 2008

H We G L E 3rd there�s r S C H To O D C Electronic R Capital t I N I C AT Elizabeth E By A Meters I D AT I O D

Mathematics

Basic Instructions • Reading time – 5 mins • Doing work time – 3 hours • Publish using dark or blue pen • Board-approved calculators may be used • A stand of standard integrals is usually provided behind this newspaper • Most necessary doing work should be shown in every issue

Total markings – 120 • Look at Questions 1–10 • Your concerns are of equal value

212

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– 2 –

Total markings – 120 Attempt Questions 1–10 All questions are of equal benefit Answer every single question inside the appropriate writing booklet. Extra writing pamphlets are available.

Signifies Question one particular (12 marks) Use the Question 1 Publishing Booklet.

(a)

Evaluate 2 cos

π correct to three significant numbers. 5

2

(b)

Factorise 3x 2 + times – 2 .

2

(c)

Simplify

a couple of 1 . − n in +1

a couple of

(d)

Fix 4 back button − 3 = 7.

2

(e)

Expand and simplify

(

3 −1 2 several + a few.

)(

)

2

(f)

Find the sum of the first twenty one terms of the arithmetic series several + six + 14 + ···.

2

– 3 –

Marks Issue 2 (12 marks) Use the Question two Writing Report.

(a)

Differentiate with respect to by: (i) (ii) (iii)

( x two + 3) 9

back button 2 loge x sin x. x+4

2 two 2

(b)

Let Meters be the midpoint of (–1, 4) and (5, 8). you

Find the equation with the line through M with gradient

. 2

a couple of

(c)

(i)

� dx Find

⎮. x ⌡

+ five

π � 12

you

(ii)

two Evaluate ⎮ sec

3x dx

.

⌡0

3

– 4 –

Represents Question several (12 marks) Use the Issue 3 Publishing Booklet.

(a)

y C (1, 5) D

To A (0, –1)

two times –y –1 =

M (0, 3)

NOT

TO

SCALE

zero

x

In the diagram, ABCD is a quadrilateral. The formula of the collection AD is usually 2x – y – 1 = 0. (i) (ii) (iii) (iv) (v) Show that ABCD is actually a trapezium simply by showing that BC can be parallel to AD. The line CD is definitely parallel to the x-axis. Locate the heads of D. Find the length of BC. Show that the perpendicular distance from B to AD can be 4 your five. 2 1 1 two 2

Hence, or otherwise, locate the area from the trapezium ABCD.

(b)

(i)

Differentiate loge (cos x) with respect to x.

2

(ii)

⌠4 Consequently, or otherwise, examine

⎮ tan x dx.

⌡0

π

2

– 5 –

Markings Question 5 (12 marks) Use the Problem 4 Publishing Booklet.

(a)

P TO NOT SCALE X Y

a couple of

Q In the diagram, XR bisects ∠PRQ and XY QR.

Ur

Copy or trace the diagram into the writing booklet. Prove that ΔXYR is a great isosceles triangle.

(b)

The zoom function in a program multiplies the dimensions of your image by simply 1 . 2 . In an picture, the height of any building is definitely 50 logistik. After the zoom function is definitely applied once, the height in the building in the image is definitely 60 mm. After a second application, its height is definitely 72 millimeter. (i) Calculate the height of the building in the image following the zoom function has been utilized eight times. Give your solution to the nearest mm. The height in the building inside the image is needed to be more than 400 logistik. Starting from the first image, what is the least quantity of times the zoom function must be utilized? 2

(ii)

2

(c)

Consider the parabola times 2 = 8( sumado a – 3). (i) (ii) (iii) (iv) Write down the coordinates from the vertex. Find the runs of the target. Sketch the parabola. Determine the area bordered by the allegoria and the collection y = 5. 6 – one particular 1 1 3

Represents Question your five (12 marks) Use the Problem 5 Publishing Booklet.

(a)

The lean of a contour is given by the point (0, 7). Precisely what is the formula of the shape?

dy = 1 − 6 sin 3 x. The shape passes through dx

several

(b) Consider the geometric series five + 10x + 20x 2 + 40x three or more + ···. (i) For what values of x performs this series possess a limiting sum? (ii) The limiting sum with this series is usually 100. Get the value of times. 2 2

(c)

Lumination intensity can be measured in lux. The sunshine intensity with the surface of a lake is definitely 6000 lux. The light intensity, I lux, a range s metre distances below the area of the pond is given simply by I = Ae –ks where A...

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