zhonghua secondary school - top school math · pdf filezhonghua secondary school 7...

ZHONGHUA SECONDARY SCHOOL

MID-YEAR EXAMINATION 2012 Name of Pupil : ____________________________ ( )

Class : 3T1

Subject / Code : MATHEMATICS SYLLABUS T / 4043

Level : Sec 3 Normal(Tech)

Date : 10 May 2012 (Thursday)

Duration : 2 hours

Setter :

r Vetted by :

READ THESE INTRUCTIONS FIRST

Write your class, register number and name on this page.

Write in dark blue or black pen.

You may use a pencil for any diagrams or graphs.

Do not use paper clips, highlighters, glue or correction fluid.

Answer all questions.

The number of marks is given in brackets [ ] at the end of each question or part question.

If working is needed for any question, it must be shown in the space below that question.

Omission of essential working will result in loss of marks.

The total of the marks for this paper is 80.

You are expected to use a scientific calculator to evaluate explicit numerical expressions.

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. _____________________________________________________________________________

This question paper consists of 13 printed pages, including this cover page.

Score

/ 80

______________________________________________________________________________________________

Zhonghua Secondary School 2 2012Mid-Year Exam

Mathematical Formulae

Numbers and Algebra Compound interest

Total amount =

nr

P

1001

Quadratic equation ax

2 + bx + c = 0

a

acbbx

2

42

Geometry and Measurement

Curved surface area of a cone = rl

Surface area of a sphere = 24 r

Volume of a cone = hr 2

3

1

Volume of a pyramid = heightareabase 3

1

Volume of sphere = 3

3

4r

Area of triangle ABC = Cabsin2

1

C

A B

a b

c

______________________________________________________________________________________________


SECTION A (50 marks)

Answer ALL the questions in the spaces provided.

1. (a) Write 0.003 84 in standard form.

(b) Express 510291.8 in ordinary notation.

(c) Evaluate 2

6

1019.2

1032.7

, giving your answer in standard form correct to 3 significant

figures.

Answer (a) _____________________ [1]

(b) _____________________ [1]

(c) _____________________ [2]

2. Simplify the following algebraic expressions.

(a) )75()32( yxyx

(b) )2(5)21(3 qq

Answer (a) _____________________ [2]

(b) _____________________ [2]

______________________________________________________________________________________________


3. (a) Complete the number sequence below.

______,13______,,2,5.9,17

(b) Express 25

3

(i) as a decimal.

(ii) as a percentage.

Answer (a) _________ , __________ [2]

(b)(i) ___________________ [1]

(ii) ___________________ [1]

4. The diagram below shows a right-angled triangle LMN . Given that LM = 10cm and MN =

8cm. Find the length of LN, stating your reasons clearly.

Answer _______________________ [2]

5. Simplify the following and leave your answer in index notation.

(a) rrqrqp 34

(b) 4

32

2

3

6

2

m

x

nx

mn

Answer (a) _____________________ [1]

(b) _____________________ [2]

L

M N

10cm

8cm

______________________________________________________________________________________________


6. Given that ABC and ADE are similar, find the values of x and y .

Answer x = ___________________ [1]

y = ___________________ [2]

7. Given that x = – 1, y = 3 and z = 2

1 , evaluate 3

2

2yz

x without the use of a calculator.

Give your answer as a fraction. [All workings must be shown clearly]

Answer _____________________ [2]

y

5cm

3cm

A

B

C

D

E

x 37o

4cm

______________________________________________________________________________________________


8. Find the values of the unknown angles x and y. Give reasons for your answers.

Answer: x = ___________________ [2]

y = ___________________ [3]

9. A normal six-sided die is thrown.

(a) Find the probability that a prime number occurs.

(b) Find the probability that a number less than 5 occurs.

Answer (a) ____________________ [1]

(b) ____________________ [1]

96°

y

x

______________________________________________________________________________________________


10. A model of an oven is advertised in two shops.

Super Courts Ultra Gain City

$215 $225

+ 7% GST including GST

(a) Which shop is offering a better deal? How much cheaper is the oven in that shop?

(b) Ultra Gain City is also offering the following hire-purchase terms for the oven.

How much more would you pay by hire purchase?

Answer (a) __________________, ________________ [3]

(b) _____________________ [2]

Deposit $100 + 12 monthly instalments of $11.50

______________________________________________________________________________________________


11. Elizabeth deposits $5000 in a bank which pays 2% compound interest per year. Calculate

the amount of money in her account at the end of 3 years.

Answer $____________________ [3]

12. Angeline makes a 25% profit on each shirt that she sells.

(a) If shirt A costs Angeline $12.00, how much does she sell it for?

(b) If she sells shirt B for $22.50, calculate the amount of profit she makes.

Answer (a) $____________________ [2]

(b) $____________________ [2]

13. Complete the figures if the dotted line is the line of symmetry.

(a) [1] (b) [1]

______________________________________________________________________________________________


14. The diagram below shows a map. The distance on the map from Town A to Town B is

4.5cm.

(a)

(b)

(c)

Given that the scale of the map is 1 : 200 000, calculate the actual distance between

Town A and Town B. Give your answer in km.

A pond in Town A is 6km2. Calculate the area of the pond on the map. Give your

answer in cm2.

If Andrew cycled at a speed of 4 km/h, how long would he take to reach the Town

A from Town B? Leave your answer in hours and minutes.

Answer (a) __________________km [2]

(b) __________________cm2 [2]

(c) ______hours _______min [3]

Town A Town B

4.5cm

______________________________________________________________________________________________


SECTION B (30 marks)

Answer ALL the questions in the spaces provided.

1.

Triangle T is shown on the graph above.

(a) Triangle T is reflected along the line x = 9. Draw the line x = 9 on the graph above and

hence draw the image under the reflection. Label the image A. [2]

(b) Triangle T is rotated 90° clockwise about the point R. Draw the image under the rotation

and label the image B. [2]

(c) Triangle T undergoes an enlargement, scale factor 2, centre ( 0, 0 ). Draw the image under

enlargement and label the image C. [2]

y

x

0 1 2 3 4 6 7 8 9 10 5 11 13 14 15 16 17 12

0

1

2

3

4

5

6

7

8

9

10

11

12

T

R

______________________________________________________________________________________________


2. The sum of 3 consecutive numbers is 69.

(a) If the first number is x, write down the algebraic expression for the next 2 numbers?

(b) Form an equation involving x and solve this equation to find the value of x.

Answer (a) ___________, ___________ [2]

(b) x = ___________________ [2]

3. The information below shows the time taken (in minutes) for 9 students to reach home on a

particular day.

33 27 38 36 40 22 30 40 40

(a) What is the mean time taken for a student to reach home?

(b) What is the median time taken for a student to reach home?

(c) What is the modal time (mode) taken for a student to reach home?

(d) If a tenth student’s time is taken into consideration, the mean time taken becomes 35

minutes. Find the time taken for the tenth student to reach home.

Answer (a) _____________________ [2]

(b) _____________________ [1]

(c) _____________________ [1]

(d) _____________________ [2]

______________________________________________________________________________________________


4. The diagram below shows a prism with a square base ABGH of length 11cm. ABCD is in

the shape of an isosceles trapezium (ie AD = BC). CD = EF = 5cm.

(a) Given that the height of the trapezium ABCD is 4cm, find the length of BC.

Answer (a) BC = ______________ cm [2]

(b) Find the area of the trapezium ABCD.

(c) Hence or otherwise, find the volume of the prism.

(d) Find the total surface area of the prism.

(b) Area = ______________ cm2 [2]

(c) Vol = _______________ cm3 [2]

(d) Area = ______________ cm2 [3]

11cm

11cm

5cm

5cm

A B

C D

E F

G H

A B

C D 5cm

11cm

4cm

______________________________________________________________________________________________


x 7 1 2 3 4 5 6 8 1 2 3 4 5 6 7 8 0

1

2

3

4

5

6

7

8

y

1

2

3

4

5

6

7

8

5. (a) Complete the table of values below for y = 3 x. [2]

x 4 0 2

y = 3 x 3

(b) On the grid below, draw and label clearly the following lines:

(i) y = 3 x, [1]

(ii) x = – 2. [1]

(c) Write down the coordinates of the intersection of the two lines in (b).

Answer: (c) (________,________) [1]

~ End of Paper ~

______________________________________________________________________________________________


Answer Key

Q Section A

1a 810342.3 M1

81034.3 (3sf) A1

b 31084.3 B1

c 829 100 B1

2a yxyx 7532 M1

xy 310 A1

b 10563 qq M1

711 q A1

3a 5.5, 18.5 B1, B1

bi) 0.12 B1

bii) 12% B1

4 222 810 LN (Pythagoras theorem)

M1

LN = 6cm A1

5a 3212 rpq B1

b

3

2

2m

nx B1

6 37x (corres angles) B1

y

4

8

5 M1

y = 6.4cm A1

7 3

2

)2

1)(3(

2

)1(

M1

= 8

1 A1

8

2

96x (ext angles of triangle, issos

triangle) M1

48x A1

xp (issos triangle) M1

pq (corres angles) M1

48qy (alt angles) A1

14a 1cm : 2km M1

9km A1

b 22 4:1 kmcm M1

1.5cm2 A1

c

4

9 hr M1

4

12 hr M1

2 hours 15 min A1

______________________________________________________________________________________________


Section B

1

2a 2,1 xx B1, B1

b 6921 xxx M1

x = 22 A1

3a

9

306 M1

= 34min A1

3b 36min B1

3c 40 min B1

3d 35

10

306

x M1

x = 44min A1

4a 222 34 BC (Pythagoras theorem) M1

BC = 5cm A1

4b )4)(15(

2

1 M1

32cm2

A1

4c 3211 M1

352cm2 A1

4d Area of 3 rectangles = 3( 511 ) M1

Area of sq base = 1111 M1

Total = 350cm2

5a 7, 1 B1, B1

______________________________________________________________________________________________


5b

5c) (- 2 , 5) B1

zhonghua secondary school - top school math · pdf filezhonghua secondary school 7...

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