    • Describe the probability of two equally likely events occurring from given experiments
    • Model and solve real life problems involving conditional probabilities
    • Model and solve real life problems involving binomial probability
  • Use the concepts of permutation and combination to solve real life problems
    • Model and solve real life problems involving permutation and combination
    • Determine areas in business, commerce and industry where permutations and combinations can be applied to improve systems
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