Further Maths Units 3 & 4 2008 Trial Exam 1 Solutions

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FURTHER MATHEMATICS

Units 3 & 4 – Written examination 1

2008 Trial Examination

SOLUTIONS

SECTION A – Multiple-choice questions (1 mark each)

Core – Data analysis

Question 1

Answer: C

Explanation:

See last column of the table.

Subject Maurie’sgrade

Class average Class standarddeviation

x s x x z −=

Art 60 52 6 1.33

Biology 72 65 7 1

Chemistry 78 72 3 2

Drawing 65 48 15 1.13

English 82 80 10 0.2

Question 2

Answer: A

Explanation:

×

82

10037 Number of females in favour as a percentage of the total female vote.



2008 FURMATH EXAM 1


Question 3

Answer: E

Explanation:

The graph slopes down and 91.0−=r

Question 4

Answer: D

Explanation:

This is 2r not r so it is positive.

Question 5

Answer: C

Explanation:

470190752.252

752.25.2

886.0

86.0852

5.2190

−=×−=

=×

=

===

==

c

m

r s y

s x

y

x

Question 6

Answer : A

Question 7

Answer: B

Explanation:

The graph shows a decreasing trend without a true cyclic nature.

0

2

4

6

8

10

12

14

0 2 4 6 8 10

x

y

Explanation:

The equation of the line should be y = 4.133 +0.8 xor The line is parallel to the line

joining the upper and lower summary points and one third of the waytowards the middle summary point.



2008 FURMATH EXAM 1


Question 8

Answer: D

Explanation:

Week 4 803

927870 =++ Week 8 543

524862 =++

Question 9

Answer: D

Explanation:

2.135.182.085.078.05 =−−−−

Question 10

Answer: C

Explanation:

1646382.0

13500=

Question 11

Answer: C

Explanation:

A log x transformation will compress the upper end of the x scale thus linearising the points.Or by recognising that log x is the only possible Answer .

Question 12

Answer: D

Explanation:

Calculated using a TI graphics calculator. Advertising in L1, sales in L2 and use STAT CALC8.



2008 FURMATH EXAM 1


Question 13

Answer: B

Explanation:

36.17355.17145.775.94145.777.085.8345.18 ==−=×+=S



2008 FURMATH EXAM 1


SECTION B: Multiple-choice questions (1 mark each)

Module 1: Number patterns

Question 1

Answer: C

Explanation:

A finite geometric sequence – the sequence does not continue, 5.0&8 =−= r a

Question 2

Answer: D

Explanation:

12−=a 5.2=d 1135.2501251 =×+−=t

Question 3

Answer : D

Explanation:

72813

)13(2

23918162

6

6

224

=−

−=

=====

S

ar r ar ar

Question 4

Answer: B

Explanation:

The fourth term is t 3

t 0 t 1 t 2 t 3-2 4223 −=+−× 10243 −=+−× 282103 −=+−×

Question 5

Answer: D

Explanation:

No common difference so cannot be arithmetic. There is a common ratio of -0.5 so thesequence is geometric with a = 8 and r = -0.5



2008 FURMATH EXAM 1


Question 6

Answer: C

Explanation:

Check by trial and error. Also, the sequence is geometric and C gives the correct value of r

Question 7

Answer: E

Explanation: Increase of 5% each year gives 105.1 −= nn A A and initial value is 2500.

Question 8

Answer: B

Explanation:

The sequence generated is 1, 4, 5, 9, 14, 23, 37, 60..... Thus 23 is the sixth term.

Question 9

Answer: B

Explanation:

Use nr P A )1( += with a = 6000 1243 =×=n and 01.0

4

04.0==r



2008 FURMATH EXAM 1


Question 6

Answer: B

Explanation:

oo 3011832180 =−−=b km y 2.10118sin

30sin18 ==

Question 7

Answer: E

Explanation:

oo

o

1265418090

54)27

22sin58(sin

27

22sin

58

sin 1

=−=>

=== −

x xbecause

x x

Question 8

Answer: B

Explanation:

o105)1321802

250132180(cos

2221 =

××

−+= −

U

Question 9

Answer: D

Explanation:

17000563011450

11450)14910131281(

2812

180132250

56302

140sin146120

≈+=

=×××=∆

=++

=

=××

=∆

Area

STU

s

RST



2008 FURMATH EXAM 1


Module 3: Graphs and relations

Question 1

Answer: E

Explanation:

R & S have positive gradients with +1 & -1 intercepts, Q & P have negative gradients with +1& -1 intercepts.

Question 2

Answer: C

Explanation:

75.50 – 50 = 25.50 35.850.25 = . Therefore the tutor worked for more than one and a half

hours i.e. after 12 pm, but less than 12:16 pm.

Question 3

Answer: D

Explanation:

401005.2250151505.17 ==+=+ x x x x x

Package 2 becomes the better option at more than 40 hours.

Question 4

Answer: C

Explanation:

From the shape this is a cubic graph. From the point given the coefficient of x3 must be2

1.

Question 5

Answer: A

Explanation:

5134160103 <−−≥−+≤−≥



2008 FURMATH EXAM 1


Question 6

Answer: C

Explanation:

Region required is shaded.Valid points are (0,10), (0,12) and (2,8)Maximum value is obtained from (2,8):

14823 =+×

Question 7

Answer: C

Explanation:

The first equation shows the constraints for cabernet. The second equation shows theconstraints for shiraz and the third equation shows the constraints for merlot.

Question 8

Answer: A

Explanation:

The cost of x litres of blend 1 is 2.75 x and the cost of y litres of blend 2 is 2.7 y.

Question 9

Answer: E

Explanation:

Optimal points ( x,y) Volume litres Cost ($) = 2.75 x + 2.7 y

(0,475) 475 1282.50(50,475) 50 + 475= 525 1420

(100,450) 100 + 450 = 550 1490

(375, 0) 375 + 0 = 375 1031.25

(2,8)

6 10 x

y

12

10



2008 FURMATH EXAM 1


Module 4: Business-related mathematics

Question 1

Answer: B

Explanation:

67.2011

4.227=

Question 2

Answer: E

Explanation:

42500015.0)3000042500(3.03600 ×+−×+

Question 3

Answer: C

Explanation:

503.145000×

Question 4

Answer: D

Explanation:

Use table feature of graphics calculator trialling each interest rate given in turn.OrRecognise from the shape of the graph that it is compound interest and use P = $2000 andnote that the investment value is $5400 after 5 years.

22.12000

5400

54002000

5

5

==

=

R

R

And this gives an interest rate of 22%.OrUsing the TVM Solver:

N = 5I = 0 * Alpha enter 21.9755PV = -2000PMT = 0FV = 5400P/Y = C/Y = 1



2008 FURMATH EXAM 1


Question 5

Answer: C

Explanation:

25.441000

86.16910010086.116904.11000

4

=×

×==

=×==

PT

I r

PR An

Question 6

Answer: E

Explanation:

626000

75.512

13000100100 =

××==

r Q P

Question 7

Answer: B

Explanation:

6500550012000

1200048250

1245500

6500100100

55009006400

=−

=×

××

×

===− PT

I

r

Question 8

Answer: D

Explanation:

Use the TVM solver with N = 60, PV = 26000, PMT = -550,

12,12,0 ===Y

C

Y

P FV



2008 FURMATH EXAM 1


Question 9

Answer: D

Explanation:

book value = 1180082.026000 4≈×=

n PR



2008 FURMATH EXAM 1


Module 5: Network and decision mathematics

Question 1

Answer: A

Explanation:

The adjacency matrix shows the number of connections from each point A, B, C , D & E toeach point.

Question 2

Answer: E

Explanation:

These are the only two of the listed graphs which can be rearranged to look the same.

Question 3

Answer: B

Explanation:

6213 =++SDCA

Question 4

Answer: C

Explanation:

This matrix shows that A has one arrow pointing away, B has 3 etc.

Question 5

Answer: B

Explanation:

Order would be FG, CG, CD, DH, FI, IJ, BF, AB, AE

Question 6

Answer: D

Explanation:

CB, DA, EM, FS = 500 + 200 + 300 + 500 = 1500



2008 FURMATH EXAM 1


SourceSink

4 2 3

4

2

5 3 3 6

3

Question 7

Answer: B

Explanation:

Minimum cut of 8 shown above is 2 + 3 + 3 = 8

Question 8

Answer: D

Explanation:

This path takes the longest time i.e. 23 days

Question 9

Answer: C

Explanation:

Activity C is not on the critical path and Activity A is too expensive



2008 FURMATH EXAM 1


Module 6: Matrices Solutions

Question 1

Answer: B

Explanation:

2a = -2, a = -1, 6b = 24, b = 4, -2c = 4, c = -2, d = -9

Question 2

Answer: C

Explanation:

Non-conformable matrices cannot be multiplied. B.C.A involves multiplying matrices oforder: 332332 ××××× thus AC × is not possible

Question 3

Answer: D

Explanation:

The second row of matrix C multiplied by the second column of matrix B

Question 4

Answer: E

Explanation:

I B 2−=×

I 220

02

24322442

23322342

22

34

42

32−=

−

−=

−×−+−×−×−+−×−

×+−××+−×=

−

−−

−−

Question 5

Answer: E

Explanation:

The matrix

− 31

45

19

1 is the inverse of

−

51

43



2008 FURMATH EXAM 1


Question 6

Answer: B

Explanation:

The rows in T must represent Saturday & Sunday and the columns Running & Walking if D isa column matrix with Saturday then Sunday distances.

Question 7

Answer: C

Explanation:

This relationship multiplies T -1 by D.

Question 8

Answer: A

Explanation:

Note columns on T must add to 1.

Question 9

Answer: D

Explanation:

=

=

70.0

30.0

20.0

80.0

85.035.0

15.065.050

50 N T

Further Maths Units 3 & 4 2008 Trial Exam 1 Solutions

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