WRP Examination Extension 1 2012

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2012PreliminaryFinal Examination Extension 1 Mathematics

2

Section I

10 marks

Attempt Questions 1-10

Allow about 15 minutes for this section

Use the multiple choice answer sheet for questions 1 10.

1. Factorise 54x3

+ 16

(A) 2(3x + 2) 9x

2+ 6x + 4

(B) 2(3x + 2) 9x

26x + 4

(C) 2(3x + 2)

9x2

12x + 4

(D) 2(3x + 2) 3x

26x + 4

2. State the largest possible domain of the function:

f(x) = x + 3 3x

(A) x 3, x3 (B) x3 (C) -3x3 (D) x3, x3

3. Simplifysin

180+

cos90

.

(A) tan

(B) 1

(C) -1

(D) tan90


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4. Evaluate limx 2

x38

x2

(A) 0

(B) undefined(C) 4

(D) 12

5. Find the number of ways the letters of the word RHOMBUS can be arranged in a

straight line so that the vowels are together.

(A) 720

(B) 5040

(C) 1440

(D) 360

6. Find the Cartesian equation formed from the parametric equations:

y = 1t1

and x = t22t + 1

(A) x =1

y2

(B) y=1x

(C) x=1y

(D) y =1

x2

7. A(-7,5) and B(3,1) are two points. Find the coordinates of the point P which divides the interval

AB externally in the ratio 3:1.

(A) (-12, 7)

(B) (-1, 4)

(C) (8, -1)

(D) ( 12

, 2)


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8. The sketch of the graph (x) = |x|x

forx0 is:

(A)

(B)

(C)

(D)

9. Given that sin = 14

, find the value of cos 2 .

(A) 12

(B) 78

(C) 34

(D) 2 1516


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10. If 2x

= 5y

= 10z

thenz= ?

(A) xyx +y

(B)x +y

xy

(C) 1x

+1

y

(D) 1x

1y

End of Section 1


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Section II

Total Marks (40)

Attempt Questions 11 - 14Allow about 1 hours for this section.

Answer all questions, starting each question on a new sheet of paper with your name and

question number at the top of the page. Do not write on the back of sheets.

All necessary working should be shown in every question.

Question 11 (10 marks) Start a new sheet of writing paper. Marks

(a) Solve 164x

=1

8x

.2

(b) Find the obtuse angle between the lines 2x3y + 4 = 0 and y = 3x + 7 . 2

(c) Solve x24x

> 0 , for x0 . 2

(d) Find the equation of the tangent to the curve y =x x1 at the point where

x = 5.

2

(e) When P(x) = x3

+ x2a is divided by x2 the remainder is 4. Find the

remainder when P(x) is divided byx.

2

End of Question 11


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(a) Prove by Mathematical Induction that 72n

33n

is divisible by 11. 3

(b) In the diagram A, B and C are 3 points on the circle. CX and CY are chords cutting

AB at L and M respectively. AC=CB, CAB = and ACX= .Copy the diagram onto your paper.

(i) State why CLB = + . 1

(ii) Explain why AYC= and AYX= . 1

(iii) Prove that XYML is a cyclic Quadrilateral. 1

Question 13 continued on next page


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Question 13 continued

(c) In the diagramX,YandZare 3 points on the circle. The tangent to the circle at Xmeets

YZproduced atM.Nis a point on YZsuch thatXNbisects ZXY.

Show thatMX =MN, giving reasons.

Marks

4

End of Question 13


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(a) In the diagram, the points B, C and D are in the same plane. A is a point

vertically above point B. Points C and D are 850 metres apart and CBDis110.

If CABis 60 and DAB is 30 find the height of A above B.

3

(b) If t= tan2

and using the expansion for tan(A +B) show that:

tan

45 +2

=1 + sin

cos.

3

(c) (i) Show that 1cos 2x1 + cos 2x

= tan2x . 2

(ii) Hence or otherwise, show that the exact value of tan 22 12 = 2 1 . 2

End of Examination


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Preliminary ExaminationExtension 1 Mathematics 2012Multiple Choice Answer Sheet

Name ______________________________

Completely fill the response oval representing the most correct answer.

1. A B C D

2. A B C D

3. A B C D

4. A B C D

5. A B C D

6. A B C D

7. A B C D

8. A B C D

9. A B C D

10. A B C D


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Section I

10 marks

Attempt Questions 1-10

Allow about 15 minutes for this section

Use this multiple choice answer sheet for questions 1 10.

Select the alternative A, B, C or D that best answers the question. Fill in the response oval completely.

Sample

2 + 4 = ? (A) 2 (B) 6 (C) 8 (D) 9

A B C D

If you think you have made a mistake, put a cross through the incorrect answer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be the correct answer, then indicate this

by writing the word correctand drawing an arrow as follows:

correct

A B C D

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WRP Examination Extension 1 2012