Math - Sec2 - SA2 - 2023 - Canberra Sec

163 CANBERRA SECONDARY SCHOOL 2023 End-of-Year Examination Secondary Two Express MATHEMATICS Paper1 9 October 2023 1 hour 15 minutes 1020h - 1135h Name: ( ---------------- ) READ THESE INSTRUCTIONS FIRST Write your full name, class and index number on all the work you hand in. Write in dark blue or black ink pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. Class: The use of an approved scientific calculator is expected, 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 TC, use either your calculator value or 3.142, unless the question requires the answer in terms of TC. At the end of the examination, fasten all your work securely together. 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 50. FOR MARKER'S USE Marks Max Awarded Marks Total 50 BP-159

164 2 1 Simplify 4a(b+c)-3b(a- 7c). A ns,ver . .......... ... ..................... ... [2] 2 Factorise 12a 1 - 75. Ans1-ver ..... ....... ... . ....... .... .. ..... .. .. [2] 3 A triangle has sides AB = 8 cm, BC== l 5 cm and AC = 17 cm. (a) Explain why triangle ABC is a right-angled triangle. Answer (b) Calculate LACB Canberra Secondary School 2023 End-<>f-Year Examination [2] Annver ... .. ...................... .. ........ [2] Mathematics Paper 1 Secon,dary 2 Express BP-160

165 3 Tuitio11 4 A bag contains 5 red marbles, 6 green marbles and 3 yellow mar~les1 Matilda draws a marble at random. W} t · ·· (a) Find the probability that a green marble is drawn. Answer ...................................... [1] (b) Find the probability that the marble drawn is not red. Ansiver ...................................... [ 1] (c) If Calos adds 3 blue marbles into the bag. find the probability that Matilda draws out a blue marble. Answer ...................................... [l] 5 Given that a sphere has a volume of 700 cm3 and a cube has a volume of 729 cm3. Explain, with calculations, why even though the sphere has a smaller volume compared to the cube, the sphere cannot fit inside the cube. Answer [4) Canberra Secondary School 2023 End-of-Year Examination Mathematics Paper 1 Secondary 2 Express I.Turn Over

166 4 6 The stem and leaf diagram below states the data collected on the scores of two classes during a Mathematics te~t. Class A Stem 5 4 9 0 1 0 2 6 6 7 8 2 Key: Class A 9 I O neans 9 marks (a) How many students took the test? (b) What is the highest E.core obtained? (c) The passing mark was 15. Class B ., 4 4 2 5 8 8 9 0 0 5 Class B 0 i 2 means 2 marks Ans,-ver ...... ................................ [1] Anslver ...................................... [ 1] Find the percentage of students who passt::d the test in Class B. Answer .................................... % [2] 7 The braking distance of a vehicle is directly proportional to the square of its speed. When the speed is v metres per second, the braking distance is 6 m. When the speed is increased by 100%, find (a) an expression for the new speed of the car, in terms of v, Ansv.,·er .. .... ... ... ......... ................. [l] (b) the braking distance, Answer .................................. m [2] (c) the percentage increase in the braking distance. Canberra Secondary School 2023 End-of-Year Examination AnsH·er .................... .............. % [2] Mathematics Paper 1 Secondary 2 Express

167 8 5 l O men take 16 days to complete a project. After 4 days, 2 men left the project. Tuitio:-1 (a) How many more days will it take for the remaining 8 men liDj;: the project? W l L Answer ........................... days [3] (b) What assumption is made to calculate part (a)? Ans1ver ......................................................................................... [I] Canberra Secondary School 2023 End-of-Year Examination Mathematics Paper 1 Secondary 2 Express [Turn Over

168 6 9 The two quadrilaterals A BCD and PQCR are congruent. R B 22 cm 14 cm ~ C 116° A Find (a) the length of CD, (b) the length of DQ, (c) LEAD (d) LCRP. Canberra Secondary School 2023 End-of-Year Examination Q Answer .................................... cm [l] Ansi,·er ..... ............................... cm [I] An.nrer ......................................... [l] Answer ........................................ [2] Mathematics Paper 1 Secondar/ 2 Express

169 7 10 (a) Solve the inequality 3x- 7 ~ 12. Answer ...................................... [2] (b) Represent the solution for (a) on the number line below. Answer (c) Hence state the greatest value of x if (i) x is a prime number, (ii) x is a perfect square. [l] X Answer x ................................ [1] A ns1ver x = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ I ] Canberra Secondary School 2023 End-of-Year Examination Mathematics Paper 1 Secondary 2 Express [Turn Over

170 11 Simplify (a) 4a 2bc3 (b) pq+l 3p 2 q +3p-2pq -2 (c) (c+d)(c-d). 1 (c-d) 2 -:- (c-d) Canberra Secondary School 2023 End-of-Year Examination 8 Answer ...................................... [l] Ansiver ................................... ... [3] Ansiver ......... . ....... .... ..... ...... .... ... [2] Mathematics Paper 1 Seconda1y 2 Express

171 12 9 . Tuition The table below shows the number of hours students m a class of 40 spend playing on the computer each day. \ 1V it No. of homs spent 0 2 3 4 5 6 7 8 No. of students 2 7 X 6 13 3 2 (a) Find the value of x. A nswer x = ... ...... ..... ... ... ... .. ...... .... [ 1] (b) Find the mode of the distribution. Answer .. .... .. .... ... .............. ... .... h [I] (c) Find the median of the distribution . Answer ..... ......... .................... .. h [I] (d) Find the mean number of hours spent on the computer per student each day. Answer .. .. .... .... .. ... .. . ... .. .. ...... ... h [2] (e) Find the probability that one student chosen at random spent more than six hours playing on the computer each day. Ans iver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1 ] End of Paper Canberra Secondary School 2023 End-of-Year Examination Mathematics Paper 1 Secondary 2 Express

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