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CTVET · 17 topics

Mathematics

G3N tutors you through the full CTVET Mathematics syllabus offline — from Sets and Operations on Sets, Number Bases, Ratio and Rates 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 CTVET curriculum.

Form 1 (Grade 10)

5 topics
Sets and Operations on Sets
  • Demonstrate the knowledge of sets
    • Explain sets.
    • Identify symbols used in sets.
    • Distinguish between types of sets (Finite, Infinite, Equal, Equivalent, Null, Universal, Complement, Disjoint, Subset, Intersection and Union).
    • State ways of describing sets (Words, List, Set notation).
  • Demonstrate knowledge in operations on sets
    • Explain operations on sets.
    • Perform intersection operation on two or more sets.
    • Perform union operation on two or more sets.
    • Find complement from a given universal set.
    • State the properties of operation on sets (Commutative, Associative, Distributive).
  • Demonstrate knowledge in solving practical set problems
    • Explain the uses of Venn diagrams.
    • Identify regions in Venn diagrams.
    • Use Venn diagrams to solve two-set problems.
    • Use Venn diagrams to solve three-set problems.
Number Bases
  • Demonstrate knowledge in conversion of number bases
    • Explain number bases.
    • Convert from other number bases to base ten numerals.
    • Convert from number base ten to other number bases.
    • Convert from a non-decimal numeral to another non-decimal numeral.
    • Arrange number bases in a given order of magnitude (ascending, descending).
  • Demonstrate knowledge in operations of number bases
    • Add and subtract numbers in a given base.
    • Multiply numbers in a given base.
    • Construct addition and multiplication tables of numbers in given bases.
    • Use constructed tables to find truth set in given number bases.
  • Demonstrate knowledge in Modular Arithmetic
    • Explain modulo arithmetic.
    • Solve simple problems involving positive modulo arithmetic.
    • Simplify modular arithmetic involving large figures.
    • Apply modulo arithmetic to convert time zone from GMT to a.m. or p.m.
Ratio and Rates
  • Demonstrate knowledge in ratio
    • Explain ratio.
    • Express a given ratio as a fraction.
    • Simplify a given ratio.
    • Explain scale used in drawing graphs and plans.
  • Demonstrate knowledge in calculating ratio
    • Divide a quantity in a given ratio.
    • Find the unknown variable in a given ratio.
    • Convert a given currency to another.
    • Outline practical activities that involve ratio (building, catering, painting, finance).
  • Demonstrate knowledge of rates
    • Explain and list the various types of rates (speed, population density, pay, consumption).
    • Change one unit to another (inches to meters, feet to meters, miles to kilometres).
    • Apply rates in solving real life problems.
    • Draw and interpret travel graphs (velocity-time, distance-time).
    • Calculate and compare population densities.
Linear Equations and Inequalities
  • Demonstrate knowledge in linear equations
    • Explain linear equations.
    • Perform simple calculations involving linear equations.
    • Perform calculations on linear equations involving brackets.
    • Work out problems on linear equations involving fractions.
    • Compute word problems involving linear equations.
  • Demonstrate knowledge in linear inequalities
    • Explain linear inequalities and the inequality signs involved.
    • Apply the rules of linear inequalities and solve simple problems.
    • Solve linear inequality problems involving brackets.
    • Solve linear inequality problems involving fractions.
  • Demonstrate knowledge in application of linear inequalities
    • Represent inequalities on a number line.
    • Solve two-in-one linear inequality problems and represent on a number line.
    • Establish linear inequality relations from given statements.
Simultaneous Linear Equations
  • Demonstrate knowledge of linear equations in two variables
    • Explain a pair of simultaneous linear equations and its importance.
    • Explain substitution as a method of solving simultaneous equations.
    • Explain elimination as a method of solving simultaneous linear equations.
  • Demonstrate knowledge of methods of solving simultaneous linear equations
    • Solve a pair of simultaneous linear equations using the elimination method.
    • Solve a pair of simultaneous equations using the substitution method.
    • Solve simultaneous linear equations involving fractions.
    • Solve a pair of simultaneous linear equations involving indices.
  • Demonstrate knowledge of graphs in solving simultaneous linear equations
    • Explain the graphical method of solving simultaneous equations.
    • Draw straight line graphs from given linear equations.
    • Solve a pair of simultaneous equations using the graphical method.
    • Solve word problems involving simultaneous linear equations.

Form 2 (Grade 11)

5 topics
Quadratic Functions
  • Demonstrate knowledge of quadratic functions and equations
    • Explain quadratic functions.
    • Identify various quadratic functions.
    • Construct table of values of a quadratic function in a given range.
    • Plot a quadratic graph from a constructed table of values.
  • Demonstrate knowledge of features of quadratic equations and curves
    • Explain the equation of axis of symmetry of a curve.
    • Explain the turning point of a curve.
    • Find the coordinates at the turning point and determine maximum/minimum values.
    • Explain the range of x-values for which y increases or decreases, positive or negative.
  • Demonstrate knowledge of methods of solving quadratic equations
    • Solve quadratic equations by factorisation.
    • Solve quadratic equations using the quadratic formula.
Relations and Functions
  • Demonstrate knowledge of relations and functions
    • Explain relations.
    • Identify types of relations and functions (one-to-one, one-to-many, many-to-one, many-to-many).
    • Explain functions.
    • Identify types of mapping (linear, exponential).
  • Demonstrate knowledge in solving functional values
    • Find the rule for a mapping.
    • Find the image of a given function.
    • Construct the table of values for a given function.
  • Demonstrate knowledge in functions
    • Draw graphs for given functions (linear, quadratic).
    • Determine the gradient of a straight line.
    • Find the equation of a straight line.
    • Calculate the distance between two points.
Vectors and Bearings
  • Demonstrate knowledge of vectors
    • Distinguish between vector and scalar quantities.
    • Explain and draw diagrams for vectors.
    • Perform simple calculations involving addition and subtraction of vectors.
    • Multiply a vector by a scalar.
  • Demonstrate the application of vectors
    • Explain and solve simple problems involving equality of vectors.
    • Find vectors from two given vertices.
    • Apply equality of vectors to find coordinates at vertices of a parallelogram.
  • Demonstrate knowledge of bearings
    • Find bearings from diagrams.
    • Determine the reverse of a bearing.
    • Find the equivalence of a compass bearing.
    • Explain bearing.
    • Find the bearing of a point from another point.
    • Calculate the distance and bearing of one point from another.
Rigid Motion
  • Demonstrate knowledge in transformations — reflection and rotation
    • State the rules of reflection in rigid motion.
    • Solve simple problems involving reflection.
    • State the rotation rules of rigid motion.
  • Demonstrate knowledge of rules of translation and enlargement
    • Perform simple calculations on translations.
    • Explain enlargement as a rule of rigid motion.
    • Perform simple calculations on enlargement.
  • Demonstrate knowledge of application of rigid motions
    • Determine single transformation which maps one figure onto another.
    • Find the gradient of a line between two points.
    • Solve typical problems on rigid motion.
  • Demonstrate skills of rotation
    • Explain Rotation.
    • Identify shapes with rotational symmetry.
    • Find the image of an object under a given rotation.
    • Determine the relationship between the object and its image under rotation.
  • Demonstrate knowledge in enlargement
    • Explain enlargement.
    • Enlarge a plane figure from the origin.
    • Enlarge a plane figure from a given point.
    • Enlarge a plane figure by a given scale factor.
    • Find the scale factor when object and image are given.
Variation
  • Demonstrate knowledge in direct variation
    • Explain direct variation.
    • Find the constant of proportionality for direct variation.
    • Solve simple problems involving direct variation.
    • Solve practical problems involving direct variation.
  • Demonstrate knowledge in inverse variation
    • Explain inverse variation.
    • Determine equations connecting two quantities in inverse variation.
    • Solve simple problems involving inverse variation.
    • Solve practical problems involving inverse variation.
  • Demonstrate knowledge in joint variation
    • Explain joint variation.
    • Determine equation connecting variables in joint variation.
    • Solve simple problems involving joint variation.
  • Demonstrate knowledge in partial variation
    • Explain partial variation.
    • Write down mathematical statements for partial variations.
    • Solve problems involving partial variations.

Form 3 (Grade 12)

7 topics
Indices and Logarithms
  • Demonstrate knowledge in laws of indices
    • Write in exponent form the repeated factors of a number.
    • State the laws of indices (addition, product and quotient law).
    • Apply laws of indices on indicial expressions.
  • Demonstrate knowledge in solving indicial equations
    • Simplify an expression involving indices.
    • Solve indicial equations in one variable.
    • Solve indicial equations in two variables.
    • Solve indicial quadratic equations.
  • Demonstrate knowledge in logarithm
    • Explain logarithm.
    • Relate indices to logarithms in base ten.
    • State laws of logarithm.
    • Simplify expressions involving logarithm.
    • Solve logarithmic equations in one variable.
    • Solve logarithm quadratic equations.
Statistics
  • Demonstrate knowledge of statistics
    • Explain statistics.
    • Explain variables (qualitative and quantitative).
    • Differentiate between types of data (qualitative and quantitative).
    • Identify grouped and ungrouped data.
    • Explain the various terms used in statistics (population, sample, parameter, statistic).
  • Demonstrate skill in data collection
    • Explain data collection.
    • Collect and display data in tables and charts (bar chart, pie chart, histogram).
    • Interpret charts.
    • Construct the cumulative curve (ogive).
    • Use the ogive to estimate measures of position (Quartiles, Deciles, Percentiles).
  • Demonstrate knowledge in computing measures of central tendency
    • Compute mean of grouped and ungrouped data.
    • Compute median of grouped and ungrouped data.
    • Compute mode from ungrouped data.
    • Compute mode using the histogram.
  • Demonstrate knowledge in measures of dispersion
    • Explain the measures of dispersion.
    • List the measures of dispersion (range, inter-quartile range, variance, standard deviation).
    • Compute measures of dispersion of ungrouped data.
    • Compute measures of dispersion of grouped data.
Introduction to Probability
  • Demonstrate knowledge in probability theorem
    • Explain terminologies in probability (event, sample, population, number of elements, chance).
    • Explain experimental and theoretical probability.
    • List the sample space of a simple experiment.
    • List the sample space of two-staged experiments.
  • Demonstrate knowledge in applying probability theorem to events
    • Calculate the probability of an event.
    • Interpret 'or' in probability as addition.
    • Interpret 'and' in probability as multiplication.
    • State conditional probability.
    • Calculate simple conditional probability events.
  • Demonstrate skill in selection
    • Explain selection of an event.
    • Determine the chance of selection with different samples.
    • Determine experiments on selection without replacement.
    • Determine experiments on selection with replacement.
Sequences and Series
  • Demonstrate knowledge in sequence and series
    • Explain sequence of numbers.
    • Explain series of numbers.
    • State the types of sequence and series (arithmetic and geometric progression).
    • List series of numbers.
    • List sequence of numbers.
  • Demonstrate knowledge in Arithmetic Progression (A.P.)
    • Recognise an arithmetic progression (A.P.).
    • Identify first term and calculate common difference of an A.P.
    • Find the general (nth) term of an A.P.
    • Calculate the sum of the first nth terms of an A.P.
  • Demonstrate knowledge in Geometric Progression (G.P.)
    • Recognise a geometric progression (G.P.).
    • Identify first term and calculate common ratio of a G.P.
    • Find the general (nth) term of a G.P.
    • Calculate the sum of the first nth terms of a G.P.
Construction
  • Demonstrate knowledge in line segment and angle
    • Explain the term line segment.
    • Explain angle.
    • Draw various line segments.
    • Bisect a line segment.
  • Demonstrate skills in constructing angles
    • Construct acute angles.
    • Construct obtuse angles.
    • Bisect given angles.
    • Demonstrate measurement of line segments.
    • Demonstrate measurement of angles.
  • Demonstrate skills in plane figures construction
    • Explain plane figures.
    • Explain Loci.
    • Construct three-sided plane figures (triangles).
    • Construct four-sided plane figures (quadrilaterals).
    • Construct loci.
Trigonometry
  • Demonstrate knowledge in trigonometric ratios in the first quadrant
    • Explain trigonometric ratios.
    • Compute trigonometric ratios of complements and cofunctions of acute angles.
    • Use a calculator to read values of trigonometric ratios.
    • Use a calculator to read values of the inverse of trigonometric ratios.
  • Demonstrate knowledge in special angles
    • Explain special angles.
    • Derive the special angle for sine 30° and cos 60°.
    • Derive the special angle for sine 60° and cos 30°.
    • State the special angles for sine 45°, cos 45° and tan 45°.
  • Demonstrate skills in the application of trigonometric ratio measures
    • Explain angle of elevation.
    • Explain angle of depression.
    • Calculate angles of elevation.
    • Calculate angles of depression.
    • Use trigonometric ratios to calculate distance.
    • Use trigonometric ratios to calculate height of real objects.
Matrices
  • Demonstrate knowledge in matrix notation
    • Explain array of numbers.
    • Represent data in matrices.
    • Identify the order of matrices.
    • Explain special matrices.
  • Demonstrate knowledge in matrix operations
    • Add matrices.
    • Subtract matrices.
    • Multiply matrices by a scalar factor.
    • Multiply matrices.
  • Demonstrate skills in matrix operations
    • Find the transpose of a matrix.
    • Find the determinant of a matrix.
    • Compute the inverse of a matrix.
    • Represent matrices of linear transformation.
    • Solve simultaneous equations using matrices.
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