LINEAR EQUATIONS

1.  Find the value of p:

     7p - 5 = 9

2.  Find the value of m :

     m/2   + 7  = 10

3.  Find the value of k :

     0.5( k - 3) = 6

4.  Find the value of r :

    3( r + 5) = 12

5. Find the value of t :

    2( 3t - 1) = 16



Happy trying!

SIMULTANEOUS EQUATIONS

Solve the following simultaneous equations :


1.       x +  y =  10

         2x - y  =  11


2.     3x - 2y = 11

         x + 2y =  9


3.    0.5x - y =  3

         x + 2y = 14


4.    7x - 2y  = 16

         5x + y =  9


5.     5x - 3y  = 22

        2x  -  y  = 9




     

POLYNOMIALS : Factors and Zeroes of Polynomials

Example 1

A polynomial P  is  given as  P(x) = x^3- 2x^2 -5x + 6.  

(a) Show that  x = 1, x=-2 and x=3 are zeroes of P(x). 

(b) Express P(x) as the product of linear factors;

Happy trying

Hafsah

MACLAURIN SERIES: Standard Power Series

1.   sin x = x - (x^3)/3! + (x^5)/5!-  for all values of x.

2.   cos x = 1 -  (x^2)/2! + (x^4)/4!- for all values of x.

3.   e^x   = 1 + x + (x^2)/2! +  (x^3)/3! +  (x^4)/4!+  for all values of x.

4.   ln(1+x) = x - (x^2)/2 +  (x^3)/3-...   for all x in the interval of   ( -1,1]

MACLAURIN SERIES : Power series for ln(1+x)

Let   f(x)  = ln(1+x)    so     f(0) = ln 1 = 0
       f '(x)  = 1/(1+x)    so   f '(0) = 1
       f ''(x)  = -1/(1+x)^2    so   f ''(0) =  -1
       f '''(x)  =  2/(1+x)^3    so   f '''(0) =   2
       .....
Therefore,

ln(x+1) =  x - (x^2)/2! + 2(x^3)/3! -6 (x^4)/4! + ...
             =  x -(x^2)/2 + (x^3)/3 - (x^4)/4!  + ....+ ((-1)^(n+1))(x^n)/n +...

MACLAURIN SERIES : Power series for Sin x

Let     f(x) =  sin x   so    f(0)    =  0
        f '(x)  = cos x   so    f '(0)  =  1
        f ''(x) = - sin x  so    f ''(0) =  0
        f '''(x) = -cos x  so    f '''(0)= -1
        .
        .
        .

using Maclaurin Theorem,

sin x = f(0) + xf '(0) + ( (x^2)/2!) f ''(0) + ( (x^3)/3!) f '''(0) + ...

sin x = x - ( (x^3)/3!) + ( (x^5)/5!)+...+ ((-1)^n) (x^(2n+1))/(2n+1)!)+...

INDICES

Answer all of the following :

1.   Simplify
   
      (a)    16 ^(3/2)


      (b)    (2/3)^(-2)


2.   Find the value of x for
   
      (a)     x^3 = 27


      (b)   2x^4  = 32


      (c)   5x^3 = 5000


3.  Find the value of y  for      2y^(4/4) = y^(1/2)


Happy trying !

   

MACLAURIN 'S SERIES

STANDARD SERIES

Exponential Series :

f(x)     = e^x =>    f(0)   = e^0 = 1
f '(x)   = e^x =>   f''(0)   = e^0 = 1
f ''(x)   = e^x =>   f ''(0) = e^0 = 1
.
.
.
f (n)(x) = e^x =>   f(n)(0) = e^0 =1

Hence,  

 e^x  = 1+ x + (x^2)/2! + (x^3)/3! +...+(x^n)/n! ....     for all value of x.

there are more.....

ALGEBRAIC EXPRESSIONS

Simplify the following

1.  x - 3x + 7x

2.  5m - 12m + 13m

3.  h + 2h - 3h + 4h - 5h

4.  k - 2k + 3k + 4k

5.  7r - 2r + 5r - 3r

Happy Trying !

LINEAR EQUATION

Solve the following linear equation :

1.   2x -1 = 19

2.   5x +2 = 22

3.   5x - 7 = 53

4.   15x  - 3 = 42

5.   -3m + 1 = 7

Happy trying !

MACLAURIN'S SERIES

Show that    1/(1-x)  =   1+ x+x^2+x^3+...


[ Note: use Maclaurin's theorem]


Happy Trying!


huffy64@gmail.com

WHOLE NUMBER

Whole Number : 0,1,2,3,4,5,...


Answer all of the following:

1.   Calculate the following

(a)  22 + 89

(b)  135 - 68


2. Round off the following numbers to the nearest hundreds

(a)  3217

(b)  21591


3. Find the value of x

(a)  2x - 7 = 13

(b) 7x - 3 = 32




Happy Trying !

huffy64@gmail.com

MODULUS

Find the solution for the following


(a)  |2x-1| > 3

(b) |2/(1-x)| < 1/2


Happy Trying !

STATISTICS : Mean, Mode and Median

MEAN  is   the sum of all data over numbers of data.

MODE  is the data with the highest frequency.

MEDIAN is the data that is located in the middle in an ascending or descending order.



The   following are Mathematics  marks of a group of students.

73  50  48  32  86
60  58  90  53  65 

Find the mean, mode and median of the above data.


Happy trying !

DIFFERENTIATION

Differentiate the following :

1.  y= 2x

2. y= 3x^2 - 7x

3. y= 4x^3 + 5x^2 - 7

4. y= -5x^3+7x^2-2

5. y=7x^2-6x+8

6. y=(7x^2-14x)/2

7. y=(5x^3-4x^2+7x)/x


Happy trying  ....

huffy64@gmail.com

INTEGER

Answer all of the following.

1. 123+72÷12+13          =
2. 215 -  (-75) + 25        =
3. 180÷6 + 3(45÷(-3))   =  
4.  320 ÷(-8) +72÷3       =
5.  35-(-28)+325+(-17) =

Dear readers, if you want me to respond to you feedback, email me your answer along with the original questions so that i could help you with your working....

ENJOY!, 

hafsah

My email : huffy64@gmail.com

INTEGERS

Answer all of the following.

1.   34+18+12+125

      Answer :


2.    (120-60) + (80-44)

     Answer :


3.   220-(190+75)

  
     Answer :


4.   34 x 5 - (-2) x15


    Answer :


5.   13 x 5 + (-3)x7

    Answer :




Happy Trying !

hafsah

Percentages

Answer all of the following

1. There are  120 students participate in a quiz and 30   of them scored full mark. What is the percentage of the students that scored full marks ?

2. Calculate 30% of RM3000

3. Three out of twenty students wear spectacles. What is the percentage of students who do not wear spectacles?

4. Pn Fatimah deposit RM5000 in a saving account. At the end of the yearshe received 5% dividend for her saving. Calculate her dividend at the end of the year?


Happy Trying

Whole Number- Combined Operations

Answer all of the following

1.  2(30-12)-3(15-7)

2.  3(72-48) + 6(3+2)

3.  5(45-36) - 2( 18-12)

4.   7(32-16) + 5(24-15)

5.   9(33 - 7) - 11(13-4)


Happy trying

huffy64@gmail.com

Whole Number- combined operations

Calculate all of the following.

1. 235 +2(12-5)
2. 528 -3(27-9)
3. 97+15(7+3)
4. 3(15-7)+2(4+11)
5. 8(27-12)-2(15-8)
7. 12(12-7)-5(8-3)
8. 337-5(25-15)+123
9. 321+21(15-7+2)
10. 42(7-5)+3(12-4)-25

happy trying!

Pn hafsah