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www.h2maths.comGeneral Certificate of Education Advanced LevelHigher 2

MATHEMATICS 9740Mock Examination 3 November 2013

1 hours 30 minutesAdditional Materials: Answer Paper

List of Formulae (MF 15)

READ THESE INSTRUCTIONS FIRST

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 paper clips, highlighters, glue or correction fluid.

Answer allthe questions.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case ofangles in degrees, unless a different level of accuracy is specified in the question.You are expected to use a graphic calculator.Unsupported answers from a graphic calculator are allowed unless a question specifically statesotherwise.Where unsupported answers from a graphic calculator are not allowed in a question, you arerequired to present the mathematical steps using mathematical notations and not calculatorcommands.You are reminded of the need for clear presentation in your answers.

At the end of the examination, arrange your answers in NUMERICAL ORDER. Place thiscover sheet in front and fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question or part question.

Question No. Marks Question No. Marks

1 / 6 4 / 8

2 / 6 5 / 9

3 / 8 6 / 13

TOTAL / 50

This document consists of 3printed pages, including this cover page.

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Q1.

Do not use a calculator in answering this question.

The complex numberzis given by i kz , where kis a non-zero real number.

(i) Find 3z in the form yx i . [2]

(ii) Given that 3z is purely imaginary and 0k , find the value of 100argz . [4]

Q2.

(a) Explain how a systematic sample could be carried out to sample 2% of the students in a

school in order to find their amount of pocket money received in a month. [3]

(b) The amount of pocket money, in dollars, received by a student in a month is assumed to be a

random variable with the distribution 2160,752N . The mean amount of pocket money

received by nrandomly chosen students in a month is denoted by M .

Given that 0359.0800P M , find the value of n. [3]

Q3.

(a) Find xx

xd

12

. [2]

(b) (i) Use implicit differentiation to show that 1,1

1)(sec

d

d

2

1

xxx

xx

. [2]

(ii) Hence or otherwise, find the exact value of xxx dsec2

2

1

. [4]

Q4.

On 1 January 2010 MrBeanborrowed $10000 from a bank, and on the second day of each month

the bank charged interest at the rate of 2% per month on the outstanding balance. Mr Beanrepaid

$500 on the last day of each month.

(i) Use the formula for the sum of a geometric progression to find an expression for the value of

Mr Beans outstanding balance (after payment) on the last day of the nth month (where

January 2010 was the 1st month, February 2010 was the 2nd month, and so on). Hence findin which month the value of MrBeans outstanding balance (after payment) first became

lower than $3000. [5]

(ii) MrBeanwanted the value of his account to be $3000 on 3 February 2012. What interest rate

per month, applied from January 2010, would achieve this? [3]

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Q5.

It is given that a random variableAhas the distribution p,60B .

(i) Given that 25.0p , find 135P A . [2]

(ii) Given that 36.0p , find 28P A using a suitable approximation. [2]

(iii) For an unknown value ofp, it is given that 2P25P AA .

Show that p satisfies an equation of the form kp

p

1, where k is a constant to be

determined, to a suitable degree of accuracy. Hence find 10P A using a suitable

approximation. [5]

Q6.

The line lhas the cartesian equation

5 31

3 2

x yz

.

(i) Show that the shortest distance of the pointA 2,6, 1 from the line lis14

33 . [3]

The plane1

p contains the line land the pointA.

(ii) Find the cartesian equation of the plane1

p . [2]

The plane 2p has the cartesian equation

7x y z .

(iii) Without using a calculator, show that the planes1

p and2

p intersect along the line l. [2]

(iv) The line from the point A meets the plane2

p at the pointNwhere isANis perpendicular to

2p . Find the position vector ofN. [3]

(v) Find a cartesian equation of the plane3

p which is a reflection of the plane1

p in the plane2

p .

[3]

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