Name ( ) Class 4

Thursday 13 September 2012 2hours 30 minutes Paper 2

INSTRUCTIONS TO CANDIDATES Answer all questions. Write your answers on the writing papers provided. Omission of essential working will result in loss of marks.

Calculators should be used where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of .

Attach this page on top of your answer scripts. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. Question 1 2 3 4 5 6 7 8 9 10 11 12 13 Marks

This question paper consists of 10 printed pages.

ANGLICAN HIGH SCHOOL Preliminary Three Examination

Secondary Four MATHEMATICS (4016/02)

For Examiners Use

100

Signature of Parent/Guardian & Date

Name of Parent/Guardian

2

Mathematical Formulae

Compound Interest

Total amount = nrP

+100

1

Mensuration

Curved surface area of a cone = rl Surface area of a sphere = 24 r

Volume of a cone = hr 231

Volume of a sphere = 334 r

Area of triangle ABC = Cab sin21

Arc length = r , where is in radians

Sector area = 221 r , where is in radians

Trigonometry

Cc

Bb

Aa

sinsinsin==

Abccba cos2222 +=

Statistics

Mean = ffx

Standard deviation = 22

ffx

ffx

3

Answer all the questions.

1. Given that y is inversely proportional to the cube root of x and that x = 64 when y = 2, (a) find the equation connecting x and y, [2]

(b) find the exact value of x when y = 316 . [2]

_______________________________________________________________________________ 2. The price of a new truck in a showroom is $90 000. (a) Samuel bought the truck by cash and was given a special discount by the sales agent. Given that he paid $82 350, calculate the percentage discount he received. [2] (b) Gary bought the new truck on hire purchase without discount. He paid a down-payment of $5100 followed by a monthly installment of $1752.50 for 5 years. Calculate. (i) the additional cost incurred when paying by hire purchase, [2] (ii) the interest rate charged per annum. [2] ________________________________________________________________________________ 3. Solve the following equations. .

(a) 0123

21

=+

+

x

x [2]

(b) 21

311

=+

xx

[4]

(c) 02

51

122 =+

+

+

xxxx [4]

_______________________________________________________________________________

4

4. (a) The sum of two numbers is 64. The difference between of one number and of the other is equal to 28. Find the value of the larger number. [2] (b) William drove his car from Town A to Town B at x km/h. The distance between the two towns is 40 km. On the way back, William drives 20 km/h faster and arrives 10 minutes earlier. (i) Form an equation in x and show that it reduces to x2 + 20x 4800 = 0. [4] (ii) Solve this equation and state the speed at which William drives back from Town B to Town A. [3] ________________________________________________________________________________ 5. (a) The diagram shows a sequence of figures made up of dots and lines.

(i) Find the number of dots in Figure 10, [1] (ii) Figure n has 169 dots. Find the value of n. [1] (b) Consider the following number pattern:

Line 1: 0 1 2 = 13 1 = 0 Line 2: 1 2 3 = 23 2 = 6 Line 3: 2 3 4 = 33 3 = 24 Line 4: 3 4 5 = 43 4 = 60

: : : Line p: _ p _ = 883 88 = q : : :

(i) Write down the sequence for line 5. [1] (ii) Find the value of p and of q. [2] (iii) Given that r = n3 n where n is a whole number, express r in terms of n as a product of three consecutive numbers [1]

______________________________________________________________________________

5

6. Answer the following questions:

(a) Given a cone with a base radius of 8 cm and a vertical height of 15 cm,

find the curved surface area of the cone taking = 3.142. [6]

(b) The figures below shows a cube of sides 28 cm that had its corners removed as shown in the

side view.

Taking = , find,

(i) the volume of the solid [2] (ii) the total surface area of the solid [3]

______________________________________________________________________________

7. The diagram below shows part of a regular heptagon. Find,

(a) ABC, [2] (b) CBD. [2]

______________________________________________________________________________

6

8. In the diagram, BCDEF are points on the circumference of a circle with centre O. BAD = 26

and BTD = 122. Given AD is a straight line and AB is tangent to the circle, find,

(a) BOF, [1]

(b) BEF, [1]

(c) DFE, [2] (d) BCE. [3] __________________________________________________________________________________

9. Given that A is a point at (-3,4) and

=15

AB ,

(a) Show that 29=OB units. [2]

(b) Given also that M and N are midpoints of OA and OB respectively, express MN

uuuur as a column vector. [2]

(c) Given that D is the point (27 , 3) and OBkOAhOD += . Calculate the value

of h and of k. [3] (d) Make 2 statements about the points D, M and N. [3]

_________________________________________________________________________________

7

10. In the figure, A, B and C are three points on a horizontal plane such that AB = 2BC and TC is a vertical tower of height 116 m. The bearings of B from A and C from B are 050 and 110 respectively. The angle of elevation of T from A is 30. Calculate, (a) ABC, [1] (b) the length of AC, [2] (c) the length of AB, [3] (d) the angle of depression of B from T, [2] (e) the bearing of C from A, [2] (f) the shortest distance from B to AC. [2] __________________________________________________________________________________

50 30

110

North

T

C B

A

North

116m

8

11, The time taken for 500 students from School A taking the 2.4 km run was illustrated with an incomplete box and whisker diagram below with the following information, the 50th percentile was 12.2 minutes, interquartile range was 4 minutes and minimum time taken was 9 minutes.

School A

11 m r 19 Time (in minutes)

Using the given information, (i) Calculate the range. [1] (ii) Calculate the value of r. [1]

School Bs timings of the 2.4 km run for 500 students were presented in the form of a cumulative frequency curve below.

(iii) Compare the time taken to complete the run by the students from both schools in two different ways. [3]

__________________________________________________________________________________

10 12 14 16 18 20

500

450

400

350

300

250

200

150

100

50

0

Cumulative frequency Curve of School B

Time in Minutes

9

12. A class planned a dart game for a school carnival where students throw darts at a target board

comprising two concentric circles in a square as shown below. The square is of side 50 cm, the radius of the small circle is 5 cm.

A dart landing on the circumference of the small circle or within the small circle scores 5 points. If the dart lands between the small circle and the large circle, the score is 2 points. A shot landing elsewhere inside the square scores 1 point.

Assuming that every dart will definitely land on the target board, calculate the probability of scoring, leaving your answers in terms of where applicable.

(a) 1, 2 or 5 points with one throw, [1]

(b) 1 point with one throw, [2]

(c) 7 points with 2 throws, [3]

(d) 8 points with 2 throws. [1]

__________________________________________________________________________________

10

13. Answer the whole of this question on a sheet of graph paper. The table shows some corresponding values of y and t. represented by the equation

.2193

41 23 ttty +=

t 0 1 1.5 2 2.5 3 3.5 4 5 y 0 6.75 8.3 9 8.9 8.25 7.2 a 3.75

(a) Calculate the value of a. [1] (b) Using a scale of 2 cm to represent 1 unit on the horizontal and vertical axes,

draw the graph of ,2193

41 23 ttty += for the values of 0 t 5. [3]

(c) From the graph, state the coordinates of the maximum point. [1]

(d) Use your graph to find the values of t when y = 4. [2] (e) By drawing a tangent at t = 3.5, estimate the value of the gradient. [2] (f) Using the graph and by drawing a suitable graph, solve the equation [4]

0102213

41 23 =+ ttt .

______________________________End of Paper________________________________