kfccalmt9709 - exam paper - 200508 - maths p3 - trial exam - taylor

7/26/2019 Kfccalmt9709 - Exam Paper - 200508 - Maths p3 - Trial Exam - Taylor

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TAYLOR SCOLLEGE

f1.dom .ln1e rlty E ..tleneeCAMBRIDGE A LEVEL PROGRAMMEA2 TRIAL EXAMINATION AUGUST/SEPTEMBER 2005 July 2004 Intake)

Tuesday

MATHEMATICS

30 August 2005 1.00 pm - 2.45 pm

9709/3

PAPER 3 Pure Mathematics 3 P3)

Additional materials: Answer Booklet/PaperList of formulae MF9)

READ THESE INSTRUCTIONS FIRST

1 hour 45 minutes

If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet.Write your name and class on all the work you hand in.Write in dark blue or black pen on both sides of the paper.You may use a soft pencil for any diagrams or graphs.Do not use staples. paper clips, highlighters, glue or correction fluid.

~ I Answer all the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of anglesin degrees. unless a different level of accuracy is specified in the question.At the end of the examination, fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question or part question.The total marks for this paper is 75.

Questions carrying smaller numbers of marks are printed earlier in the paper, and questions carrying largernumbers of marks later in the paper.The use of an electronic calculator is expected, where appropriate.You are reminded of the need for clear presentation in your answers.

This document consists of 5 printed pages.

Taylor s College Subang Jaya 2004 [Turn over


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6. i) Express JOiintheform r cos8+isin8), wherer> o and 0


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I. The real polynomial P x) = ax_b 3 has a remainder of -8 on division by x I and

a remainder of 27 on division by x

2. Find the constants a and b. 3 ]

3

2. i) Show that the iterative formula Xn+1 = 2xn 2 5 can be rearranged into the, 3xn +2

form x3 +ax+b = 0, . [I]. .

ii )With these values of a and b, u~e an iteration based on this rearrangement

with initial approximation xo = 1 to find a solution to the equation .Leave

your answer correct to three decimal pl~es

3. Given the equation of a curve is 2X2 3xy y2 = 5; find the equation of the

tangent to the curve at the point 4,3 ).

4 E 5x2-4x+12. ICo. xpress 2 m partla lractlOns. x 2 x +4

H b 5x2 4x 12 . f d f dence 0 tam 2 as a senes 0 ascen mg powers 0 x up to an x-2 x +4

including the term in x3 .

5. By means ofthe substitution x = tan ) or otherwise, find the exact value of

2

[3 ]

[ 5 ]

[ 3 ]

[ 3 ]

[7]


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8. The sketch below shows the curve with equation y =x21n 2x

y

y =~ln 2x

x

{i) Find the exact coordinates of the stationary point. [ 5 ]

ii ) Find the x-coordinate of the point where the curve cuts the x- axis.

Hence calculate the area of the shaded region. [ 5 ]

9. i) Show that tan e cot 0 == 2cos ec20 2 ]

i i ) Find all solutions of the equation 2cos ec20 = 3tan 0 1 for - 1r S 0 S 1r

]

iii )Express 3cose - sin 0 in the form R cos O where R > 0

and 0 < < 90 . Hence or otherwise, solve the equation3cose-sinO=-1 for -180 SOS1800.

4

[4 ]


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i Show that the lines II and intersect and find the coordinates of the point of

[ ]

\ ../J

J L/o I

intersection.

10. Two lines IJ and 2 have equations given by

ii Show that the vector equation ofthe plane Jrl which contains and is

perpendicular to the plane - x 4y 7, = 36 is ;. ~~4 J = 12 .

iii Find the angle between 7[1 and II

[ 4 ]

[ 3 ]

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kfccalmt9709 - exam paper - 200508 - maths p3 - trial exam - taylor

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