2004 roseville assessment 1 math hsc

8/12/2019 2004 Roseville Assessment 1 Math HSC

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Question 1 Show all working (18 marks)

(u) For the parabola with equation , - 3)' : 72y + 24 find:

(i) the vertex

(ii) the focus

(b) A bag contains 8 green discs and 6 red discs

One disc is drawn at random, ts colour noted, and t

Find the probability that:

(i) both discs are green

(ii) at east 1 disc s red

(Marks)

(2)

identical o each other except or colour. (2)

is then set aside. A second disc is then drawn.

(c) Thequadrat icequat ion x2-3x+ 8:0hassolut ionsgivenby a and, .

Evaluate:

(2)

( i ) a *

(ii) 1 *d

(d) Draw two separate ketches o represent section of curve y: f(x) which satisfies (4)

the following conditions:

(i)

(ii)

domain 31x13, range


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R

I

V

E

R

(Marks)

(e) A section of paddock with a straight iver running along one side s to be fenced (4)

using 100rn of fencing. The section enced s in the shape f a rectangle with a

length y m and a width x m as shown. The side along he river does not need o be fenced.

?,)1-t \o{)qft^

(i) Express in terms of x.

(ii) Find an expression, n terms of x, for

the area of this field.

(iii) Find the dimensions f this field so hat

the area t contains s a maximum

A," /

\ \ rt l . A

' )l l r '' \

) ) ftt-[ocl*-

Given hat : (5x- 1) ' and ha t f x :3 , : 4 , f ind he va lue fy i fx :0 .dx

The equation y0 - 4) : 4(2x - 7) tepresents parabola.

Determine he equation of its directrix.

Question 2 Show all working (Start a new page)

(a) Given that f '(x) : 9 J; , find an expression orflx) (1)

(b) The function drawn below is a gradient unction. Copy or trace his gradient unction and

on the same axes draw a sketch of a function which could have ed to this gradient unction. (2)

4 *l - ' ) "

(2)

Q)

V ? \. ,{ i ]18 marks -

+

r , -n)

(0

(e)


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(c) Two players are playing a game with two dice. They take turns to roll the two (4)

dice to produce a score. A score s found by multiplying the difference between he uppermost

faces on the two dice by the higher of the two uppermost aces.

(i ) Find the probability hat on the first turn, a player scores score of 1.2.

Find the probability hat on any given hrow, a score of at least 12 rs achieved.

If a player scores ero, hey are allowed to have he next turn. Find the probability that a

given player has exactly 4 turns n a row.

(ii)

(iii)

(d)

(e)

Solve 3x" I 4x

For the function v : 2x3 6x2 48x + 10- , ' t 4

' 1 1 - 1 1 b - + ( t

Find the stationary points and determine heir nature.

End of Paper

T Lq "

|- L

a ,= Q > L - z - - \ L ) . - q 8

. \ t -

j1(

(2)

(s)

,a)r , - /rt- -q|.

/-a-

- r . 1f_" )

(i)

(iD Find the co-ordinates f the point of inflexion, and explain why it is a point of inflexton.

(iiD Use he nformation fiom parts (i) and (ii) and anything else you consider necessaf,y o

sketch his function for the domain - 4 < x < 5.

\z'6 ,4O7 5 e ' '

The point P(xy) moves such hat PA l- PB. Given that A and B have co-ordinates (4)

(-1,2) and 7,6) respectively, ind the ocus ofP in algebraic orm and describe hislocus geometrically n detail.

.q?- t / '

(0

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2004 roseville assessment 1 math hsc

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