Binary Operations Part 1
At the end of this lesson, the students should be able to understand Binary Operations
Change of Base Formula: Logarithm
Change of Base Formula: Logarithm
Integration
Students should be able to understand integration as the reverse process of differentiation
Integrate Algebraic polynomials including 1/X
Apply integration to kinematics problems, including velocity-time graphs
Use the definite integral to calculate the area under a curve
Partial fractions
Students should be able to resolve rational functions into partial fractions (degree of numerator less than
that of numerator which is less than or equal to 4)
Matrices & determinants(2*2, 3*3)
Understanding the array as a linear transformation
Finding determinants and apply to solve simultaneous equations in two or three unknowns
Inequalities
Solve quadratic inequalities and inequalities in two dimension
Replacement model
Understand the concept of replacement of items.
Identify the various type of replacement analysis
Solve problems on replacement of sudden failure items
Solve problems on items that wear off gradually
Inventory model
Explain the concept of inventory
Define important terms in inventory
Compute the optional quantity in inventory model
Dynamics II
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
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.