PROGRESSIVE SCIENCE INITIATIVE® (PSI®) - PROGRESSIVE MATHEMATICS INITIATIVE® (PMI®)

The West African Exam Council (WAEC) core maths syllabus covers 7 major topics: A. Number and Numeration, B. Algebraic Processes, C. Mensuration, D. Plane Geometry, E. Trigonometry, F. Statistics and Probability and G. Vectors and Transformations in a Plane. The majority of these topics are covered in PMI Grades 7 and 8, Algebra I, Geometry, and Algebra II units. Select the appropriate PMI unit link to access materials that correspond to the WAEC core maths topics below. The WAEC syllabus outline can be accessed under Teacher Resources.

Fraction and Decimal Computation

Fractions, decimals and approximations; A (b)

Number System

Positive and negative integers. Rational numbers; A (h)

Ratios and Proportions

Ratio, proportion and rates; A (j)

Percents

Discount, profit, loss; A (l)

Equations with Roots and Radicals

Scientific Notation

Indices (ii) numbers in standard form; A (c)

Expressions

Algebraic Expressions (i) expression of statements in symbols (ii) formulating algebraic expressions from given situations (iii) evaluation of algebraic expressions;

Equations - from Pre-Algebra

Solution of linear equations (i) linear equations in one variable; B (c)

Equations - from Algebra I

Change of subject of a formula/relations (i) Change of subject (ii) Substitution; B (d)

Solving and Graphing Linear Inequalities

Linear inequalities (i) Solution of linear inequalities in one variable and representation; B (g)

Quantitative Reasoning

Graphing Linear Equations

Graphs of linear and quadratic functions (i) interpretations of graphs, coordinates of points, table of values (v) equation of a line; B (f)

Systems of Linear Equations

Solution of linear equations (ii) simultaneous linear equations in two variables; B (c)

Solving and Graphing Linear Inequalities

Linear inequalities (ii) graphical solution of linear inequalities in two variables; B (g)

Functions

Relations and functions (i) relations (ii) functions; B (h)

Numbers, Operations and Expressions - Algebra I

Indices (i) laws of indices; A (c)

Polynomials

Simple operations on algebraic expressions (i) expansion (ii) factorisation; B (b)

Quadratic Equations

Quadratic equations (i) solution of quadratic equations (ii) construction of quadratic equations with given roots; (ii) application of solution of quadratic equations in practical problems; B (e)

Graphs of linear and quadratic functions (i) drawing quadratic graphs and obtaining roots from graphs (ii) graphical solution of a pair of equations of the form y=ax2 + bx + c and y = mx + k; B (f)

Nonlinear Functions

Graphs of linear and quadratic functions; B (f)

Points, Lines, Planes and Angles

Graphs of linear and quadratic functions (v) equations of a line; B (f)

Angles at a point (i) angles at a point add up to 360 (ii) adjacent angles on a straight line are supplementary; D (a)

Construction (i) bisectors of angles and line segments (iii) an angle of 90, 60, 45, 30 and an angle equal to a given angle; D (e)

Loci (i) points at a given distance from a given point (ii) points equidistant from two given points (iii) points equidistant from two given straight lines (iv) points at a given distance from a given straight line; D (f)

Parallel and Perpendicular Lines

Angles at a point (iii) vertically opposite angles are equal; D (a)

Angles and intercepts on parallel lines (i) alternate angles are equal (ii) corresponding angles are equal (iii) interior angles are supplementary; D (b)

Construction (ii) line parallel or perpendicular to a given line; D (e)

Triangles

Angles and intercepts on parallel lines (iv) intercept theorem; D (b)

Triangles and other polygons (vi) properties of similar triangles; D (c)

Trigonometry of Right Triangles

Lengths and perimeters (i) use of Pythagoras theorem, sine and cosine rules to determine lengths and distances; C (a)

Sine, cosine and tangent of an angle (i) sine, cosine and tangent of an acute angle; E (a)

Angles of elevation and depression; E (b)

Congruent Triangles

Triangles and other polygons (i) the sum of the angles of a triangle is 2 right angles (ii) the exterior angle of a triangle equals the sum of the two interior opposite angles (iii) congruent triangles (iv) properties of special triangles - isosceles, equilateral, right-angled; D (c)

Transformations

Transformations in the Cartesian Coordinate plane (i) reflection (ii) rotation (iii) translation; G (b)

Quadrilaterals

Triangles and other polygons (v) properties of special quadrilaterals - parallelogram, rhombus, rectangle, square, trapezium (vii) the sum of the angles of a polygon (viii) property of exterior angles of a polygon; D (c)

Circles

Lengths and perimeters (ii) lengths of arcs of circles, perimeters of sectors and segments; C (a)

Circles (i) chords (ii) the angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumference (iii) any angle subtended at the circumference by a diameter is a right angle (iv) angles in the same segment equal (v) angles in opposite segments are supplementary (vi) perpendicularly of tangent and radius (vii) if a straight line touches a circle at only one point and from the point of contact a chord is drawn, each angle which this chord makes with the tangent is equal to the angle in the alternative segment; D (d)

3D Geometry

Areas (i) triangles and special quadrilaterals – rectangles, parallelograms and trapezia (iii) Surface areas of cube, cuboid, cylinder, right triangular prisms and cones. *Spheres; C (b)

Volumes (i) volumes of cubes, cuboid, cylinders, cones and right pyramids, * spheres (ii) volumes of similar solids; C (c)

Rational Expressions and Equations

Variation; B (k)

(i) Algebraic fractions (i) with monomial denominators (ii) with binomial denominators; B

Radical Functions and Rational Exponents

(i) Surds; A

Exponential and Logarithmic Functions

Logarithms (i) relationship between indices and logarithms (ii) basic rules of logarithms (iii) use of tables of logarithms, base 10 logarithm and antilogarithm tables; A (d)

Sequences and Series

Sequence (i) patterns of sequences, determine any given sequence (ii) arithmetic progression, geometric progression; A (e)

Trigonometry

Sine, cosine and tangent of an angle (ii) use of tables (iii) trigonometric ratios of 30, 45, and 60 (iv) sine, cosine and tangent of angles from 0 to 360 (v) graph of sine and cosine; E (a)

Logic & Reasoning

Logical reasoning; A (g)

Probability and Statistics

Sets (i) idea of sets, universal set, finite and infinite sets, subsets, empty sets and disjoint sets; idea of and notation for union, intersection and complement of sets. (ii) solution of practical problems involving classification, using Venn diagrams; A (f)

Statistics (i) frequency distribution (ii) pie charts, bar charts, histograms and frequency polygons (iii) mean, median and mode for both discrete and grouped data (iv) cumulative frequency curve, median; quartiles and percentiles (v) measures of dispersion: range, interquartile range, mean deviation and standard deviation from the mean; F (a)

Probability (i) experimental and theoretical probability (ii) addition of probabilities for mutually exclusive and independent events (iii) multiplication of probabilities for independent events; F (b)

Vectors

Vectors in a plane (i) vector as directed line segment, magnitude, equal vectors, sums and differences of vectors (ii) parallel and equal vectors (iii) multiplication of a vector by a scalar (iv) Cartesian components of a vector; G (a)

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