Mathematics N2 August 2011 question paper Memo

Mathematics N2

Mathematics N2 Question Paper

August 2011 question paper

Question 1
1.1
1.1.1 answer C
1.1.2             B
1.1.3             B
1.1.4             B
1.1.5             D although the correct answer ia actually 0,096 [34,4 / 360]
1.1.6             A
1.1.7              B
1.1.8             C
1.1.9             B
1.1.10           A

1.2
1.2.1                True
1.2.2                 True
1.2.3                False
1.2.4                True
1.2.5                 False
1.2.6                True
1.2.7                True
1.2.8                True
1.2.9                 False
1.2.10               False

Question 2

Factorisation, LCM, algebraic fractions and simplification.
Since I have dificulty in expressing powers, I will only post the answers here.
2.1
2.1.1 Answer         sin @/4 (x - y)(x + y)
2.1.2 Answer         (1 - p)(3x +b)
2.1.3 Answer         3a(a + 5)(a - 2)
2.1.4 Answer         3x(1 + 4y^2)

2.2
         Answer                  LCM = 2x(x - y)^2(x + y)(2x + 3y)

2.3 
2.3.1 Answer          (3p + 4y)/xyp                 
2.3.2 Answer             1

Question 3

3.1 We have to solve for x and y: if y = x^2 - 4 and y = - x - 2
The easiest method is to equate the right hand side of each equation, since the left hand sides are equal, therefore                                     x^2 - 4 = - x - 2
which we must rearrange as a quadratic equation of x,  all to the left hand side
then we have to factorise , then  x = -2, or x = 1
then we have to calculate the corresponding y-value for each x-value
(-2;0) and (1;-3) are the final answers

3.2          answer : d = eT/mv by applying the rules of manipulation

3.3 
3.3.1       answer: a^(x + 7)  [read a raised to the power(x + 7)
3.3.2      answer: 1
3.3.3      answer: the answer is difficult to express here
                             1 / 6th root of (ab)^5 [reads: THE 6th root of (ab) raised to the power 5
3.4
3.4.1     using LCM of 3 and 4 which is 12 to help us, and rules
               we get that x = 4
3.4.2 we have to use the rule that (anything)^0 = 1 [reads anything raised to the power of 0 = 1]
and also the rule (root x)^2 = x [reads: the square root of x, squared = x]
then x =1

3.4.3 here we have to rewire square root of x, as well as 32, into power form first.
then x = 2^10 = 1024

3.5 the answer, applying the rules of logs = 3,071

3.6 
3.6.1
 log 100 base 5 - log 4 base 5 = log 100/4 base5
                                                        = log 25 base 5
                                                        = 2 log 5 base 5
                                                        = 2

3.6.2 
4 raised to the power log 16 base 4
we can first simplify the power part, which is log 16 base 4 = log 4^2 base 4 = 2 log 4 base 4
                                                                                                = 2 x 1 = 2
then finally we have 4 raised to the power log 16 base 4 = 4 ^2
                                                                                            16

Question 4

4.1 convert degrees, minutes and seconds to radians. First we have to convert everything to degrees. Convert 12 seconds into minutes first (by dividing by 60), then add the answer to 36 minutes. Now convert the total minutes into degrees (by dividing by 60), and add this answer to 58. now we have a value expressed in degrees only. To convert the degrees into radians we multiply by pi, and divide by 180.

4.2 angular motion
4.2.1   w = 2 x pi x n where n is the rotational frequency in revs per sec.
4.2.2    angular displacement = angular velocity x time
4.2.3   no of revs in 1 minute [ here we have to divide our previous answer of 4.2.2 by 2 pi to convert the radians into revs.

4.3 here we apply the applicable formulae from the formula sheet

Answers
4.1     answer = 1,023 radians

4.2
4.2.1     n = 47, 746 revs/sec
4.2.2     theta = 18000 radians
4.2.3     theta = 2864,789 revs

4.3
4.3.1          s = 418,879 mm
4.3.2        A  = 83 775,804 mm^2

4.4
4.4.1                   Volume = 3 078 760,801 mm^3
4.4.2           surface area = 118 752,202 mm^2

Question 5

5.1      A graph has to be drawn, and answers need to be determined off of the graph:

The answers are as follows:

5.1.1    x = 30 degrees, and x = 150 degrees

5.1.2    x = 15 degrees and x = 165 degrees

5.1.3 amplitude = 2

5.2 graph of y = x^2 - 2x - 8

y-intercept (0; - 8)

roots           (-2;0) and (4;0)

axis of symmetry   x = 1

turning point  (-1; -9)