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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
Question 2 (12 marks) Start on the appropriate page of your answer booklet
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
Question 3 (12 marks) Start on the appropriate page of your answer booklet
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
Question 4 (9 marks) Start on the appropriate page of your answer booklet
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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