ODOQ

WEEK 1 : 10/8/20 – 14/8/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 1: NUMBER SYSTEM AND EQUATIONS

1. Given the sets of numbers A  x : x  8 and B  (2,10). Find A  B and give your final

answer in interval notation form.

2. Evaluate log 3 125  log 3 5

3. Simplify x y
(a) x2  y 2

(b) 5 x73 x

(c) 2  1
3 1 2  2

WEEK 2 : 17/8/20 – 21/8/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 1: NUMBER SYSTEM AND EQUATIONS

1. Solve the equation of log 2 x  log 4 x  log16 x  7
2. Solve the equation of 22x  2x  6  0
3. Solve the equation of 2  7x  2x  0

AM015 WEEK 3 : 24/8/20 – 28/8/20

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 2 : INEQUALITIES AND ABSOLUTE VALUES

1. Solve the following inequalities

a) 2x  1 x  3 0

52
b) 8 1 3x  7

2. Find the interval of 2x 1x  5  x2  5x  4

3. Find the set of values of x for which 1  3 x  2  1
22

WEEK 4 : 31/8/20 – 6/9/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 3: SEQUENCES

1. The nth term of an arithmetic sequence is = 40 + 7 . Find the common difference.
Which term of the sequence is 215.

2. Given the arithmetic series 3 7 1115 ...  79 . Find the sum of all the terms of

the above series.

3. An arithmetic sequence has 11 terms. The first and last terms are 5 and 75 respectively.
a) Find the 7th term.

b) Find S6

WEEK 5: 7/9/2020 – 11/9/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 3: SEQUENCES

1. Find the sum of the first twelve terms of a geometric sequence that has a first term
of 1 and the 8th term of 243.
9

2. The third term of a geometric series is 24 and the sixth term is 3. Find the first
term and the common ratio.

3. The sum of the first three terms of a geometric series is 16 and the sum of the
next three terms is 128. Determine the first term and the sum to 10th terms of
geometric series.

WEEK 6: 14/9/20 – 18/9/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 4: MATRICES AND SYSTEM OF LINEAR EQUATIONS

1 3 1  1 2 0
   
1. If P =  2 1 0  and Q   4 0 1  ,
4 2 1 3 2
 0

a) find PT and QT

b) show that (PQ)T= QTPT

5 0 4
  1 and A  7 . Find
2. Given A   3x 2

 3  1 x 

a) the value of x
b) AT

2 2 1
3. Given B  1 3  4. Find

2 1  2

a) B
b) Adjoint B
c) B1

WEEK 6: 14/9/20 – 18/9/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 4: MATRICES AND SYSTEM OF LINEAR EQUATIONS

1 3 1  1 2 0
   
1. If P =  2 1 0  and Q   4 0 1  ,
4 2 1 3 2
 0

a) find PT and QT

b) show that (PQ)T= QTPT

5 0 4
  1 and A  7 . Find
2. Given A   3x 2

 3  1 x 

a) the value of x
b) AT

2 2 1
3. Given B  1 3  4. Find

2 1  2

a) B
b) Adjoint B
c) B1

WEEK 7: 21/9/20 – 25/9/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 4: MATRICES AND SYSTEM OF LINEAR EQUATIONS

5 0 3  2 0 3
1. Given A  2 1 1 and B  1 1 
1  . Find AB and hence find A-1.

3 0 2 3 0 5 

5 0 3 x 4
If 2 1  y 6 ,
1   find the value of x, y and z.

3 0 2  z  2

2. A stationary shop offers three packages A, B and C for writing pads, liquid ink and ball
pens. The number of each item and the offer price for each package are shown in the
following table.

Sales Package Writing pads Liquid ink Ball pens Offer price (RM)
A 3 2 5 31
B 4 3 7 44
C 2 1 5 21

If the selling prices of a writing pad, a bottle of a liquid ink and a ball pen are RMx, RMy and
RMz respectively, form a system of linear equations based on the information given. Write
the system of linear equations in the form of AX=B and find the selling price of each item by
using adjoint method.

3. Solve the following system of linear equations by using Cramer’s Rule:

x  2y 5
3x  2y  z 10
2x  4y  z 13

WEEK 8: 28/9/2020 – 2/10/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 5: FUNCTIONS AND GRAPH

1. Sketch the graph and state the domain and range of the following functions.
a) f (x)  x  3
b) f (x)  x2  2x  3, x  1.

2. If f (x)  x2 1, and g(x)  2 find
x

a) ( f  g)(x)
b) (g  f )(x)

3. a) Find f (x) such that (g  f )(x)  x 1 and g(x)  x 1.
b) Given ( f  g)(x)  4x2  2x 1, find f (x) if g(x)  2x 1.

WEEK 9: 5/10/2020 – 9/10/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 5: FUNCTIONS AND GRAPH

1. By using the algebraic method, determine whether f is one-to-one function or
not.
a) f (x)  x  3, x  0
b) f (x)  4  2x  3

c) f (x)  3x 12  4, x 1

2. Find the inverse of the following function, then state its domain and range.

a) f (x)  x2  2x  3, x  1
b) f (x)  x  3, x  0

3. Find the value of q if the function f (x)  4x  22  q, x  2 and f 15  3; x  2.

.

WEEK 10: 12/10/2020 – 16/10/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 5: FUNCTIONS AND GRAPH

1. Find the inverse function and graph the functions and its inverse. Determine the domain and

range.

a) f(x) = 1 – ex b) f(x) = 3 + 2x

2. Find the inverse function and graph the functions and its inverse. Determine the domain and

range.

a) f(x) = ln(2x + 5) b) f(x) = 3 + ln x

3. Given functions f (x)  e2x , x  R and g(x)  ln8  3x, x  8 . Find f  g(x) and f  g(3).

3

WEEK 11: 26/10/2020-30/10/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 6: POLYNOMIALS

2x3  2x  5
1. Find the quotient and remainder for x2  3x
2. When x2  2 px  9 is divided by (x+3), the remainder is 4. Find the value of p.

3. Using remainder theorem, find the remainder when P(x)  x3  2x2  3x  5 is divided by
(x2  4) .

WEEK 12: 2/11/2020-6/11/2020

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 6: POLYNOMIALS

x 1
1. Express the following as partial fractions x(x2 1)

Express the following as partial fractions x5

x2  4 x  2
 2.

3. Express 4x2  6x 1 as a sum of partial fractions
(x  2)(x2  2x  3)

AM015 WEEK 13 : 9/11/20 – 13/11/20

PROGRAM MATH MANIA KATEGORI 2
CHAPTER 7 : LIMITS

1. Evaluate lim x2 1
x2 .
x

2. Evaluate lim 2x2  7x  3 .
3 x6
x3

3. Find the value of k and m if lim f (x) and lim f (x) exist
x2 x1

x  2k ; x  2
f (x)  3kx m
; 2 x 1.
3x  2m ; x 1

Week 14: 16/11 – 20/11/2020

PROGRAM MATHS MANIA KATEGORI 2
CHAPTER 8: DIFFERENTIATIONS

1. Find dy for the function y  4x2  7x  5 by using the first principle method.
dx

2. Differentiate each of the following function with respect to x .

a) f (x)  x2  2x . b) h(x)   1  x  1  x 
 x   x 

3. Find the second order derivative of the following function.

a) f (x)  63 x4  3  7 b) f (x)  1
2x2 9 2x 3

Week 15: 23/11 – 27/11/2020

PROGRAM MATHS MANIA KATEGORI 2
CHAPTER 8: DIFFERENTIATIONS

1. Find the derivatives of each of the following:

a) y  2x35  x2 b) y  x2
x 1

c) y  ex d) y  e2x ln x
ex 1

2. If y  ex ln1 2x, show that dy  y  2ex .

dx 1 2x

3. Given y  e2x . Show that d2y  3 dy  2y  0.
dx 2 dx

Week 16: 30/11 – 4/12/2020

PROGRAM MATHS MANIA KATEGORI 2
CHAPTER 8: DIFFERENTIATIONS

1. Differentiate the function of 2xy3  3x2 y  1 and find the gradient at a point (1,1)

and (2,3).

2. If 3x2y + y2 = x + 9, show that  3x2 2y  dy  1
 1 6xy  dx
 

3. Find dy , if x2 ln y  e2y  3xy.
dx

Week 18 : 14/12 – 18/12/2020

PROGRAM MATHS MANIA KATEGORI 2
CHAPTER 9 : APPLICATION OF DIFFERENTIATIONS
1. The total cost (in RM) to produce x units of keyboard per day is given by the cost function
C(x) = 2x3 – 30x2 + 126x + 30. Find the
(a) average cost function
(b) average cost when 7 units of keyboard are produced.
(c) marginal cost function
(d) number of keyboards to be produced so that the cost is minimum.

2. Product S can be produced at cost RM 10 per unit. The demand equation for this product is
p = 90 – 0.02x, where p is the price in RM and x is the number of units. Find
(a) the revenue function
(b) the marginal revenue
(c) the marginal cost
(d) the number x for which marginal revenue equals marginal cost.

3. The demand function and the cost function (in RM) for a manufacturing is given by
P(x) = 6 – x and C(x) = 2x + 2, where x is the number of unit produced. Find the
(a) total revenue function
(b) maximum revenue
(c) profit function
(d) average profit function
(e) marginal profit function
(f) maximum profit.

WEEK 17 : 7/12 – 11/12/2020

PROGRAM MATHS MANIA KATEGORI 2

CHAPTER 9 : APPLICATION OF DIFFERENTIATIONS
1. Find the points on the curve y = x3 – 9x2 + 20x where the tangents are parallel to the line

y = – 4x + 3 .

2. The tangent to the curve y = px2 + 1 at the point (1,q) is parallel to the point y – 6x = 2.
Find the values of p and q.

3. Find the equations of the tangent and the normal to the curve xy2 + x2y – 6 = 0 at the point
(1, – 3).