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Index:……………………..……. ISLAMIC CULTURAL COLLEGE

PORT LOUIS

Third Term Examination 2011

FORM IV ADDITIONAL MATHEMATICS TIME: 2 h

INSTRUCTIONS TO CANDIDATES.

This questionnaire consists of 16 printed pages and 10 questions.

Answer all questions. The number of marks is given in brackets [ ]. The total number of marks for this paper is 100.

Use of a calculator is expected where needed.

1. Find the coordinates of the points of intersection of the line and

the curve [5]

2

2 (a) Rationalise the denominators

(i)

[2]

(ii)

- [3]

2 (b) Find the range of values of x for which [4]

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3 (a) Find the term independent of x in the expansion of

[3]

3 (b) (i) Write down and simplify the first four terms in the expansion, in ascending powers of

x, of [3]

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(ii) Hence or otherwise, find the coefficient of in the expansion of [3]

4 (a) Solve

(i) [2]

(ii) [3]

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(iii) [2]

(iv) [3]

(v) [3]

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(b) By using the substitution , solve . [4]

5 (a) The expression leaves a remainder of 17 when divided by .

Determine the value of a. [2]

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5 (b) Solve the cubic equation: . [5]

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6. The diagram shows sector OAB with radius 7 cm and the angle between the radii is 2.4 rad.

Find

( a ) Length of arc AB. [2]

( b ) Area of triangle OAB [2]

.

( c ) Area of sector OAB. [2]

( d ) Hence, find the area of the shaded region.

(d) Hence, find the area of the shaded region. [1]

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7. Solve for .

( a ) [2]

( b ) [3]

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( c ) [4]

( d ) [5]

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8 (a) Express in the form , where a, b and c are integers. [3]

(b) State the coordinates of the maximum or minimum point. [1]

( c ) Sketch the graph of by stating the y-intercept and its range. [3]

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9. Functions f and g are defined, for by

, .

(a) Find and in terms of x, stating the value of for which is not defined. [3]

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(b) Find an expression for in terms of x. [4]

( c) Evaluate . [2]

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10 The diagram shows a kite ABCD with AB = AD and CD = CB. The point B is ( 4, 6 ) and the

point D is ( 13, 9 )

(a) Find the gradient of line BD and hence the gradient of line AC. [3]

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The line AC is the perpendicular bisector of line BD.

(b) Find the coordinates of the midpoint of line BD and hence find the equation of line AC [3]

( c) Find the coordinates of A given that A lies on the x-axis. [1]

(d) Given that the equation of line BC is , find the coordinates of C. [3]

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(e) Find the length of BD and of AC giving your answer in Surd form. [4]

(f) Hence or otherwise, find the area of the kite ABCD. [2]