Waec Mathematics 2021 Syllabus And Topics
It is no longer news that Waec 2021 registration has begun and the May/June examination is very close. So many Waec candidates have been asking questions about the 2021 Waec syllabus and topics to read so as to pass Waec 2021 without much stress.
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In this article, I will bread down the Waec mathematics syllabus for you.
See Also: How to pass Waec without expo
For all papers which involve mathematical calculations, mathematical and statistical tables published for WAEC should be used in the examination room. However, the use of non-programmable, silent and cordless calculator is allowed.
The calculator must not have a paper printout. Where the degree of accuracy is not specified in a question the degree of accuracy expected will be that obtainable from the WAEC mathematical tables.
Trigonometrical tables
in the pamphlet have different columns for decimal fractions of a degree, not for minutes and seconds.
No mathematical tables other than the above may be used in the examination. It is strongly recommended that schools/candidates obtain copies of these tables for use throughout the course.
Candidates should bring rulers, protractors, pair of compasses and set squares for all papers.
They will not be allowed to borrow such instruments and any other materials from other candidates in the examination hall. It should be noted that some questions may prohibit the use of tables and /or calculators. The use of slide rules is not allowed.
Aims of Waec Mathematics Syllabus
The syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use
their own National teaching syllabuses. The aims of the syllabus are to test:
(i) computational skills;
(ii) the understanding of mathematical concepts and their applications to everyday living;
(iii) the ability to translate problems into mathematical language and solve them with
related mathematical knowledge;
(iv) the ability to be accurate to a degree relevant to the problems at hand;
(v) precise, logical and abstract thinking.
WAEC EXAMINATION FORMAT
There will be two papers both of which must be taken.
PAPER 1 – 11/2 hours
PAPER 2 – 21/2 hours
Wassce General Mathematics Syllabus
TOPICS CONTENTS NOTES
A. NUMBER AND NUMERATION
(a) Number Bases
(i) Binary numbers
**(ii) Modular arithmetic
Conversions from base 2 to base 10 and vice versa. Basic operations excluding division. Awareness of other number bases is desirable.
Relate to market days, the clock etc.
Truth sets (solution sets) for various open
sentences, e.g. 3 x 2 = a(mod) 4, 8 + y =
4 (mod) 9.
(b) Fractions, decimals and approximations
(i) Basic operations on
fractions and decimals.
(ii) Approximations and
significant figures
Approximations should be realistic e.g. a road is not measured correct to the nearest cm. Include error.
(c) Indices
(i) Laws of indices.
(ii) Numbers in standard
form.
Include simple examples of negative and
fractions indices.
e.g. 375.3 = 3.753 x 102
0.0035 = 3.5 x 10-3
Use of tables of squares,
square roots and reciprocals.
(d) Logarithms
(i) Relationship between indices and logarithms e.g.
y = 10k †’ K = log10 y
(ii) Basic rules of logarithms i.e.
log10 (pq) = log10P + log10q
log10 (p/q) = log10 P – log10q
log10Pn = nlog10P
(iii) Use of tables of logarithms, Base 10 logarithm and Antilogarithm tables. Calculations involving multiplication, division, powers and square roots.
(e) Sequence
(i) Patterns of sequences.
Determine any term of a
given sequence.
*(ii) Arithmetic Progression (A.P)
Geometric Progression (G.P).
The notation Un = the nth term of
a sequence may be used.
Simple cases only, including word
problems. Excluding sum Sn.
(f) 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.
The use of Venn diagrams restricted to at most 3 sets.
**(g) Logical reasoning Simple statements. True and false statements. The negation of statements.
Implication, equivalence and valid
arguments.
Use of Venn diagrams preferable.
(h) Positive and Negative
integers. Rational numbers
The four basic operations on rational numbers
Match rational numbers with points on the number line.
Notation: Natural numbers (N),
Integers (Z), Rational numbers
(Q)
(i) Surds
Simplification and Rationalisation of simple surds.
(j) Ratio, Proportion
and Rates
Financial partnerships; rates of work, costs, taxes, foreign exchange, density (e.g. for population) mass, distance, time and speed. Include average rates.
(k) Variation
Direct, inverse and partial variations.
*Joint variations.
Application to simple practical problems.
(l) Percentages
Simple interest, commission, discount, depreciation, profit and loss, compound interest and hire purchase.
Exclude the use of compound
interest formula.
B. ALGEBRAIC
PROCESSES
(a) Algebraic
Expressions
(i) Expression of
statements in symbols.
(ii) Formulating algebraic
expressions from given
situations.
(iii) Evaluation of algebraic
expressions.
eg. Find an expression for the
cost C cedis of 4 pears at x cedis
each and 3 oranges at y cedis each
C = 4x + 3y
If x = 60 and y = 20.
Find C.
(b) Simple operations on
algebraic xpressions.
(i) Expansion
(ii) Factorisation
e.g. (a+b) (c+d). (a+3) (c+4)
Expressions of the form
(i) ax + ay
(ii) a (b+c) +d (b+c)
(iii) ax2 + bx +c
where a,b,c are integers
(iv) a2 – b2
Application of difference of two
squares e.g.
492 – 472 = (49 + 47) (49 – 47)
= 96 x 2 = 192
(c) Solution of linear
equations
(i) Linear equations in one variable
(ii) Simultaneous linear equations
in two variables.
(d) Change of subject of
a formula/relation
(i) Change of subject of a
formula/relation
(ii) Substitution
(e) Quadratic equations
(i) Solution of quadratic equations
(ii) Construction of quadratic
equations with given roots.
(iii) Application of solution of quadratic equations in practical problems.
(f) Graphs of Linear and quadratic functions.
(i) Interpretation of graphs, coordinates of points, table of values. 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
(iii) Drawing of a tangent to
curves to determine
gradient at a given point.
(iv) The gradient of a line
** (v) Equation of a Line
Finding:
(i) the coordinates of the maximum and minimum points on the graph;
(ii) intercepts on the axes. Identifying axis of Symmetry. Recognising sketched graphs.
Use of quadratic graph to solve a related equation
e.g. graph of y = x2 + 5x + 6 to solve x2 + 5x + 4 = 0
(i) By drawing relevant triangle to determine the gradient.
(ii) The gradient, m, of the line
joining the points
(g) Linear inequalities
(i) Solution of linear
inequalities in one variable
and representation on the
number line.
(ii) Graphical solution of linear
inequalities in two variables
Simple practical problems
(h) Relations and functions
(i) Relations
(ii) Functions
Various types of relations
One – to – one,
many – to – one,
one – to – many,
many – to – many
The idea of a function.
Types of functions.
One – to – one,
many – to – one.
(i) Algebraic fractions
Operations on algebraic
fractions
(i) with monomial
denominators.
(ii) with binomial
denominators.
C. MENSURATION
(a) Lengths and Perimeters
(i) Use of Pythagoras
theorem, sine and cosine
rules to determine
lengths and distances.
(ii) Lengths of arcs of
circles. Perimeters of
sectors and Segments.
*(iii) Latitudes and Longitudes.
No formal proofs of the theorem
and rules are required.
Distances along latitudes and
longitudes and their
corresponding angles.
(b) Areas
(i) Triangles and special
quadrilaterals – rectangles,
parallelograms and trapezia.
(ii) Circles, sectors and
segments of circles.
(iii) Surface areas of cube, cuboid,
cylinder, right triangular prisms
and cones. *Spheres.
Areas of similar figures.
Include area of triangles is
½ base x height and *1/2 abSin C.
Areas of compound shapes.
Relation between the sector of a
circle and the surface area of a
cone.
(c) Volumes
(i) Volumes of cubes, cuboid,
cylinders, cones and right
pyramids. * Spheres.
(ii) Volumes of similar solids
Volumes of compound shapes.
D. PLANE GEOMETRY
(a) Angles at a point
(i) Angles at a point add up to
360ï‚°.
(ii) Adjacent angles on a
straight line are supplementary.
(iii) Vertically opposite angles are
equal.
The results of these standard theorems stated under contents must be known but their formal proofs are not required. However, proofs based on the knowledge of these theorems may be tested.
The degree as a unit of measure.
Acute, obtuse, reflex angles.
(b) Angles and intercepts on parallel lines
(i) Alternate angles are equal.
(ii) Corresponding angles are equal.
(iii) Interior opposite angles are
supplementary.
*(iv) Intercept theorem
Application to proportional division of a line segment.
(c) 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.
(v) Properties of special quadrilaterals – parallelogram, rhombus, rectangle, square, trapezium.
(vi) Properties of similar triangles.
(vii) The sum of the angles of a polygon.
(viii) Property of exterior angles of a polygon.
(ix) Parallelograms on the same base and between the same parallels are equal in area.
Conditions to be known but proofs not required. Rotation, translation, reflection and lines of symmetry to be used. Use symmetry where applicable. Equiangular properties and ratio of sides and areas.
(d) 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.
Angles subtended by chords in a circle, at the centre of a circle. Perpendicular bisectors of chords.
(iv) Angles in the same segment are equal
(v) Angles in opposite segments are supplementary.
(vi) Perpendicularity 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.
(e) Construction
(i) Bisectors of angles and line
segments.
(ii) Line parallel or perpendicular
to a given line.
(iii) An angle of 90º, 60º, 45º, 30º
and an angle equal to a given
angle.
(iv) Triangles and quadrilaterals
from sufficient data.
Include combination of these
angles e.g. 75º, 105º, 135º,
etc.
(f) Loci
Knowledge of the loci listed below and
their intersections in 2 dimensions.
(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.
Consider parallel and
intersecting lines.
E. TRIGONOMETRY
(a) Sine, cosine and
tangent of an angle.
(b) Angles of elevation
and depression.
(c) Bearings
(i) Sine, cosine and tangent
of an acute angle.
(ii) Use of tables.
(iii) Trigonometric ratios of
30º, 45º and 60º.
*(iv) Sine, cosine and
tangent of angles
from 0º to 360º.
*(v) Graphs of sine and
cosine.
Calculating angles of elevation and depression. Application to heights and distances.
(i) Bearing of one point from another.
(ii) Calculation of distances and angles.
E. STATISTICS AND PROBABILITY
(a) 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.
Reading and drawing simple inferences from graphs and interpretations of data in histograms.
Exclude unequal class interval. Use of an assumed mean is acceptable but nor required. For grouped data, the mode should be estimated from the histogram and the median from the cumulative frequency curve.
Simple examples only. Note that mean deviation is the mean of the absolute deviations.
(b) Probability
(i) Experimental and theoretical probability.
(ii) Addition of probabilities for mutually exclusive and independent events.
(iii) Multiplication of probabilities for independent events.
Include equally likely events e.g. probability of throwing a six with fair die, or a head when tossing a fair coin.
Simple practical problems only. Interpretation of ”˜and’ and ”˜or’ in probability.
**(G) VECTORS AND TRANSFORMATIONS IN A PLANE
(a) Vectors in a Plane.
(i) Vector as a 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.
Column notation. Emphasis on graphical representation.
(b) Transformation in the Cartesian Coordinate plane.
(i) Reflection
(ii) Rotation
(iii) Translation
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