ZHONGHUA SECONDARY SCHOOL MID-YEAR EXAMINATION 2012

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ZHONGHUA SECONDARY SCHOOL MID-YEAR EXAMINATION 0 Name of Pupil : ( ) Class : T Subject / Code : MATHEMATICS SYLLABUS T / 404 Level : Sec Normal(Tech) Date : 0 May 0 (Thursday) Duration : hours Setter

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.

1 ZHONGHUA SECONDARY SCHOOL MID-YEAR EXAMINATION 0 Name of Pupil : ( ) Class : T Subject / Code : MATHEMATICS SYLLABUS T / 404 Level : Sec Normal(Tech) Date : 0 May 0 (Thursday) Duration : hours Setter : 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.4. This question paper consists of printed pages, including this cover page. Score / 80

2 Mathematical Formulae Numbers and Algebra Compound interest Total amount = r P 00 n Quadratic equation ax + bx + c = 0 x b b 4ac a Geometry and Measurement Curved surface area of a cone = rl Surface area of a sphere = 4 r Volume of a cone = r h Volume of a pyramid = base area height Volume of sphere = 4 r Area of triangle ABC = C absin C b a A c B Zhonghua Secondary School 0Mid-Year Exam

3 . (a) Write in standard form. SECTION A (50 marks) Answer ALL the questions in the spaces provided. (b) Express in ordinary notation (c) Evaluate.9 0 figures., giving your answer in standard form correct to significant Answer (a) [] (b) [] (c) []. Simplify the following algebraic expressions. (a) ( x y) (5x 7y) (b) ( q ) 5( q ) Answer (a) [] (b) [] Zhonghua Secondary School 0Mid-Year Exam

4 . (a) Complete the number sequence below. 7, 9.5,,, (b) Express 5 (i) as a decimal. (ii) as a percentage., Answer (a), [] (b)(i) [] (ii) [] 4. The diagram below shows a right-angled triangle LMN. Given that LM = 0cm and MN = 8cm. Find the length of LN, stating your reasons clearly. L 0cm N 8cm M Answer [] 5. Simplify the following and leave your answer in index notation. (a) 4 p q r q r r mn x (b) 4 6nx m Answer (a) [] (b) [] Zhonghua Secondary School 4 0Mid-Year Exam

5 6. Given that ABC and ADE are similar, find the values of x and y. A 5cm D cm B 4cm 7 o C y x E Answer x = [] y = [] x 7. Given that x =, y = and z =, evaluate yz without the use of a calculator. Give your answer as a fraction. [All workings must be shown clearly] Answer [] Zhonghua Secondary School 5 0Mid-Year Exam

6 8. Find the values of the unknown angles x and y. Give reasons for your answers. y 96 x Answer: x = [] y = [] 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) [] (b) [] Zhonghua Secondary School 6 0Mid-Year Exam

7 0. A model of an oven is advertised in two shops. Super Courts Ultra Gain City $5 $5 + 7% GST including GST (a) (b) Which shop is offering a better deal? How much cheaper is the oven in that shop? Ultra Gain City is also offering the following hire-purchase terms for the oven. How much more would you pay by hire purchase? Deposit $00 + monthly instalments of $.50 Answer (a), [] (b) [] Zhonghua Secondary School 7 0Mid-Year Exam

8 . Elizabeth deposits $5000 in a bank which pays % compound interest per year. Calculate the amount of money in her account at the end of years. Answer $ []. Angeline makes a 5% profit on each shirt that she sells. (a) If shirt A costs Angeline $.00, how much does she sell it for? (b) If she sells shirt B for $.50, calculate the amount of profit she makes. Answer (a) $ [] (b) $ []. Complete the figures if the dotted line is the line of symmetry. (a) [] (b) [] Zhonghua Secondary School 8 0Mid-Year Exam

9 4. The diagram below shows a map. The distance on the map from Town A to Town B is 4.5cm. 4.5cm Town A Town B (a) (b) (c) Given that the scale of the map is : , calculate the actual distance between Town A and Town B. Give your answer in km. A pond in Town A is 6km. Calculate the area of the pond on the map. Give your answer in cm. 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 [] (b) cm [] (c) hours min [] Zhonghua Secondary School 9 0Mid-Year Exam

10 . y SECTION B (0 marks) Answer ALL the questions in the spaces provided R 4 T x Triangle T is shown on the graph above. (a) (b) (c) 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. [] Triangle T is rotated 90 clockwise about the point R. Draw the image under the rotation and label the image B. [] Triangle T undergoes an enlargement, scale factor, centre ( 0, 0 ). Draw the image under enlargement and label the image C. [] Zhonghua Secondary School 0 0Mid-Year Exam

11 . The sum of consecutive numbers is 69. (a) If the first number is x, write down the algebraic expression for the next numbers? (b) Form an equation involving x and solve this equation to find the value of x. Answer (a), [] (b) x = []. The information below shows the time taken (in minutes) for 9 students to reach home on a particular day (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 5 minutes. Find the time taken for the tenth student to reach home. Answer (a) [] (b) [] (c) [] (d) [] Zhonghua Secondary School 0Mid-Year Exam

12 4. The diagram below shows a prism with a square base ABGH of length cm. ABCD is in the shape of an isosceles trapezium (ie AD = BC). CD = EF = 5cm. E 5cm F D H 5cm C G cm A B cm (a) Given that the height of the trapezium ABCD is 4cm, find the length of BC. D 5cm C 4cm A cm B Answer (a) BC = cm [] (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 = cm [] (c) Vol = cm [] (d) Area = cm [] Zhonghua Secondary School 0Mid-Year Exam

13 5. (a) Complete the table of values below for y = x. [] x 4 0 y = x (b) On the grid below, draw and label clearly the following lines: (i) y = x, [] (ii) x =. [] (c) Write down the coordinates of the intersection of the two lines in (b). 8 y x Answer: (c) (, ) [] ~ End of Paper ~ Zhonghua Secondary School 0Mid-Year Exam

14 Answer Key Q Section A a b a 8 0 (sf).84 0 B c B x y 5x 7y 0y x b 6q 5q 0 q 7 a 5.5, 8.5 bi) 0. bii) % 4 B, B B B 0 LN 8 (Pythagoras theorem) LN = 6cm 5a pq r B b nx m B 6 x 7 (corres angles) B y y = 6.4cm ( ) = 8 ()( ) 96 x (ext angles of triangle, issos triangle) x 48 p x (issos triangle) q p (corres angles) y q 48 (alt angles) 4a cm : km Zhonghua Secondary School 4 0Mid-Year Exam 9km b c cm : 4km.5cm 9 hr 4 hr 4 hours 5 min

15 Section B a x, x B, B b x x x 69 a x = 06 9 = 4min b 6min c 40 min d 06 x 5 0 x = 44min B B 4a BC 4 (Pythagoras theorem) 4b BC = 5cm (5 )(4) cm 4c 5cm 4d Area of rectangles = ( 5) 5a 7, Area of sq base = Total = 50cm B, B Zhonghua Secondary School 5 0Mid-Year Exam

16 5b 5c) (-, 5) B Zhonghua Secondary School 6 0Mid-Year Exam

EAST VIEW SECONDARY SCHOOL SECOND SEMESTRAL EXAMINATION 2017 SECONDARY ONE EXPRESS

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