Moodle  : Mathematical Methods

blueline

Quizzes

Welcome to the Math Methods course. I believe this is one of the hardest courses to teach, as people with a wide range of abilities take this class. I'll try my best by making useful resources and quizzes that will aid you with your revision. I'll be updating this page every Wednesday from now on with questions, and on the following week will provide you with the answers.

Good luck with your studies

blueline

This week's quiz:

1. Write the following in logarithmic form:

   a) 32 = 9

   b) 73 = 343

   c) xy = z

2. Write the following in exponential form:

   a) log5125 = 3

   b) log2128 = 7

   c) logx y = z

3. Use the logarithmic rules to solve the following (don't use your calculator)

   a) log3x + log34 = log312

   b) log4y - log43 = log45

   c) 5x = 7

   d) lognx + logny -lognz


Answers

1.a) log39=2

   b) log7343=3

   c) logxz=y

2.a) 53=125

   b) 27=128

   c) xz=y

3.a) log3x + log34 = log312

       log34x=log312

       4x=12

       x=3

   b) log4y - log43 = log45

       log4 y/3 = log45

       y/3 = 5

       y=15

   c) 5x = 7                 

       log57=x                     or        log5x=log7

       x= log7 / log5                       xlog5=log7

                                                 x=log7 / log5

   d) lognx + logny -lognz

       logn (xy) /z

blueline

Algebra and Sequence - part 1

Answer the following questions. Keep your answers until next wednesday.

1. Complete the following sequence and note down whether the sequence is Arithmetic or Geometric:

     a) 3,7,11, _ , _

     b) 2,6,18, _ , _

     c) 2,-4,8, _ , _

2. Write down the general formula of Arithmetic Sequence and Geometric Sequence.

3. Your company invest $8,000 at 6% interest compounded annually.

     a) How much do the company earn in 3 years?

     b) How long will it take for this company to have $15,000?

     c) How much money will the company have in n years?

4. Find the nth term of the following sequences:

     a) 1,2,4,8,16,....

     b) 2,8,14,20,....

     c) 13,-39,117,....

5. Find the sum of first 10 terms of the following sequences:

     a) 5,25,125,....

     b) 1,-3,9,-27,....

     c) 25,28,31,34,....

6. Write the general formula for Arithmetic Series and Geometric Series.


Answers

1.a) 15,19

   b) 54, 162

   c) -16, 32

2. Arithmetic Sequence: nth term= a+(n-1)d

    Geometric Sequence: nth term= ar(n-1)

3.a) approximately $9528

   b) 11 years

   c) x=8000(1.06)n

4.a) nthterm=1 x 2(n-1)

   b) nthterm=2 + (n-1)6

   c) nthterm=13 x -3(n-1)

5.a) 12207030

   b) 14762.5

   c) 385

6.Arithmetic Series: Sn= ( n/2 )( 2a + d(n-1) )

   Geometric Series: Sn=( a ( 1 - rn )) / ( 1 - r )

blueline

This week's quiz:

1. Find the slope and y-intersect of following functions:

   a) y = 3x + 1

   b) y = 7x - 5

   c) f(x) = (1/2)x + 4

2. Define the term "Asymptote".

3. For the following functions, solve for the horizontal and vertical asymptotes if present:

   a) y = 3 / (x2 - 9)

   b) f(x) = (x + 5) / (x2 + 5x + 6)

   c) y = (x + 1) / (x2 - 16)