CONTENT AREAS COMPETENCIES DESCRIPTIVE STATEMENTS

NUMBER AND OPERATIONS

• real number system Demonstrate understanding in • Identify and group numbers into the number types.
the various numbers in the • Perform operations such as addition, subtraction,
number system and their multiplication and division on the various numbers
operations (e.g. natural numbers, whole numbers, integers, rational
numbers)
• Binary operations and • Demonstrate knowledge and
properties (e.g. closure, identity understanding of binary • Define the properties of real numbers (closure,
element, commutativity, operations e.g. closure, commutativity, identity, associativity, distributive
associativity and distributive commutativity identity, property) and perform calculations on them
properties) associativity distributive
property)
• Surds, radical equations, indices • Demonstrate understanding • Simplify expressions using the laws of exponents for
and logarithms of definition of surds, rational exponents
exponents and logarithms • Establish between which two integers a
and any laws needed to solve given simple surd lies.
real life problems • Add, subtract, multiply and divide simple surds.
• Solve simple equations involving surds
• Simplify logarithmic expression and equation and
apply them in solving real life problems.

• Explain and use common rates such as Km/h, rate of

• Ratio, rates, and percentages • Demonstrate understanding payment per hour, payment of wages and those used in
in ratios and rates and utility bills.
percentages
• Express one quantity as a percentage of the other
• Calculate percentages of given quantities.
 • Calculate percentage changes.
• Apply percentages in
• Simple interest income tax
• Compound interest
• Depreciation

ALGEBRA AND FUNCTIONS

Manipulate algebraic expressions by
• Factorizations and expansion Demonstrate understanding in • multiplying a binomial by a trinomial;
of algebraic expressions factorizing, binomials, • factorizing trinomials
trinomials, • factorizing the difference and sums of two cube
Quadratic expressions • factorizing by grouping in pairs; and
• simplifying, adding and subtracting
• algebraic fractions with denominators of squares (limited to
• Change of subject sum and difference of squares).

• Solve literal equations (changing the subject of formulae);

Demonstrate understanding in
• Perform substitutions and evaluation when given certain
changing subject in given
values.
formula
• Perform operations such as addition, subtraction,
multiplication and division in polynomials
• polynomials • Find the zeros of polynomials
Demonstrate understanding in
polynomials Solve:
• Equations  linear equations in one variable
 quadratic equations making use of:
• factorization
 Demonstrate understanding in • quadratic formula
solving different types of Completing of squares
equations. • Write a quadratic equation in the form
y = (x ± a)2 ± c
• use y = (x ± a)2 ± c to find the minimum value,
maximum value, sketch a quadratic curve and explain
the shifts from y = x 2
• exponential equations
• logarithmic equations
• linear inequalities
• system of linear equations up to two variables
• word problems.
• Demonstrate competencies in solving System of linear
equation (Up to two variables) and inequalities

Solve
• sequences and series • number pattern (linear number pattern and quadratic
(arithmetic sequences and pattern)
series and geometric • arithmetic progression (AP)
sequences and series) • geometric progression (GP)
• sum of first in terms of AP and GP
• Variations (e.g. direct Demonstrate understanding in
indirect and joint) sequences and series Solve questions on
• direct variation
• indirect variation
• joint variation
 Demonstrate understanding in
solving questions on variations
Geometry and measurement Demonstrate understanding in • Know definition for lines and line segment and give
geometry and measurement examples in real life.
• Points and line segments • Know the definition of the different types of angles
e.g., acute, obtuse, reflex, right angles.
• Angles (angles at a point, • Solve questions relating to angles at a point, adjacent
angles properties of parallel angles on a straight line, angles in a triangles and
lines quadrilaterals, properties of angles of parallel lines e.g.
(corresponding, alternate and co-interior) on the angles.
• Identify various geometrical shapes in 2 Ds and 3Ds
• Properties of 2 D figures e.g., • Solve related problems including areas and perimeters
triangle and quadrilaterals of 2Ds and Perimeters and areas and volumes and
• Perimeters and areas of 2D and surfaces areas of and 3 Ds e.g. cuboid cubes cones and
3D figures. cylinders
• Volume and surface areas of
3D figures • Locate points in the Cartesian plane, drawing lines to
join plotted points and determine the equation of lines
• Coordinate geometry drawn in the Cartesian plane.
Solve for
• slopes of a lines and its interpretations.
• equation of a circle when given three points on the
circle, the center and a point on the circle and the end
points of the diameter finding the radius of a circle
• mid-points between two points and distance between
two points.
• know the parts of a circle e.g., center, radius, diameter,
• Geometrical construction chord, segment, sector circumference,
 • Use reflection, rotation, translation and enlargement
techniques in transformation
• Apply the concepts of similarity, dilations in solving
real life problems
• Construct geometrical figures making use of pair of
compasses and ruler only.
• Apply locus in circle geometry
• Trigonometry and vectors • Demonstrate understanding Solve questions on
• Right angled triangles, in the concepts of • right angled triangles
• Pythagorean triples trigonometry • Pythagorean triples
• Pythagoras theorems and its • Pythagoras theorems and its applications (finding the
applications (e.g. finding the length of a ladder leaning against a wall, angles of
length of a ladder leaning elevation and depression)
against a wall, angles of
Solve
elevation and depression)
• questions by applying trigonometric ratios
• Trigonometric ratios
• trigonometric equations
• Trigonometric equations
• on double angle
• phase shift of sine graphs,
• on multiple angle
cosines graphs and tangents
• Sine rule
Amplitude and period
• Cosine rule
• apply the concepts of phase shift of sine graphs and
cosine graphs, Amplitude and period to solve problems
limited to sine, cosine and tangent graphs
Vectors and Bearing Demonstrate knowledge in the Solve questions on
concepts of vectors • vector representation notations (distance-bearing
• Algebra of vectors, vector 𝑥𝑥
(𝐾𝐾, ∅), component forms (𝑦𝑦), Cartesian forms 𝑥𝑥𝑖𝑖 + 𝑦𝑦𝑗𝑗
• representation notation
components of vector, vector • components of vector
• operations, magnitude and • vector operations
direction of a vector. • magnitude and direction of a vector
• Teaching types of bearings • types of bearings and their applications
and their applications.
Calculus Demonstrate knowledge in the • Find limits of polynomial functions.
concepts of calculus • Find derivatives of polynomial functions up to second
• Limits of functions order.
(Excluding indeterminate • Apply the techniques such as quotient, product, chain
forms) rules to find derivative of functions.
• Derivative of polynomial and • Solve questions on integral calculus (Definite and
rational functions (up to second indefinite integrals. Excluding integration by parts and
order derivatives) product, substitution method
quotient, chain rules • Apply differential and integral calculus in Maxima and
• Application of differential minima values, equations of tangents and normal to
calculus (e.g. maxima and curves
minima values, equations of • Apply differential calculus in solving problems on
tangents and normal to curves) curve sketching.
• Integral calculus (definite and
indefinite integrals)
• Curve sketching
Data handling and probability
• data collection methods Demonstrate knowledge in data • state data collection procedures and when to apply
• scales of measurement collection procedures and them.
• processing of data statistical processes. • Construct tally tables and frequency distribution tables
(frequency distribution), • Find the averages (mean, mode and median) from a
• Representation of data grouped and ungrouped data,
(e.g. bar graphs, pie chart • Solving questions on graphical interpretation of data
histogram and line graphs, and analysis e.g. bar graph, pie chart, histogram,
cumulative frequency cumulative frequency
graphs) • Calculate and interpret
• Measure of central measure of dispersions e.g. range, variance and
tendencies (mean, median, standard deviation, quartiles and percentiles and apply
mode and their (averages) them to solve real life statistical problems
• Measures of dispersion • Define probability
(range variance, standard • State the axioms of probability.
deviation) • define sample spaces and events.
• Quartiles and percentiles • state conditions for mutually exclusive events and give
• Definition of probability real life of mutually exclusive events
• Axioms of probability • state conditions for independent events
• Events • state the addition law of probability of two events A
• Mutually exclusive events, and B: 𝑃𝑃 (𝐴𝐴 𝑜𝑜𝑜𝑜 𝐵𝐵) = 𝑃𝑃 (A) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃 (𝐴𝐴 and 𝐵𝐵)
inclusive events, • State the product rule
Demonstrate understanding in
complementary events • apply techniques such as tree diagrams, contingency
• probability
independent events table and Venn diagrams in solving probability
• samples and events
• Addition law problems.
• mutually exclusive
• Product rule • State the conditional probability. Give real life events
events
• Techniques in solving of conditional probability.
• independent events
probability problems such
• complementary events
 as tree diagrams, • addition law • Use the fundamental counting principles and counting
contingency tables and • product rule rules to solve practical probability problems
Venn diagrams • Venn diagrams (combination and permutations)
• Conditional probability • contingency tables
• tree diagrams
• conditional probability
 SHS - MATHEMATICS
Subject Outcomes (Depth of Knowledge)
Content Areas Level 1 Level 2 Level 3 Level 4 Total
Remembering Understanding Applying Analyzing/Evaluating/Creating
(Recall) (Skill/Concepts) (Strategic (Extended Thinking)
Thinking)
Number and Operations 2 3 3 2 10

Algebra and Functions 1 3 3 3 10

Geometry and 1 3 2 3 9
Measurements
Trigonometry and Vectors 2 2 4 3 11

Calculus 1 2 1 3 7

Data Handling and 2 2 5 4 13

Probability
Total 9 (15%) 15 (25%) 18 (30%) 18 (30%) 60
(100%)