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THEKINGSSCHOOL

General Mathematics

Year 12Assessment TestFebruary 2003

General Inst ructions

Working time 50 minutes

Start a new page for each Part.

All questions may be attempted.

The value of each question is indicated.

Marks may be deducted for careless orbadly arranged work.

Approved calculators may be used.

Begin each question on a new sheet.

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Part A (10 marks) Marks

1 (a) What is the future value of an annuity of $2000 per year at 8?% pa investedfor 18 years? 3

(b) What is the total interest? 1

2 Tom and Dick want to have $30 000 in 6 years' time to expand their business. Toachieve this goal, how much do they need to invest per fortnight at 12% pacompounded fortnightly? 3

3 A playing field is in the shape of an ellipse. The length of the field is 130m and itis 60m wide. Find the area of the field to the nearest square metre. 3

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Part B (8 marks) Marks

4 Use Simpson's Rule to find an approximation to the area of this shape. 3

5 Find the surface area of a closed hemisphere with radius 30 mm (answer to

nearest square mm). 3

13

10

10

10

12

30 mm

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6 Find, to the nearest minute, the measure of the angle in the diagram. 2

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Part C (10 marks) Marks

7 Find the length of the side 'e' to 1 decimal place. 2

8 In the quadrilateral WXYZ,XY = 95, WXY= 38, WZY= 59, WYX= 115and YWZis a right angle. (Measurements in cm.)

Find the length YZ to 1 decimal place. 4

7.1

12.3

e

1467cm5cm

W

X Y

Z59

115

95 cm

38

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9 (a) Draw a sketch diagram for this field notebook entry. 2

(b) Calculate the area of the block of land. All measurements in metres. 2

L64

45 5038 25 0

K

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Part D (14 marks) Marks

10 Consider the following distribution:

x f fn

1 3 32 5 103 9 274 6 245 7 356 4 247 6 42

=f =fx

(a) Find f 1

(b) Find fx 1

(c) Find the mean. 1

(d) Find the median. 1

(e) Find the mode. 1

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11 The following sets of data show the ages of males and females who went on acruise during the holidays.

(a) Display these sets of data on an ordered back-to-back stem-and-leaf plot.

Males

15, 30, 25, 18, 10, 28, 32, 35, 23, 2118, 10, 23, 32, 31, 42, 38, 41, 23, 25

Females

18, 16, 25, 19, 12, 27, 31, 32, 36, 4348, 31, 16, 27, 31, 27, 32, 16, 31, 43 3

(b) How many people were in the group? 1

(c) How many were females. 1

(d) Find the range of the female ages. 1

(e) How many 32 year old males went on the cruise? 1

12 Consider the following box-and-whisker plot:

0 5 10 15 20 25 30 35 40 45 50

Find:

(a) the median 1

(b) the interquartile range 1

End of Assessment Task

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AnswersYear 12 General Feb 2003

1a) $74900.49b) $38900.49

2) $131.743) 6126m3

4) 2163

2or 216.6 or 217

5) 8482 mm2

6) 54045

7) 11.5cm8) 150.39a) See teacher

b) 2240m210a) 40=f

b) 125.4=fx

c) Median=4d) Mode=3

11a)

b) 40 in the groupc) 20 femalesd) Range=36e) 2x32 yo males

12a) Mediam=30b) Interquartile range=25

45

1225

38

15

18 8 5 0 0

8 5 5 3 3 3 1

8 5 2 2 1 0

2 1

2 6 6 6 8 9

5 7 7 7

1 1 1 1 2 2 6

3 3 8

2

3

4