2012 Preliminary Extension 1 Assessment Task 2 Final

7/29/2019 2012 Preliminary Extension 1 Assessment Task 2 Final

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Student Number:

Preliminary Extension 1 MathematicsAssessment Task Two

18th

May 2012 (Day 10, Week 4)

Period: 4

Venue: D104

Time: 45 minutesWeighting: 30%

Functions and Their Geometrical

Representation/10

Geometry /10

Circle Geometry /10

Total /30

General Instructions:

Attempt all parts of the exam All necessary working must be shown. Marks

may be deducted for careless or badly arranged

work.

Write on the paper provided. Board Approved Scientific Calculators may be

used(Graphic Calculators are not allowed) Included diagrams are not drawn to scale Write answers to the multiple choice questions

on your answer sheet.

Outcomes:

The student:

P2 provides reasoning to support conclusions which are appropriate to the context

P4 chooses and applies appropriate arithmetic, algebraic, graphical, trigonometric and geometric

techniques

P5 understands the concept of a function and the relationship between a function and itsgraph

PE2 uses multi-step deductive reasoning in a variety of contexts

PE3 solves problems involving circle geometry

PE6 makes comprehensive use of mathematical language, diagrams and notation for communicating ina variety of situations


2/5

Question 1: (10 Marks) star t a new booklet

(a) Which of the following is not a function?(A) (B)

(C) (D)

(b) In the functiony = 2x, asx,

(A) y (B) y 0

(C) yx (D) y

(c) Draw a sketch and shade the region represented by2

16 xy 2

(d) Consider the function2

2

100)(

x

xxf

.

(i) Find any intercepts. 1

(ii) Show thatf(x) is an even function. 1

(iii) Identify any asymptotes off(x). 2

(iv) Using limits to assist, sketch the curve, showing all essential features. 2


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Question 2: (10 Marks) star t a new booklet

(a) The test you could use to prove that TRS SUT is:

(A) SAS (B) AAS(B) RHS (D) SSS

(b) The value of the pronumeral b in the figure below is:

(A) 6.16 (B) 7.0

(C) 10.5 (D) 15.4

Do NOT copy these diagrams into your Writing Booklet use the ones in the Question Booklet(c)

ABCD is a parallelogram.

(i) Find the value ofx, giving reasons. 2

(ii) Find the value of y, giving reasons. 2

(d) Find the exact area, in terms of x, of an equilateral triangle with a side length ofx cm.

2 marks

A B

CDE

110

K

y

48

30

x


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(e) PQRST is a regular pentagon. PQ and SR are produced to intersect at U.

Find, giving reasons, the size of RUQ. 2

Question 3: (10 Marks) star t a new Booklet

(a) Find the value ofx.

(A) 5 (B) 6

(C) 7 (D) 9

(b) If AB is a diameter of the circle, findx.

(A) 70 (B) 45

(C) 80 (D) 90

P

Q

RS

T

U


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(c)

AOB is a diameter. DC is a tangent at D. 0ABD .x 0 0DAB 90 .x

Find DCB in terms of0

x giving full reasons. 2 marks

(d)

LetEGNLFbe a circle such thatEF=EG, EL meetsFG atKandENmeetsFG atM, as in the diagram. Let GEN and EGF .

(i) Do not copy this diagram into your Writing Booklet use the one in the

Question Booklet

(ii) Prove that GLN 1

(iii) Prove that GLE 2

(iv) Prove that LKMN is a cyclic quadrilateral.3

END OF THE EXAM

D

O B C.A

E

F

G

N

K

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2012 Preliminary Extension 1 Assessment Task 2 Final