Extension Math 2014

8/15/2019 Extension Math 2014

1/11

Trinity Catholic College2014

PRELIMINARYASSESSMENT

TASK 2

MathematicsExtension 1

General Instructions• Reading Time – 5 minutes• Working Time – 1.5 hours• Questions 1 – 10 are multiple

choice and are to be answeredon the answer sheet provided.

• Write using blue or black pen• Board-approved calculators may

be used.• Start each question on a new

page.• Write your name and teachers

name on each page used.• Staple multiple sheets together.• All necessary working should be

shown in every question asmarks may be awarded forcorrect working out.

•

All diagrams are not to scaleunless otherwise stated.

Total marks (55)Section I• Attempt Questions 1 – 10 (10 marks) Section II• Attempt Questions 11 – 13 (45 marks)

NAME: !!!!!!!!! .!!! ...

TEACHER: !!!!!!!!!!! .

YEAR 11


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BLANK PAGE


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SECTION 1. Objective Response Questions (10 marks)

Complete your answers for Questions 1 – 10 on the Multiple Choice Answer Sheet provided.

11 Ext1 Task 2 2014 version 2.doc Trinity Catholic College1

Question 1. 1

What is the solution to the equation 4 9(2 ) 8 0 x x! + = ?

(A) 0 x = and 3 x =

(B) 1 x = and 4 x =

(C) 1 x = and 3 x =

(D) 0 x = and 4 x =

Question 2. 1

What is the solution to the inequality 2 5 7 x! < ?

(A) 1 x < ! or9

5 x <

(B) 1 x > ! or9

5 x >

(C) 1 x < ! or 95

x >

(D) 1 x > ! or9

5 x <

Question 3. 1

Simplify3 2

2 2

1 4 5

1 4 4 4

x x x

x x x

! ! !"

! + +

(A)( 5)

4

x !

(B)( 1)

4

x !

(C)( 1)

4

x +

(D)2( 1)

4

x x+ +


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Question 4. 1

Which graph best represents 24 y x= ! ?

(A) (B)

(C) (D)

Question 5. 1

Which of the following is true for the function 2( ) 3 f x x x= ! ?

(A) Even function

(B) Odd function

(C) Neither odd or even

(D) Zero function


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Question 6. 1

The diagram shows the graph of the function 25 y x x= ! .

x

y

y = 5 x – x2

A

What pair of inequalities specify the shaded region?

(A) 25 y x x! " and 0 y ! .

(B) 25 y x x! " and 0 y ! .

(C) 25 y x x! " and 0 y ! .

(D) 25 y x x! " and 0 y ! .

Question 7. 1

What are the coordinates of the point that divides the interval joining the points ( 7,5) A ! and( 1, 7) B ! ! externally in the ratio 1:3?

(A) ( 10,8)!

(B) ( 10,11)!

(C) (2,8)

(D) (2,11)


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Question 8. 1

What is the value of k if the sum of the roots of 2 ( 1) 2 0 x k x k ! ! + = is equal to the product of theroots?

(A) 3!

(B) 2!

(C) 1!

(D) 1

Question 9. 1

Let ! and ! be roots of the equation 2 8 5 0 x x! + = . What is the value of ! 2 + " 2 ?

(A) 44

(B) 54

(C) 64

(D) 74

Question 10. 1

What is solution to the equation 2 cos 3 ! = " for 0 360 ! " "! ! ?

(A) 30 or 330 ! = ! !

(B) 60 or 300 ! = ! !

(C) 150 or 210 ! = ! !

(D) 120 or 240 ! = ! !


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SECTION 2. Short-answer questions (45 marks)


Question 11. (start a new page) 15 marks

(a) Factorise fully 4 8 p p! . 2

(b) If 2 22 and 8a b a b+ = + = , evaluate a 3 + b 3 . 2

(c) On a number plane, shade the region that satisfies ( )2 21 1 4 x y< ! + " . 3

(d) Solve the inequality2 x ! 1

x

" x

for x . 3

(e) Consider the function ( ) 21

4 f x

x=

! .

(i) Find the equations of the vertical and horizontal asymptotes. 2

(ii) Find the point(s) of intersection of f x( ) with the axes. 1

(iii) Hence sketch the graph of f x( ), clearly labeling the 2 intercepts and asymptote(s).

End of Question 11


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(a) The diagram shows the points A , B and C have coordinates 1, ! 2( ), ! 4, ! 3( ) and ! 1,3( ) respectively.

(i) Calculate the exact length of the interval BC . 2

(ii) Find the gradient of BC . 1

(iii) Hence, show that the equation of BC is y = 2 x + 5 . 1

(iv) Find, to the nearest degree, the acute angle between the x -axis 1 and the line BC .

(v) Find the perpendicular distance between A and the line BC . 2

(vi) Find the coordinates of D , in the first quadrant, so that ABCD 2is a parallelogram.

(vii) Find the exact area of the parallelogram ABCD . 2

(b) Find the coordinates of the point P x , y( ) that divides the interval joining 2 the points A ! 4,5( ) and B 5, ! 1( ) internally in the ratio 2 :1 .

(c) Find, correct to the nearest degree, the acute angle between the lines 22 x + y ! 3 = 0 and x ! 3 y + 2 = 0 .

End of Question 12


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(a) Solve 2sec 2 x + 4tan x = 8 . 3

(b) A mountaineer stands at point A , which is due south of a high mountain OH of height h km .The angle of elevation of the top of the mountain is 45̊ . The mountaineer then walks 10 km on a bearing of 60˚ T to point B , from where she measures the angle of elevation to the top ofthe mountain to be 30˚ .

(i) Express the length of OA and OB in terms of h . 1

(ii) Hence find the bearing of B from mountain OH . 3

(c) Find the values of m for which mx 2 + m + 3( ) x + 4 = 0

(i) has one root equal to 1. 1

(ii) has real roots. 2

(d) Solve the equation 2 2 3 3 0 x x! ! ! = . 3

(e) If ( ) ( )24 3 5 1 1 x x Ax x B x C + ! " + + + + , find B and C . 2

END OF THE EXAM

600

h km

30 °

45 °

H

B

A

O

NOT TOSCALE

10 km

N


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Name:

Teacher:

Year 11 Extension 1 Mathematics Task 2 Assessment

SECTION 1 Multiple Choice Answer Sheet

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Extension Math 2014

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