3ab trial calculatorfree 2011

8/11/2019 3AB Trial CalculatorFree 2011

1/8

Semester 2 Examination 2011

Question/Answer booklet

Hale School

MATHEMATICS 3AB

Section One:Calculator-Free

Student Name : Score :(out of 40)

Teacher : STL MS MRC(Circle)

Time allowed for this sectionReading time before commencing work: 5 minutesWorking time for paper: 50 minutes

Material required/recommended for this section

To be provided by the supervisorQuestion/Answer booklet for Section One, with a formula sheet which may also be used forSection Two.

To be provided by the candidateStandard items: pens, pencils, pencil sharpener, highlighter, eraser, ruler

Important note to candidatesNo other items may be taken into the examination room. It is yourresponsibility to ensure thatyou do not have any unauthorised notes or other items of a non-personal nature in theexamination room. If you have any unauthorised material with you, hand it to the supervisorbeforereading any further.


2/8

3AB MAT Semester 2 2011 2 Section 1: CalculatorFree

See next page

Structure of this paper

Number ofquestionsavailable

Number ofquestions to be

attempted

Suggestedworking time

(minutes)

Marksavailable

Section OneCalculatorfree

6 6 50 minutes 40

Section TwoCalculatorassumed

11 11 100 minutes 80

Total marks 120

Instructions to candidates1. Answer the questions in the spaces provided.

2. Spare answer pages are provided at the end of this booklet. If you need to use them, indicatein the original answer space where the answer is continued i.e. give the page number. Fill inthe number of the question(s) that you are continuing to answer at the top of the page.

3. Show all your working clearly. Your working should be in sufficient detail to allow youranswers to be checked readily and for marks to be awarded for reasoning. Incorrect answersgiven without supporting reasoning cannot be allocated any marks. For any question or partquestion worth more than two marks, valid working or justification is required to receive full

marks. If you repeat an answer to any question, ensure that you cancel the answer you donot wish to have marked.

4. It is recommended that you do not use pencilexcept in diagrams.


3/8

Section 1: Calculator-Free 3 3AB MAT Semester 2 2011

See next page

Section One: CalculatorFree 40 marks

This section hasSIX (6) questions. AttemptALL questions.

Question 1 [6 marks]

Simplify the following expressions, expressing answers with positive indices :

(a) 2a-1

[1]

(b) (ab)3 x 3b-3

[2]

(c) If3 2

x y

5

a = a

a, determine the value of the integers x and y.

[3]


Given that f(x) = (x + 2)2 - 4, g(x) =2

+ 3x + 1

(a) Give the domain and range of function g.[2]

(b) If f(a) = 0, determine the possible value(s) of the constant a.[2]

(c) If the graph of function g is translated 3 units down and then dilated vertically aboutthe line y = 0 with factor 2, write the defining rule for the resultant transformed grapht(x).

[2]


4/8


See next page


The pair of linear equations 2x - y = 9 . . . (1)3x + 2y = 10 . . . (2)

can be solved using different methods. Solve the pair of equations using the :

(a) method of substitution[3]

(b) method of elimination

[2]

(c) It was found that another equation kx - 7y = 60 had no solution when it was solvedsimultaneously with equation (1) above.

Determine the value of the constant k.Explain.

[2]


5/8


See next page


Find the derivatives for each of the following functions. Take derivatives to a reasonable levelof simplification.

(a) f(x) = x

2

- 4x

3

+ 12 [2]

(b) Using the product rule differentiate g(x) = 2x5(4x + 3)i.e. do not expand

[4]

(c) y =2 72x - 6x

4x

[3]


6/8


See next page


A rectangle can be defined as a parallelogram with ONE right angle.

(a) Explain, why using this definition, it will mean that ALL angles of a rectangle will be rightangles.[1]

A student sets out to prove for a rectangle, the diagonals are equal in length, but he leavessome gaps in his proof as he is uncertain what to write, especially in providing the reasons forhis statements.

(b) Complete the gaps in his proof in the spaces provided.

[5]

In s ADB and ADC :

AB = DC Property of a parallelogram (given)

sBAD = sADC

AD = AD

BAD CDA

DB = AC

A B

CD


7/8


See next page


(a) Write an algebraic expression for a number that is always three more than an evennumber.

[2]

(b) Hence prove that the square of a number that is always three more than an evennumber is one more than a multiple of 4.

[4]


8/8


See next page

Additional working space

Question number(s):

3ab trial calculatorfree 2011

Documents