Mathematics N3 November 2012 Memo

Mathematics N3 Question Paper

November 2012

Mathematics N3 Question Paper

August 2012

Question 1 Answers only

1.1     C

1.2     B

1.3    B

1.4    A

1.5    D

1.6    C

1.7    B

1.8    D

1.9    D

1.10  there is a printing error: the correct answer is y = - 15cosx   

Question 2

2.1

2.1.1     Answer is 3

2.1.2     Answer is 1

2.1.3     Answer is 5/6

2.2

2.2.1     8x^2 - 2(x + 1)^2

           = 8x^2 - 2 [x^2 + 2x + 1]

          = 8x^2 -2x^2 - 4x -2

          = 6x^2 - 4x - 2

          = 2(3x^2 - 2x - 1)

         = 2(3x + 1) (x - 1)

2.2.2      (a + b)x^2 - 2ax - 2bx + b + a
            = (a + b)x^2 - 2x(a + b) + 1(a + b)
            = (a + b)(x^2 - 2x + 1)
           = (a + b)( x - 1) (x - 1)

2.2.3       m^36 - 15 m ^18  + 54
            = (m^18 - 9)( m^18 - 6)
           = (m^9 - 3) (m^9 + 3)(m^18 - 6)

2.3    x-a will be a factor of f(x) = -x^3 + (a + 3)x^2 -x(3a +3) +3a if f(a) = 0
                                          f(a)  = -a^3 + (a + 3)a^2 - a(3a +3) + 3a
                                                 = -a^3 + a^3 + 3a^2 - 3a^2 - 3a + 3a
                                                 = 0
therefore, x -a is a factor of f(x)

2.4
Answer is 6 sq rt 5/ 5

Question 3

3.1 solve for x:

3.1.1                 3^x + 3^x + 1 = 36

                         3^x  + 3^x . 3^1 = 36

                         3^x ( 1 + 3)           = 36

                         3^x                        = 9 = 3^2

                      therefore      x = 2

3.1.2    algebraic fractions : solve for x

answer : x = 0 or x = 3

3.2

3.3 answer : d = square root( d^2 - 4A/pi)

                   and d = 2,1

3.4    simultaneous equations: if it is given that L = B + 5 and 2 ( L + B) = 30, then through substitution we get that B = 5 and L = 10 

Question 4

4.1

4.1.1 x^2 / 4 + y^2 / 25 = 1

4.1.2    y = x ( x - 1 )( x + 2)

4.1.3 y = ( x - 2 ) ( x - 5 )

4.2     simultaneous equations:    y = - 2x + 14  eq 1

                                                 2y = 7x - 5     eq 2

                           eq 1 x 2:        2y = - 4x + 28

                           eq 2               2y = 7x - 5

subtract                                     0 = - 11x + 33

then x = 3 and y = 8

sketch of two graphs showing point of intersection