MATSYLBSF4
i.
Equation of a Line
§ Derive the
general equation of a straight line
ii.
Midpoint of a Line Segment
§ Determine the coordinates
of the midpoint of a line segment
iii.
Distance Between Two Points on a Plane
§ Calculate the
distance between two points on a plane
iv.
Parallel and Perpendicular Lines
§ Compute
gradients in order to determine the conditions for any two lines to be parallel
§ Compute
gradients in order to determine the conditions for any two lines to be
perpendicular
§ Solve problems
on parallel and perpendicular lines
i.
Area of any Triangle
§ Derive the
formula for the area of any triangle
§ Apply the
formula to find the area of any triangle
ii.
Area of a Rhombus
§ Derive the
formula for finding the area of rhombi in terms of the diagonals.
§ Apply the
formula to find the areas of quadrilaterals
iii.
Perimeter of a Regular Polygon
§ Derive the
formula for finding the length of a side of a regular polygon
§ The formula to
determine the perimeter of a regular polygon
iv.
Area of a Regular Polygon
§ Derive the
formula for finding the area of a regular polygon
§ Apply the
formula to calculate the area of a regular polygon
v.
Area of Similar Polygons
§ Find the ratio
of areas of similar polygons
§ Solve problems
related to ratio for areas of similar polygons
i.
Three Dimensional Figures
§ Classify three
dimensional figures
§ List the
characteristics of each class
ii.
Construction of Three Dimensional Figures
§ Construct three
dimensional figures
iii.
Sketching Three Dimensional Figures
§ Sketch three
dimensional figures
§ Identify properties
of three dimensional figures
§ Find the angle
between a line and a plane
§ Calculate the
angle between two planes
iv.
Surface Area of Three Dimensional Objects
§ Derive the
formulae for calculating the surface area of prisms, cylinder and pyramids and
cone
§ Apply the
formulae to calculate the surface area of spheres
v.
Volume of Three Dimensional Objects
§ Derive the
formulae for calculating volume of prisms, cylinders and pyramids
§ Apply the
formulae to calculate the volume of cylinders, pyramids and cones
i.
Probability of an Events
§ Determine the
probability of an event through experiments
§ Interpret
experimental results in relation to real life occurrences
§ Write the
formula for finding the probability of an event
§ Apply the
formula to calculate the probability of an event
ii.
Combined Events
§ Perform
experiments of two combined events
§ Draw a tree
diagram of combined events
§ Find the
probability of two combined events using the formula
§ Apply the
knowledge of probability to determine the occurrence of events in real life
situation
i.
Trigonometric Ratios
§ Determine the
sine, cosine and tangent of an angle measured in the clockwise and
anticlockwise directions
§ Apply
trigonometric ratios to solve problems in daily life
ii.
Sine and Cosine Functions
§ Find sines and
cosines of angles 0 such that -720°≤ᶿ≥ 720°
§ Draw the graphs
of sine and cosine
§ Interpret the
graphs of sine and cosine functions
iii.
Sine and Cosine Rules
§ Derive the sine
and cosine rules
§ Apply the sine
and cosine rules in solving problems on triangles
iv.
Compound Angles
§ Apply the
compound of angle formulae or sine, cosine and tangent in solving trigonometric
problems
i.
Displacement and Positions of Vectors
§ Explain the
concept of a vector quantity
§ Distinguish
between displacement and position vectors
§ Resolving any
vector into I and J components
ii.
Magnitude and Direction of a Vector
§ Calculate the
magnitude and direction of a vector
iii.
Sum and Difference of Vectors
§ Find the sum of
two or more vectors
§ Find the
difference of vectors
iv.
Multiplication of a Vector by a Scalar
§ Multiply a
vector by a scalar
v.
Application of Vectors
§ Apply vectors
in solving simple problems on velocities, displacements and forces
i.
Operations on Matrices
§ Explain the
concept of a matrix
§ Add matrices of
order up to 2 X 2
§ Subtract
matrices of order up to 2 X 2
§ Multiply a
matrix of order 2 X 2 by a scalar
§ Multiply two
matrices of order up to 2 X 2
ii.
Inverse of a Matrix
§ Calculate the
determinant of a 2 X 2 matrix
§ Find the
inverse of a 2 X 2 matrix
§ Apply 2 X 2
matrix to solve simultaneous equations
iii.
Matrices and Transformations
§ Transform any
point P(X, Y) into P¹(X¹,Y¹) by pre-multiplying (ᵡᵧ) with a transformation
matrix T
§ Apply the
matrix to reflect a point P(X, Y ) in the x-axis
§ Apply the
matrix to reflect a point P(X, Y) in the Y-Axis
§ Use a matrix
operator to rotate any point P( X, Y ) through 90° 180°, 270° and 360° about
the Origin
§ Use the
enlargement matrix E in enlarging figures
i.
Simultaneous Equations
§ Form
simultaneous equation from word problems
§ Solve
simultaneous equations graphically
ii.
Inequalities
§ Form linear
inequalities in two unknowns from word problems
§ Find the
solution set of simultaneous linear inequalities graphically
iii.
The Objective Function
§ Form an
objective function from word problems
iv.
Maximum and Minimum Values
§ Locate corner
points on the feasible region
§ Find the
minimum and maximum values using the objective function
