MEASUREMENT

1. Calculate the length of an arc of a circle

2. Calculate the area of a sector of a circle

Use Hero’s formula for the area of a triangle

3. Calculate the area of a segment of a circle

4. Solve problems using: the properties of faces, edges & vertices of solids

 - Cylinder

- Sphere

- Cone

5. Calculate the surface area and volume of solids

- Cylinder

- Sphere

- Cone

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STATISTICS

1. Differentiate between sample & population attributes – sample statistics & population parameters

2. Level of Measurement (Measurement scales)

– Nominal, Ordinal, Interval & Ratio

3. Differentiate between types of data:

- Discrete & Continuous variables

- Ungrouped & Grouped data

4. Construct a Frequency Table for a given set of data:

- Ungrouped

- Grouped data

5. Determine class features for a given set of data:

- Max. / Min.

- Range

- Class interval

- Class boundaries

- Class limits

- Class midpoint

- Class width

6. Construct statistical diagrams

- Histograms with Bars of equal width

- Frequency polygons

7. Interpret data presented in any of the graphical or pictorial forms named in objective 6 above

8. Determine measures of central tendency (mean, median & mode) for

- Raw data

- Ungrouped data

- Grouped data: Median Class, Modal Class, Estimate of the Mean

9. Determine when it is most appropriate to use as the average for a set of data

- Mean

- Median

- Mode

10. Determine the measures of Dispersion / Spread

       (e.g. Range, Interquartile & Semi-interquartile range), for

- Raw data

- Ungrouped data.

- Grouped data.

11. Analyze statistical data & diagrams, finding the

- Mean, mode, median

- Range

- Quartiles, Interquartile range, Semi-interquartile range

- Trends & Patterns

12. Use standard deviation to compare sets of data. No calculation of the standard deviation is required.

13. Determine the Proportion or Percentage of the sample above or below a given value from Raw data or Frequency Table

14. Identify the Sample Space for a simple experiment, including the use of contingency tables

15. Determine Experimental & Theoretical probabilities of simple events

16. Apply statistical methods to analyze data & make appropriate inference(s) from:

- Raw data

- Tables

- Diagrams

- Summary Statistics

 

ALGEBRA

1. Evaluate expressions involving Binary Operations (other than the four basic ones) & perform simple computations with them: Commutative, Associative, Distributive

2. Use the Laws of Indices to manipulate expressions with integral indices (include fractional / rational indices)

3. Formulae (change of subject, include roots & powers).

4. Use Linear Inequalities to solve word problems

5. Solve Simultaneous Linear Equations in two unknowns algebraically)

6. Use simultaneous linear equations to solve word problems

7. Represent Direct & Inverse Variations symbolically

8. Solve problems involving direct variation & inverse variation

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RELATIONS, FUNCTIONS and GRAPHS

1. Explain basic concepts associated with relations:

- Concept of a Relation 
- Types of relations
- Examples & Non-examples
- Domain
- Range
- Image
- Co-domain

2. Represent a relation in various ways:

- Set of Ordered Pairs
- Arrow diagrams
- Graphically
- Algebraically

3. State the characteristics that define a Function:

- Concept of a Function (Many-to-one or One-to-one relation)
- Examples & Non-examples

4. Use the functional notations, for example, \(f:x \to x^2\); or \(f(x) = x^2\); as well as \(y = f(x)\) for given domains
5. Distinguish between a Relation and a Function:

- Ordered pairs 
- Arrow diagrams 
- Graphically (Vertical Line Test)

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GEOMETRY AND TRIGONOMETRY

1. Determine the

(i) Sine
(ii) Cosine
(iii) Tangent ratios of acute angles in a right-angled triangle 

2. Use the

(i) Sine _____
(ii) Cosine _____
(iii) Tangent ratios _____

in the solution of right-angled triangles

3. Use simple trigonometrical ratios to solve problems based on measures
In the physical world

(a) Heights & Distances
(b) Angles of Elevation & Depression

4. Represent the relative position of two points given the Bearing of one point with respect to the other (include Cardinal points)
5. Determine the Bearing of one point relative to another point given the position of the points
6. Solve problems involving Bearings

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MATRICES

1. Explain concepts associated with matrices:

(i) Row
(ii) Column
(iii) Order
(iv) Types of matrices: square, rectangular, identity
(v) Practical use (to represent information) 

2. Perform with matrices

(i) Addition 
(ii) Subtraction 
(iii) Multiplication by a scalar
(iv) Multiplication: Non-commutativity of matrix multiplication
(v) Equality

3. Evaluate the Determinant of a \(2 \times 2\) matrix 
4. solve problems involving a \(2 \times 2\) singular matrix
5. Obtain the inverse of a non-singular \(2 \times 2\) matrix: Determinant & Adjoint of a matrix _____
6. Use matrices to solve simple problems 

(a) Arithmetic _____
(b) Algebra & Geometry: Linear simultaneous equations with 2 unknowns