Dynamics
State Newtons laws of motion
Explain clearly each of the laws
Apply Newtons laws to practical problems
Solve problems on motion along on inclined plane
Work down equations of motion of connected particles
Explain the concepts of work, energy and power
Solve problems on work, energy and power
Solve problems on impulse and momentum
Understand the concept of projectiles
Solve problems on motion of projectiles
Vectors in three dimension
Find dot or scalar product of vectors.
Solve problems involving the application of dot products.
Find the vector or cross product of two vectors.
Solve simple problems on the application of vector products.
Permutation & combinations
Understand concepts of permutation and combination
Solve problems in cyclic permutation
Solve other problems on permutation
Solve various types of problems on combination
Probability
Understand the frequential, classical and axiomatic approach to probability
Define some terms used in probability (e.g random experiment, sample space, events e.t.c)
Solve problems on dependent and independent events
Solve problems on complements of events. Solve problems on conditional probability.
Understand and use probability trees in solving problems.
Conic section: the circle
Define a circle
Explain why circles can be regarded as a conic section
Find equations of a circle given radius and center
Find the equation of a tangent to the circle
Find length of tangent to circle from extended point
Probability (II)
Understand the frequential, classical and axiomatic approaches to probability
Define some terms used in probability (e.g random experiment, sample space, events e.t.c)
Solve problems on dependent and independent events
Solve problems on complements of events. Solve problems on conditional probability.
Understand and use probability trees in solving problems.
Trigonometry
At the end of this lesson, the students should be able to understand Trigonometry
Calculus_Differentiation I
At the end of this lesson, the students should be able to understand Calculus_Differentiation
Calculus_Differentiation II
At the end of this lesson, the students should be able to understand Calculus_Differentiation
Differentiation (ii)
Find limits of a function at a given point
Differentiation from first principle
Differentiating polynomials
Differentiation of special functions like sin x, cos ax, ax
Use rules of differentiation
apply differentiation.
Differentiation(i)
Find limits of a function at a given point
Differentiation from first principle
Differentiating polynomials
Differentiation of special functions like sin x, cos ax, ax
Use rules of differentiation
apply differentiation.
Binomial expansion
Construct the pascal triangle
Write out the binomial expansion for (a+b)n for positive integer, negative integers and fractional values
Apply the binomial expansion to evaluating the power of number e.g (1.06)
Trigonometry functions
Know the six important trigonometric functions of angles of any magnitude
Identify range and dimension of trigonometric ratios
Drawing of graphs of trigonometric ratios
Identifying relationships between graphs of trig ratios e.g sin x and sin 2x graphs
Inverse trigonometric ratios
Solution of equation of trigonometric ratios
Proof of simple trigonometric identities
Logical reasoning ii
Understand basic issues in intelligent system
Give basic definitions of intelligent system
Understand modelling of the world
Learn about propositional and predicate logical resolution
Give introduction to proving of theorem
Polynomials
Define polynomials
Divide a polynomial by a polynomial of lesser degree
Use remainder theorem
Find factor of polynomials
Use roots of the cubic equation to solve a problem on cubic equations
Roots of quadratic equation
Find sum and products of roots of quadratic equation
Form quadratic equation given sum and products of roots
State condition for the quadratic equation to have equal roots, real roots and no roots
Identify related conditions for the given line to intersect a given curve, be tangent to curve, not intersect curve
Solve various types of problems on roots of quadratic equations
Models
Distinguish the models of operations research
Solve practical problems which involve the models
History and nature of operation research
Define operations research
Give the history and nature of operations research
Vectors in two dimension
State the difference between vectors and scalars
Perform simple operations on vectors
Determine the sum, difference of any combination of vectors lying in a plane
Resolve a vector in a given direction
Define the scalar (dot) product and its application
Measures of dispersion
Identify and calculate the measures of dispersion