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Unformatted text preview: INTERNATIONAL BACCALAUREATE MOI/510mm
BACCALAUREAT INTERNATIONAL
BACHILLERATO INTERNACIONAL MATHEMATICS Name
HIGHER LEVEL
PAPER 1 Number
Monday 7 May 2001 (afternoon)
2 hours INSTRUCTIONS TO CANDIDATES  Write your name and candidate number in the boxes above.
 Do not open this examination paper until instructed to do so.
° Answer all the questions in the spaces provided. ° Unless otherwise stated in the question, all numerical answers must be given exactly or
to three signiﬁcant ﬁgures, as appropriate.  Write the make and model of your calculator in the box below 6. g. Casio fx9750G,
Sharp EL—9400, Texas Instruments TI—85. Calculator Make Model EXAMINER TEAM LEADER TOTAL 2217236 15 pages — 2 — M01/510/H(1) Maximum marks will be given for correct answers. Where an answer is wrong, some marks may be
given for a correct method provided this is shown by written working. Working may be continued below
the box, if necessary. Where graphs from a graphic display calculator are being used to ﬁnd solutions,
you should sketch these graphs as part of your answer. 1. Letf(z)=z5{1—i;]. Finde(t)dt.
2t3 Ir Working: Answer: . 1: TC
2. Solve 2s1nx=tanx, where ——2— < x < E Working: Answers: 2217236 — 3 — M01/510/H(1) 3. Give a full geometric description of the transformation represented by the matrix mlwmlh
VIIbull!» Working: Answer: 221—236 Turn over —4— M01/510/H(1) 4. Find the gradient of the tangent to the curve 3x2 + 4y2 2 7 at the point where x = 1 and y > 0 . Working: (a) the set of real values of x for which f is real and ﬁnite ; (b) the range of f . Working: Answers: (a)
(b) 221236 — 5 — M01/510/H(1) 6. A machine produces packets of sugar. The weights in grams of thirty packets chosen at
random are shown below. mm memmmmm Find unbiased estimates of (a) the mean of the population from which this sample is taken; (b) the variance of the population from which this sample is taken. Working: Answers: (a)
(b) _—.— 221—236 . Turn over _ 6 _ M01/510/H(1) 7. The nth term, u" , of a geometric sequence is given by un = 3(4)"+1, n e Z+ .
(a) Find the common ratio r . (b) Hence, or otherwise, ﬁnd Sn , the sum of the ﬁrst n terms of this sequence. Working: Answers: (a) (b) sin x 8. Let f:xi—> , 7: S x S 37:. Find the area enclosed by the graph off and the xaxis.
x Working: Answer: 221—236 — 7— M01/510/H(1) 9. Find the equation of the line of intersection of the two planes —4x+ y+z=—2 and
3x— y + 22:—1 . Working: 2217236 Turn over — 8 — MOI/510/H(1) 10. (z + 21) is a factor of 223 — 322 + 82 — 12 . Find the other two factors. Working: Answers: 221—236 —9— MOI/510/H(1) 11. Given that P(X) = % P(Y X) = % and P(Y X’) = i, ﬁnd (a) P(Y’); (b) P(X’UY’). Working: Answers: (a)
(b) 12. Find an equation of the plane containing the two lines x—1=1;Z=z—2andx+1—2Ay 2+2. 2 3’3 5 221~236 Turn over — 10— M01/510/H(1) 13. Z is the standardised normal random variable with mean 0 and variance 1. Find the value of
a such that P(  Z S a)=0.75. Working: Answer: 14. Given that z = (b + i)2 , where b is real and positive, ﬁnd the exact value of b when arg Z = 60° . 221—236 — 11 — M01/510/H(1) 15. X is a binomial random variable, where the number of trials is 5 and the probability of success
of each trial is p . Find the values of pif P(X=4)=0.12. Working: 221—236 Turn over — 12— M01/510/H(1) d
16. Find the general solution of the differential equation d—): = kx(5 — x), where 0 < x < 5 , and k is a constant. Working: Answer: 221—236  13 — M01/510/H(1) 17. An astronaut on the moon throws a ball vertically upwards. The height, s metres, of the ball,
after t seconds, is given by the, equation s=401+ 0.5at2, where a is a constant. If the ball
reaches its maximum height when t: 25 , ﬁnd the value of a . Working: Answer: 18. The equation kx2 — 3x + (k + 2) = 0 has two distinct real roots. Find the set of possible values
of k . Working: Answers: 221—236 Turn over — 14— M01/510/H(1) 19. The diagram shows the graph of the functions yl and y2 . yl On the same axes sketch the graph of 21—. Indicate clearly Where the xintercepts and
y2
asymptotes occur. Working: 221—236 — 15 — M01/510/H(1) 20. The function f is given by f: x I—> e(1+5i““x) , x 2 0 .
(a) Find f ’(x) .
Let xn be the value of x where the (n +1)‘h maximum or minimum point occurs, n e N.
(i. e. x0 is the value of x Where the ﬁrst maximum or minimum occurs, x1 is the value of x where the second maximum or minimum occurs, etc). (b) Find xn in terms of n . Working: Answers: (a)
(b) 221—236 ...
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 Spring '10
 Chang
 Math, Calculus

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