maths.stithian.commaths.stithian.com/New CAPS 2017 Prelim Papers/Hilton... · Web viewThis question paper consists of 28 pages (numbered 1 – 28) as well as a yellow information

TRIAL EXAMINATIONS 2017 : MATHEMATICS : PAPER II Page

HILTON COLLEGETRIAL EXAMINATIONS

AUGUST 2017

MATHEMATICS : PAPER II

EXAMINATION NUMBER:

Time: 3 hours 150 marks

Examiner: Mr P de WetModerator: Mr T Mills

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

1. This question paper consists of 28 pages (numbered 1 – 28) as well as a yellow information sheet of 2 pages (numbered i to ii). Please check that your paper is complete.

2. Unless otherwise specified answers should be given to 1 decimal place.3. Work neatly and show all working details.

HONOUR PLEDGE:

I hereby pledge that I have neither given nor received help on this examination.

Signed: ……………………………………….

For markers’ use only

Copyright – Hilton College © 2017


SECTION A

QUESTION 1

Consider the diagram below:

(a) Determine the mid-point of line AB.

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(b) Give the equation of the perpendicular bisector of AB

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(c) Give the equation of the circle which has C as centre and the x-axis as a tangent.

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QUESTION 1 continued…

(d) Give the coordinates of point D if ABCD (in that order) is a parallelogram.

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(e) Give the angle of inclination of line AC

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QUESTION 2

(a) Answer True or False:

(1)

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(2) If then

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(3) The graph of has a period of

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(4) The minimum value of is

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12 marks



(b) Given that and that , draw a sketch on the axes below.

You should label

(c) Hence or otherwise determine:

(1) in surd form

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(2) to 1 d.p.

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(d) If then express the following in terms of p:

(1)

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(2)

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(e) Write down the equation of each of the graphs shown below:

(1) (2)

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17 marks


QUESTION 3

(a) Given the 15 ranked Mathematics results below:

34 ; 37 ; 41 ; 45 ; 52 ; 52 ; 56 ; 57 ; 63 ; 65 ; 70 ; 72 ; 78 ; 83 and 87

(1) Give the modal value.

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(2) Determine the inter-quartile range.

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(b) Three different scatter plots are given below:

Plot 1 Plot 2 Plot 3

(Images taken from http://nagysandor.eu/AsimovTeka/correlation_en/ )

Assign each plot one of the following correlation coefficients:

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Plot 1 ________________

Plot 2 ________________

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http://nagysandor.eu/AsimovTeka/correlation_en/



(c) John has some numbers such that .

Their standard deviation is .

Determine, the value of n .

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QUESTION 4

(a) Complete the following statements:

(1) If a line cuts two sides of a triangle in the same proportion then……

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(2) The angle subtended at the centre of a circle is ……

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(3) If the opposite angles of a quadrilateral are supplementary then……

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9 marks



(b) Determine the sizes of the angles marked with letters in the following diagrams. No reasons need to be given.

(1) O is the centre of the circle.

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(2) O is the centre of the circle and AB is a tangent to the circle at T.

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(c) Determine the value of k giving reasons:

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12 marks


QUESTION 5

(a) Determine, to one decimal place, the smallest angle in the triangle below:

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(b) An isosceles triangle has an area of 16 cm2. If the two equal sides are 8 cm then determine, to the nearst whole number, the angle between them.

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(c) Solve for :

(1)

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(2)

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15 marks


QUESTION 6

In the diagram, O is the center of the circle. Find, with reasons, the angles labelled a to e.

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TOTAL FOR SECTION A – 75 MARKS


10 marks


SECTION B

QUESTION 7

(a) The farm manager does an experiment by putting different number of cowsinto identical fields for three days each. At the end of the time he measuresthe length of the remaining grass in a number of places in each field in orderto arrive at an average grass length for that field. The results are as follows:

Number of cows in field Average grass length after 3 days (cm)20 6030 4040 3750 2860 1270 1080 7

(1) Determine, to 2 d.p. the correlation coefficient and comment on what it tells you about the relationship between the number of cows and

the average grass length after three days.

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(2) Determine the equation of the least squares regression line(the line of best fit) using x to represent the number of cows andy to represent the average grass length after three days.

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(3) The farm manager wonders about using the model in (2) to determinethe average grass length after three days for more than 80 cows.Comment on this.

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(b) The Final Grade 11 Mathematics results for the Grade 11 class of 2016 are portrayed in the cumulative frequency diagram below.Use the curve to answer the questions which follow.

(1) Determine the median mark.

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(2) What is the probability that a randomly selected pupil achievedbetween 60% and 80%?

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12 marks


QUESTION 8

(a) The circle has two tangents as shown. The equation of the tangent at A is given.

(1) Determine the equation of the tangent at B.

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(2) It is given that the equation of the tangent at B is .Hence, or otherwise, determine the coordinates of point C, the point at which the tangents intersect.

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(b) Determine in the diagram below.

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QUESTION 9Copyright – Hilton College © 2017

13 marks


(a) In the diagram below CEF is a tangent to the smaller circle.

(1) Prove that CE = CD.

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QUESTION 9 continued…Copyright – Hilton College © 2017


(2) Prove that

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(3) Hence, or otherwise, prove that

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(b) In the diagram CEG and DE are tangents to the circle with center O.

(1) Prove that CODE is a cyclic quadrilateral.

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(2) Prove that .

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(3) Calculate, giving reasons.

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(c) In the diagram below ABCD is a parallelogram with the diagonals drawn.,

(1) Determine, giving reasons, the value of

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(2) Determine, with reasons,

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31 marks


QUESTION 10

(a) Prove the identity:

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(b) In the picture below. Points A, B and C are on flat ground. C is a pointImmediately below the top of the flag tower F. The distance between Aand B is k meters. The angle of elevation of F from A is .

Show that the height of the top of the flag is:

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B

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10 marks


QUESTION 11

The circle with chords AB and CD is given with points A, B, C and D as shown.

Determine the equation of the circle in the form

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TOTAL FOR SECTION B – 75 MARKS


9 marks


ADDITIONAL SPACE FOR ROUGH WORKING WHICH WILL NOT BE MARKED

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Documents

maths.stithian.commaths.stithian.com/New CAPS 2017 Prelim Papers/Hilton... · Web viewThis question paper consists of 28 pages (numbered 1 – 28) as well as a yellow information