Topic 1: Coordinate Geometry
a). Equation of a Line
i. Derive the general equation of a straight line
b). Midpoint of a Line Segment
i. Determine the coordinates of the midpoint of a line segment
c). Distance Between Two Points on a Plane
i. Calculate the distance between two points on a plane
d). Parallel and Perpendicular Lines
i. Compute gradients in order to determine the conditions for any two lines to be parallel
ii. Compute gradients in order to determine the conditions for any two lines to be perpendicular
iii. Solve problems on parallel and perpendicular lines
Topic 2: Area And Perimeter
a). Area of any Triangle
i. Derive the formula for the area of any triangle
ii. Apply the formula to find the area of any triangle
b). Area of a Rhombus
i. Derive the formula for finding the area of rhombi in terms of the diagonals.
ii. Apply the formula to find the areas of quadrilaterals
c). Perimeter of a Regular Polygon
i. Derive the formula for finding the length of a side of a regular polygon
ii. The formula to determine the perimeter of a regular polygon
d). Area of a Regular Polygon
i. Derive the formula for finding the area of a regular polygon
ii. Apply the formula to calculate the area of a regular polygon
e). Area of Similar Polygons
i. Find the ratio of areas of similar polygons
ii. Solve problems related to the ratio for areas of similar polygons
Topic 3: Three Dimensional Figures
a). Three Dimensional Figures
i. Classify three dimensional figures
ii. List the characteristics of each class
b). Construction of Three Dimensional Figures
i. Construct three dimensional figures
c). Sketching Three Dimensional Figures
i. Sketch three dimensional figures
ii. Identify properties of three dimensional figures
iii. Find the angle between a line and a plane
iv. Calculate the angle between two planes
d). Surface Area of Three Dimensional Objects
i. Derive the formulae for calculating the surface area of prisms, cylinder and pyramids and cone
ii. Apply the formulae to calculate the surface area of spheres
e). Volume of Three Dimensional Objects
i. Derive the formulae for calculating volume of prisms, cylinders and pyramids
ii. Apply the formulae to calculate the volume of cylinders, pyramids and cones
Topic 4: Probability
a). Probability of an Events
i. Determine the probability of an event through experiments
ii. Interpret experimental results in relation to real life occurrences
iii. Write the formula for finding the probability of an event
iv. Apply the formula to calculate the probability of an event
b). Combined Events
i. Perform experiments of two combined events
ii. Draw a tree diagram of combined events
iii. Find the probability of two combined events using the formula
iv. Apply the knowledge of probability to determine the occurrence of events in real life situation
Topic 5: Trignometry
a). Trigonometric Ratios
i. Determine the sine, cosine and tangent of an angle measured in the clockwise and anticlockwise directions
ii. Apply trigonometric ratios to solve problems in daily life
b). Sine and Cosine Functions
i. Find sines and cosines of angles 0 such that -720°≤ᶿ≥ 720°
ii. Draw the graphs of sine and cosine
iii. Interpret the graphs of sine and cosine functions
c). Sine and Cosine Rules
i. Derive the sine and cosine rules
ii. Apply the sine and cosine rules in solving problems on triangles
d). Compound Angles
i. Apply the compound of angle formulae or sine, cosine and tangent in solving trigonometric problems
Topic 6: Vectors
a). Displacement and Positions of Vectors
i. Explain the concept of a vector quantity
ii. Distinguish between displacement and position vectors
iii. Resolving any vector into I and J components
b). Magnitude and Direction of a Vector
i. Calculate the magnitude and direction of a vector
c). Sum and Difference of Vectors
i. Find the sum of two or more vectors
ii. Find the difference of vectors
d). Multiplication of a Vector by a Scalar
i. Multiply a vector by a scalar
e). Application of Vectors
i. Apply vectors in solving simple problems on velocities, displacements and forces
Topic 7: Matrices And Transformations
a). Operations on Matrices
i. Explain the concept of a matrix
ii. Add matrices of order up to 2 X 2
iii. Subtract matrices of order up to 2 X 2
iv. Multiply a matrix of order 2 X 2 by a scalar
v. Multiply two matrices of order up to 2 X 2
b). Inverse of a Matrix
i. Calculate the determinant of a 2 X 2 matrix
ii. Find the inverse of a 2 X 2 matrix
iii. Apply 2 X 2 matrix to solve simultaneous equations
c). Matrices and Transformations
i. Transform any point P(X, Y) into P'(X’, Y’) by pre-multiplying (x, y) with a transformation matrix T
ii. Apply the matrix to reflect a point P(X, Y ) in the x-axis
iii. Apply the matrix to reflect a point P(X, Y) in the Y-Axis
iv. Use a matrix operator to rotate any point P( X, Y ) through 90° 180°, 270° and 360° about the Origin
v. Use the enlargement matrix E in enlarging figures
Topic 8. Linear Programming
a). Simultaneous Equations
i. Form simultaneous equation from word problems
ii. Solve simultaneous equations graphically
b). Inequalities
i. Form linear inequalities in two unknowns from word problems
ii. Find the solution set of simultaneous linear inequalities graphically
c). The Objective Function
i. Form an objective function from word problems
d). Maximum and Minimum Values
i. Locate corner points on the feasible region
ii. Find the minimum and maximum values using the objective function
