WRT Preliminary 2013 Mathematics - mrjwright.weebly.com€¦ · Web viewIf you change your mind and have crossed out what you consider to be the correct answer, then indicate the

2013PRELIMINARY HSCFINAL EXAMINATION

GPCC 2U Mathematics Exam

General Instructions

o Reading Time - 5 minutes

o Working Time - 2 hours

o Write using a blue or black pen. Black pen is preferred

o Board approved calculators may be used

o A table of standard integrals is provided at the back of this paper

o Show all necessary working in Questions 11-16

Total marks (70)

Section I

Total marks (10)

o Attempt Questions 1-10

o Answer on the Multiple Choice answer sheet provided on the reverse side of this page.

o Allow about 15 minutes for this section

Section II

Total marks (60)

o Attempt questions 11 – 16

o Answer on the blank paper provided, unless otherwise instructed

o Start a new page for each question

o All necessary working should be shown for every question

o Allow about 1 hour 45 minutes for this section

2013 Preliminary Final Examination Mathematics

Preliminary Final Examination – Mathematics - 2013

Section I – Multiple Choice Answer Sheet

Name ______________________________.

Allow about 15 minutes for this sectionSelect 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) 9A 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 the correct answer by writing the word correct and drawing an arrow as follows.

A B C D

StartHere

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

2


Section I10 marksAttempt Questions 1-10Allow about 15 minutes for this section

Use the multiple choice answer sheet for Questions 1 – 10.

1. Find the value, correct to 3 significant figures of:

(A) 4.02(B) 4.027(C) 4.028(D) 4.03

2. Evaluate .

(A) 0(B) undefined(C) 4(D) 1

3. Find the value of x if:

(A) 3

(B)(C) 24(D) 192

4. Simplify :

(A) 1

(B)

(C)

(D)

3


5. What is the length of the interval joining A(3,-7) and B(-6,2).

(A)

(B)

(C) 9(D) 4.5

6. Simplify :

(A)

(B)

(C)

(D)

7. Differentiate :

(A)

(B)

(C)

(D)

4


8. Which graph does not represent a function:

(A)

(B)

(C)

(D)

5


9. The solution of is:

(A)

(B)

(C)

(D)

10. In the diagram and . FC is a straight line.

AE bisects and BD bisects .

The size of is:

(A) 60°(B) 23°(C) 15°(D) 62°

End of Section I

6


Section II

Total marks (60)Attempt Questions 11-16Allow about 1 hour 45 minutes 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.

Question 11 (10 marks) Use a separate sheet of paper Marks

a) Factorise: 2

b) Solve the following equations simultaneously:

2

c) Evaluate if a has the value . Give answer with a rational denominator.

2

d) Expand and simplify as a single fraction:

2

e) Solve: 2

End Question 11

7



a) B is the point (5,-2) on the number plane and is 45°. A and C are the points of intersection of the line AB with the x and y axes respectively. A line is drawn through A, perpendicular to AC which cuts the x - axis at D.

i) Calculate the gradient of AB. 1

ii) Show that the equation of AB is . 1

iii) Find the coordinates of the points A and C. 2

iv) Show that the equation of AD is . 1

v) Find the area of . 1

b) Find the exact perpendicular distance between the parallel lines

and .

2

c) If the points and are collinear, find the value of . 2

End Question 12

8



a) Differentiate:

i) 1

ii)

1

iii)

1

iv) 1

v)

2

b) Find the gradient of the tangent to at the point where

1

c) Find the equation of the normal to the curve at the point where x = 1.3

End Question 13

9



a) Find the exact value of: 1

b) Find l correct to 1 decimal place. 1

c) Prove the identity:

3

d) A ship sails 50 km from Port A to Port B on a bearing of 63°, then sails 130 km from Port B to Port C, on a bearing of 296°.

i) Neatly copy the diagram and mark on it all the given information. 1

ii) Show that . 1

iii) Find, to the nearest km, the distance of Port A from Port C. 1

iv) Use the cosine rule to find and hence find the bearing of Port A from Port C, correct to the nearest degree.

2

End Question 14

10



a) In the diagram PQ = PR = PS, and .

Find , giving reasons.

2

b) In the diagram, parallelogram PQRS has diagonal QS with midpoint M. AB is drawn though M parallel to PS.

i) Explain why . 1

ii) By showing QAM SBM, state why M is the midpoint of AB. 3

c) Find the domain of .

1

d) Graph the region represented by the inequalities:

e) State whether the function f(x) = x2 – x is even, odd or neither.

2

1

End Question 15

11

NOT TO SCALE



a) Write the quadratic equations whose roots are 4 and -1. 1

b) If and are the roots of . Find the value of:i) + 1

ii)

iii)

1α

+ 1β

iv) 2 + 2

1

22

c) Solve the equation .

3

End of Examination

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WRT Preliminary 2013 Mathematics - mrjwright.weebly.com€¦ · Web viewIf you change your mind and have crossed out what you consider to be the correct answer, then indicate the