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Edexhell GCE

Core Mathematics C4
Slightly Advanced

Wednesday 19 February 2013 – China Time: GMT + 08:00

Materials required for examination
Brains in gear; pencil, pen with blue or black ink; appropriate calculator. 

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions to Candidates    Answer all of each question.
When a calculator is used, the answer should be given to an appropriate degree of accuracy.

Information for Candidates
A booklet ‘Mathematical Formulae and Statistical Tables’ is not provided.
Full marks may be obtained for answers to all seven questions.
The marks for individual questions and the parts of questions are shown in square brackets: e.g. [2]. This paper was largely based on the published paper for January 2012. The total mark for that paper was 75  and for this one 45.

Advice to Candidates
You must ensure that you’re all here. There are 7 questions in this question paper. Some parts of questions are clearly labelled.
You should show sufficient working to make your methods clear. Answers without working will be marked NWNM.

1.   Use integration to find the exact value of   ∫ 4x cos 3x dx    for 0≤x≤π/2                        [6]

2.   The current, I amps, in an electric circuit at time t seconds is given by I = 9–9(0.25)t, t≥0.  Use differentiation to find the value of when t = 4 .

Give your answer in the form N ln a , where a and N are constant.                                  [6]

3.   Express     3 (x+2)-1 (x-1)-1     in partial fractions                                                       [3]

     (b) Hence find  ∫ 3 (x+2)-1 (x-1)-1 dx for x>1                                                                [3]

     (c)  Find the particular solution of the differential equation   (x+2) (x-1)  dy/dx  = 3y  
for which y = 4 at x = 3 . Give your answer in the form y = f (x).                                  [6]

4.   Relative to a fixed origin O, the point A has position vector 2i − 5j + 3k and the point B has position vector −3i + j − k . The points A and B lie on a straight line l.

(a) Find AB.                                                                                                                     [2]
(b) Find a vector equation of l.                                                                                        [2]

The point C has position vector 8i + 4j +pk with respect to O, where p is a constant. Given that AC is perpendicular to l, find (c) the value of p, (d) the distance AC.                 [4,2]

* This is based on Jan 2011 Q4. Is p=9? Is this off syllabus in 2013? dot product = 0.

5.   Use the binomial theorem to expand (3−5x)−3,    |x| < 0.6   in ascending powers of x, up to and including the term in x³ . Give each coefficient as a simplified fraction.      [5]

f(x)= (a+bx) (3−5x)−3 ,   |x| < 0.6,  where a and b are constants.

In the binomial expansion of   27 f(x), in ascending powers of x, the coefficient of x is 47 and the coefficient of x² is 160. Find

(b) the value of a and the value of b,                                                                            [3]

(c) the coefficient of x³ in f(x) , giving your answer as a simplified fraction.             [3]

total [45]   

1   4/9-2π/3 ??

2   dI/dt = 512 ln2

3     B=-A=1        y = 10 (x-1)/(x+2)   

4    r =  (-3,1,-1) + π(5, -6, 4);    AC=6,9,6 |AC| = 3 √17

5    2x+9, 50/3



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