course plan year one semester 2

St Vincent & the Grenadines Community CollegeDivision of Arts Sciences & General Studies

Course Plan

Period Covered: Semester 2 12th January 2015 – 24th April 2015Module 2: Trigonometry, plane Geometry and LimitsModule 3: Calculus 1Lecturer Name: Dawn Scott

Week No.

Dates Topics Readings/assignments

1

13 Jan 2015

14 Jan 2015

Trigonometry, Plane Geometry and Vectors

Circular Measure

1. The radian measure

2. Converting from degrees to radians

3. Converting from radians to degrees

4. Length of an arc

5. Area of a sector

6. Sine rule and cosine rule

7. Area of a triangle using A=12ab sin c

Trigonometric Functions

1. Graph the functions sin kx , cos kx ,

tan kx , k∈R2. Relate the periodicity, symmetries and

amplitude of the functions above to their

graphs

3. Reciprocal functions sec x , cosec x , cot x

4. Use sin( π2 ± x)=cos x5. Trigonometrical functions for a general

angle

6. Exact values of trigonometric functions

(0 ° ,30 ° ,45° ,60 ° ,90 ° ,180 ° ,270 ° ,360 ° )

Pure Mathematics for Cape Vol. 1 pg 123 – 129


7. Negative angles (measured in a clockwise

direction)

1 15 – 16 Jan 2015

Trigonometric Identities

1. Derive the identity cos2θ+sin2θ=1

2. Use the reciprocal functions sec x ,

cosec x , cot x

3. Derive the corresponding identities for

tan2θ ,cot2θ , sec2θ , cosec2θ

4. Use compound angle identities for

sin ( A±B ) ,cos ( A±B ) , tan ( A±B )

5. Develop and use the expressions for

sin A± sinB ,cos A± cosB

6. Prove further trigonometric identities

using those above


Assignments- Circular Measure- Due Fri 16th Jan 2015- Due Tues 20th Jan 2015

2 20- 23 Jan 2015

Trigonometric Equations

1. Express acosθ+b sin θ in the form

R cos (θ±α ) and R sin (θ±α ) where R is

positive and 0≤θ< π2

2. Find the general solution of equations of

the form

a) sin kθ=c

b) cos kθ=c

c) tan kθ=c

d) acosθ+b sin θ=c

for a ,b , c , k∈ R3. Find the solutions of the equations above

for a given range

Pure Mathematics for Cape Vol. 1 pg 142 -145, 154 – 158

Obtain maximum and minimum values of

f (θ ) for 0≤θ≤2π

3 27 – 30 Jan 2015

Coordinate Geometry

1. find equations of tangents and normals to

circles;

2. find the points of intersection of a curve

with a straight line;

3. find the points of intersection of two

curves;

4. obtain the Cartesian equation of a curve

given its parametric representation.

5. Obtain the parametric representation of a

curve given its Cartesian equation.

6. Determine the loci of points satisfying

given properties.

Pure Mathematics for Cape Vol. 1 pg 98 - 122

Class Test: - Thur29th January 2015- trigonometry

4 3 – 6 Feb 2015

Vectors

1. express a vector in the form ( xyz )or

x i+ y j+zk where i, j and k are unit

vectors in directions of x-, y- and z-axis

respectively;

2. define equality of two vectors;

3. add and subtract vectors;

4. multiply a vector by a scalar quantity;

5. derive and use unit vectors, position

vectors and displacement vectors;

6. find the magnitude and direction of a

vector;

7. find the angle between two given vectors

using scalar product;

Pure Mathematics Unit 1 for Cape Examinations pg 303 – 313

5 10 – 13 Feb 2015

8. find the equation of a line in vector form,

parametric form and Cartesian form,

given a point on the line and a parallel

vector to the line;

9. determine whether two lines are parallel,

intersecting, or skewed;


Assignment- Coordinate Geometry- Vectors- Due Fri 12th Feb 2015

6 16 – 20 Feb 2015

10. find the equation of the plane, in the form

ax+by+cz=d, r . n=d , given a point in

the plane and the normal to the plane.

Review of Module 2


Class Test 2: Module 2 Thur 19th February

2015

7 24 - 27 Feb 2015

Calculus 1

Limits

1. use graphs to determine the continuity

and discontinuity of functions;

2. describe the behavior of a function f ( x )

as x gets arbitrarily close to some given

fixed number, using a descriptive

approach;

3. use the limit notation f ( x )x→alim ¿=L ,f (x )→ L¿ as

x→a;

4. use the simple limit theorems:

If f ( x )x→alim ¿=F , g (x )x →a

lim ¿=G,¿ ¿ and k is a constant,

then

kf ( x )x→alim ¿=kF , f ( x )g ( x )x→ a

lim ¿=FG,¿ ¿

{f ( x )+g ( x ) }x→alim ¿=F+G, ¿

and, provided G≠0 ,f ( x )g ( x )x→a

lim ¿=FG ¿;

5. use limit theorems in simple problems;


6. use the fact that sin xxx→a

lim ¿=1 ,¿

demonstrated by a geometric approach;

7. identify the point(s) for which a function

is (un)defined;

8. identify the region over which a function

is continuous;

9. identify the point(s) where a function is

discontinuous;

10. use the concept of left handed or right

handed limit, and continuity on a closed

interval.

8 3 – 6 Mar 2015

Differentiation 1

1. Define the derivative of a function at a

point as a limit;

2. Differentiate, from first principles, such

functions as:

a) f ( x )=k where k∈R,

b) f ( x )=xn where

n∈{−3 ,−2 ,−1 ,−12 , 12 ,1 ,2 ,3},

c) f ( x )=sin x ;

d) f ( x )=cos x .

3. Use the sum, product and quotient rule

for differentiation;

4. Differentiate sums, products and

quotients of:

a) polynomials,

b) trigonometric functions;

5. apply the chain rule in the differentiation

of


Module 2 Exam- Thur 5th March 2015

a) composite functions (substitution);

b) functions given by parametric

equations;

9 10 – 13 Mar 2015

Applications of Differentiation

1. solve problems involving rates of change;

2. use the sign of the derivative to

investigate where a function is increasing

or decreasing;

3. apply the concept of stationary (critical)

points;

4. calculate second derivatives;

5. interpret the significance of the sign of

the second derivative;

6. use the sign of the second derivative to

determine the nature of stationary points;

7. sketch graphs of polynomials, rational

functions and trigonometric functions

using the features of the function and its

first and second derivatives (including

horizontal and vertical asymptotes;

8. describe the behavior of such graphs for

large values of the independent variable;

9. obtain equations of tangents and normals

to curves.


Class Test: - Friday 13th March 2015- Limits- Differentiation

10 17 – 20 Mar 2015

Integration 11. recognize integration as the reverse of

differentiation;

2. demonstrate an understanding of the

indefinite integral and the use of the

integration notation ∫ f ( x )dx;


Assignment- Application of

Differentiation- Integration

3. show that the indefinite integral

represents a family of functions which

differ by constants;

4. demonstrate use of the following

integration theorems:

a) ∫ cf (x )dx=c∫ f ( x )dx, where c is a

constant,

b)

∫ {f ( x )± g ( x ) }dx=∫ f ( x )dx ±∫ g ( x )dx

;

5. Find:

a) Indefinite integrals using integration

theorems,

b) Integrals of polynomial functions,

c) Integrals of simple trigonometric

functions;

6. Integrate using substitution;

7. Use the results:

a) ∫a

b

f (x )dx=∫a

b

f (t )dt ,

b) ∫0

a

f (x )dx=∫0

a

f (x−a)dx , for a>0 ;

c) ∫a

b

f (x )dx=F (b )−f (a ) , where

F ¿ ( x)=f ( x );

- Due Fri 19th Mar 2015

11 24 - 27 Mar 2015

Application of Integration

1. Finding areas under the curve,

2. Finding areas between two curves,

3. Finding volumes of revolution by rotating

regions about both the x and y axes;

4. Given a rate of change with or without


Assignment- Application of

initial boundary conditions:

a) Formulate a differential equations of

the form y¿=f (x) or y¿∨¿=f ( x )¿

where f is a polynomial or

trigonometric function.

b) Solve the resulting differential

equation and interpret the solution

where applicable.

Integration- Due Fri 27th Mar 2015

12 31 Mar – 3 Apr 2015

Past Papers Class Test 2: - Module 3- Thurs 2nd April 2015

13 6 – 10 Apr 2015

Past Papers Module 3 Exam- Thur 9th April 2015

14 11 – 17 Apr 2013

Past Papers

15 20 – 24 Apr 2012

Correction of Module 3 Exam Enter IA grades in ORS

course plan year one semester 2

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