baulko 2015 y11 hy

BAULKHAM HILLS HIGH SCHOOL

2015 YEAR 11

TASK 2 JULY ASSESSMENT TASK

Mathematics

General Instructions • Reading time - 5 minutes • Working time - 60 minutes • Write using black or blue pen • Black pen is preferred • Board-approved calculators may be used • All relevant mathematical reasoning

and/or calculations must be shown

Total marks - 45 (Pages 2-5) Attempt Questions 1-4

Total Marks - 45 Attempt Questions 1 - 4

Answer each question on the appropriate page ofyour answer booklet.

Your responses should include relevant mathematical reasoning and/or calculations.

Question 1 (12 marks) Start on the appropriate page of your answer booklet

a) A line makes an angle of 60° with the positive x-axis. What is the equation of 2

the line ifit passes through the point (-1,4)?

b) Evaluate:

2 x -8x+ 15

(i) lim ---- 2 x .... 3 x-3

/+2(ii) lim 2

x -+ 00 2x-? 3x + 1

c) Differentiate 1

(i) 24x+3

2x (ii)

2 2 x + 3

3(iii) J2x 4

_7x + 1 2

END OF QUESTION 1

2


a) On a number plane the points A( -5,-3), B( -2,3), C(1O,9) and D form a trapezium in

which AD is parallel to the x axis and ABIICD.

x

(i) Show that the equation of the line DC is 2x - y II = 0 2

(ii) Find the coordinates ofD. 1

(iii) Find the perpendicular distance from B to DC 2

(iv) Find the coordinates of the midpoint ofBD. 1

(v) The point E lies on the line BA produced such that BCDE is a rhombus.

Find the coordinates of E.

1

b) Joel is trying to find the equation of a line perpendicular to x 2y + 13 = 0 which passes through the point of intersection of the line.s 3x + 2y 1 0 and

7x lly+ 3 O.

As part of his working Joel has correctly set up the following equation: 3x + 2y 1 + k(7x lly + 3) = 0

(i) Show that the gradient of the line is 3 + 7k -- 11k 2

2

(ii) Find the value of k 2

(iii) Hence determine the required equation of the line. 1

END OF QUESTION 2

3


a) The diagram below comprises three parallel lines.

P I

q+l

. 5 Pi) Explam why - - 1

q 2

ii) Find the exact value ofp and q 2

3 2b) Find the equation of the tangent to the curve y = 3x - 4x + x 1 at the point 3

where x = 1.

c) Triangles ABC and BPQ are right angled triangles and AB=AP B Q C .

A

Copy the diagram into your answer booklet

(i) Prove L CBP = L CPQ 3

(ii) Hence prove that Pc! = BC x QC 3

END OF QUESTION 3

4


a) The parabola y = ai + bx + c passes through the point (0,-2). At the point (2,-3) 3

on this curve, the equation of the tangent is 2x - Y 7 O. Find the values of a, band c.

b) In the figure triangles ACB and APO are equilateral.

NOT TO SCALE

B Copy this diagram into your answer booklet.

(i) Prove that L BAO = L PAC 2

(ii) Prove /l AOB == /l APC 3

(iii) Hence, prove OB=CP. 1

END OF EXAMINATION

5

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baulko 2015 y11 hy

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