2022-2023-S1 1st TERM EXAM-MATH.pdf

2022-2023-S1 1st TERM EXAM-MATH 2022-2023 S1 1st TERM EXAM MATH Name NLSI Lui Kwok Pat Fong College 2022  2023 Class S1 First Term Examination...

2022-2023-S1 1st TERM EXAM-MATH 2022-2023 S1 1st TERM EXAM MATH Name NLSI Lui Kwok Pat Fong College 2022  2023 Class S1 First Term Examination Class No. MATHEMATICS Question–Answer Book 4th January, 2023 8:15 am – 9:45 am (1 hour 30 minutes) This paper must be answered in English INSTRUCTIONS Sections Marks 1. Write your name, class and class number in the spaces provided on this cover. A Total /30 2. Answer ALL questions in Section A. You B Total /40 should use an HB pencil to mark all the answers on the Answer Sheet, so that wrong C Total /30 marks can be completely erased with a clean rubber. You must mark the answers clearly; otherwise you will lose marks if the answers TOTAL /100 cannot be captured. You should mark only ONE answer for each question. If you mark more than one answer, you will receive NO 量 MARKS for that question. q0 x 3. Attempt ALL questions in Sections B and C. Write your answers in the spaces provided in = 22 this Question  Answer Book. 4. Unless otherwise specified, all working must be clearly shown. 5. The diagrams in this paper are not necessarily drawn to scale. 6. NO calculator is allowed. 2022-2023-S1 S1 1st TERM EXAM-MATH-1  Section A (30 marks) Choose the best answer for each question. anumber? 1. Which of the following is a prime 5. Evaluate 2 3 3  0.5  . 5 2 7 三 A. 27 , 嘿 B. 0 C. D. 57 67 77 A. 8 7 zy 5 l B. 8 10 成 Ʃ L GM 179 38 _ 2 + 2. The H.C.F. of 2  3  7 , 2  5  7 and 2 3 4 C. … 50 22  52  7 is ① 37 D. ExT 或t 0 件 A. 2 7. 2 10 卡培 B. 22  3  5  7. C. 28  3  53  75. 6. How many integers between 4.7 and ≈ D. 2 4  3  52  7 3. 3 3 are negative? 5 4 3 - 251 θ - - , 3. o 734 is a 4-digit number. If it is divisible A. 3 , , , by 6, which of the following can be the B. 4 1 , 2 3 C. 5 , ? value of0 0 D. 8 A. 1 × 0 B. 2 7. (2)  (2)  (2)  (2)  (2)  C. 3 D. 5 A. 10. B. 6. 4. In the figure, A, B and C are three values on C. –6. the number line. Which of the following D. –10. a expression must be positive value? 7 / ~ ~~ j B 0 A C 8. (3a 4b3 )(5ab2 )  ata aaNo axb =. x ㄟ A. 4 8a b. 6 axa 沈 A. B–A = 5 a B. B×C B. 8a 5b5. C. A–C C. 15a5b5. D. A–B D. 15a 4b 6. 2022-2023-S1 S1 1st TERM EXAM-MATH-2 米 口 十 一 一一 一一一 一 一 、 一一 石 一一寸 己 、 一 十 一  以下海深品 n t 1 = 2 5 m below∞ 9. Fred is 00 sea level now and he 12. In the figure, the 1st pattern consists of 4 灣 O σ dives 4 m further every minute. Suppose dots. For any positive integer n, the “+” represents a position above sea level. Use a directed number to represent the σ (n + 1)th pattern is formed by adding (2n + 3) dots to the nth pattern. Find the ∞ position of Fred after 7 minutes. number of dots in the 7th pattern. lst Ind 了 rd A. +33 m - 5 + G4 J a B. – 16 m C. – 23 m 4 0 D. – 33 m caxb 1 : O eproditolmdb ∝ A. B. 36 49 2 :5 +⑧+ () + atb 4 10. “Divide the ossum of a and b by 3.” can be 7 θ 3 = C. 64 written in algebraic expression as D. 81 q φ : “ 5 : 1 b A. a. ① 2 1 ( 3 13. Stephen has $m. He spends $350 on a pairs a of shoes and spends all σ the rest on 3 pairs of B. b. 3 socks. How much is each pair of socks? ab 吼 C.. 3  m  350  A. $  θ 3 = ab  3  D.. 3 m B. $(  350 ) 3 ∂ = } C. $ 3(m  350) 11. For the sequence 162, 54, 18, 6, … , the  m  350  next 3 terms are D. $   3  2 2 0 A. 2, and. 3 3 逃 tc 3 9 14. Simplify (2c  c)  c. B. 0, –6 and –12. 3 3 2 C. 3, and. A. 6c ac 2 4 D. –6, –18 and –30. B. 6c 2 θ C. 9c 2 D. 6c  c 2 - ( 1 - x ) = - ( * C) = - { ex — σ 15. Solve the equation 3[2  (1  x)]  x  1. A. x  2 2 - (] ) 1 Be } 年 x - t B. x 2 2X ② 9 φ - C. x 1 D. x2 x 2 - 2 2022-2023-S1 S1 1st TERM EXAM-MATH-3 二 二 。 心 一 十  你 吃真 卡 … t + 0 ← 0 2 5 5 21. Among 150 MP3 files stored in a phone, 16. Solve the equation x  2( x  6). × 28 5 60% of them are ~σ pop music and there are 18 - recordings of oral practices.4If the rest 742150 … are 0 σ A. x  7.5 the recordings of lessons, what percentage ㉚ / of the0 z* B. ① x  5 lessons? MP3 files are the recordings of “ Eoo C. x  0.5 150 40 = 是 * x yez 8 x5 = D. 2 (和 ㄨㄟ = - 4 A. 12% 4 + 4 =| xtly { 凹 B. 22% 60% = 42 之 2y l 50 × = q0 ①. C3 - O 17. The sum of three consecutive odd numbers C. 28% _ OIcec D. 72% 8C ecey is 129. If the greatest ⇌ number of them is m, 齡嘴 )= 化 — which of the following equations can be CClt × used to find the value of m? substtrauti 22. A box of chocolates was sold for $136, with A. plasssamiaadal m  (m  2)  (m  4)  129 ① a percentage loss of 20%. Find the cost of 章些 this box of chocolates. O 8T18 - - 钟 ainces S的本B. m  (m  1)  (m  2)  129 “ 最 igeey 乒 , % eC ) ± m ∝ (m  1)  (m  2)  129 b 台 → C. 1 2o C ” d 够麻 A. 13 bc $113.3 + 7 0 D. m  (m  2)  (m  4)  129 ~ [ B. $163.2 =γ wx 3 θ 1 Gow w 今 C. $170 “ σ6w^ = a - 1 = 5 ④ h - Zc D. $680 CC 1 20% - ) = S 18. The present age of Mr. Leung is 5 times of that of his son. If the sum of their ages 4 互 c years later is 62, find the present age of 23. Tom has 16 toy cars. If the number of toy Mr. Leung. cars owned by Ken is 75% of Tom’s, how many toy cars do they have in total? A. 40 years old ① B. C. 45 years old 48 years old A. 24 B. 28 D. 50 years old C. 30 ( 20o D. 32 19. If a% of 120 is 96, find a. ⑨8. a % × 120 = q6 24. The marked price of a pair of shoes is $120. A. 24 If it is sold at 25% off, find the selling B. 75 a 品兵 price. ① 0 C. 80 a 8 ^ 08 = D. 125 A. $85 08. B. C. $90 $100 20. In an examination, 96% of the students D. $110 passed and 7 students failed. How many students sat for the examination? e A. 103 B. 118 C. 168 0 D. 175 2022-2023-S1 S1 1st TERM EXAM-MATH-4 、土 一。 一一十一一 二 二 、、 一 一 一 一 工 一 一一 一 一 辶 一一一 一 一 子 工 己 大 一  25. 20 chairs are sold for $480 each. 10 of the 29. Which of the following prisms has the chairs are sold at a profit percentage of 20% largest volume? and the other 10 are sold at a loss of 20%. After selling all chairs, A. the overall profit percentage is 4%. B. the overall loss percentage is 4%. C. the overall loss percentage is 6%. D. there is no profit and no loss. 26. Find the area of the figure. A. 37 cm 2 B. 43 cm2 C. 49 cm2 D. 86 cm 2 27. The figure shows ACD where ADC  90. B is a point on AC such that DB  AC. Find the perimeter of ACD. 30. In the figure, ABCD is a rectangle. E is a point on AD such that AE = ED. F is a point on AB such that FB = 3AF. If the area of AEF is 1 cm2, then the area of the shaded region is A. 100 cm. B. 105 cm. C. 110 cm. D. 120 cm. 28. 3 identical cubes of side length 8 cm are melted and recast into a cuboid. If the base A. 6 cm2. length and the base width of the cuboid are B. 9 cm2. 12 cm and 4 cm respectively, find the C. 10 cm2. height of the cuboid. D. 12 cm2. A. 32 cm B. 24 cm C. 16 cm 2 D. 10 cm 3 2022-2023-S1 S1 1st TERM EXAM-MATH-5 。  Section B: (40 marks) 31. Use an algebraic expression to represent each of the following. √ (a) Subtract 7 from c. 雄 0 (b) Divide the square of y by the product of 4x and z. (3 marks) 火 442 32. In a hall, there are 150 students and 60% of them are boys. If 20% of girls join a singing contest, %i find the number of girls joining the singing contest. (2 marks) 0 E 50( 5 H 0%) ] 4 [⑩ 0. 4 2 o (20 prolaesct 回 x 33. (a) Use index notation to express each of the following numbers as a product → C of prime factors. (i) 90 (ii) 84 (b) Find the L.C.M. of 90 and 84. (4 marks) 0 < a0 = * 上 84 Z 0 = 的 2 ^× × 5× 32 7 paere7 2022-2023-S1 S1 1st TERM EXAM-MATH-6 二 止 一 一 一二 一一 一 一 一  Atactoricee × the following. 34. Simplify (a) a  a  a  a  a  a a Δ ooa = 2 a a (b) 3  2 x σ 3x  2 x  12 x  3  2 了 (5 marks) 3a _ a → ( 與 = a , cb -3twt3xxx-2 ×2 dxt Gx 2 - = - 3t20 τ - 3 +2 t 20 - 4 xtbx 2 ≥ - 1 - zotbx 2 x2 35. If A  , find the value of A when x  3 and y  5. (3 marks) x  3y - ] r =⑦ p 2 n 2 } ㄎ \ ~ ~ 3 x8 “ 3 t 2 ⑱ 巡 913 - 3 f 1∞ 及2 ↑ 2022-2023-S1 S1 1st TERM EXAM-MATH-7 一一 二 一 一 二 一  出 3 - lo - 5X - 36. Evaluate the following. 2  (5)i ( ) (a). (b) (2)  (32 ) 4 (9)  (3) 4  3 1 , (c) 10  5   2   5  4 2 (8 marks) 2/(t5) [ a ] ÷ (t3 ] 望 23)÷S, - - ~< - D) (c - 10- 5X - 1 0 ) [ o (Ot} 1 -(5 - =^ [b ) z] +址 -32 4 , =- 10 X - 2 三 5元 lot @ ] 平) S. coq to [ = - = 7 8 -x π ot三 “ 8 0 - ) ( 比 知 2 - O - [ - Ʃ] 37. A wire with the length of 105 cm is cut into two pieces. One is bent to form an equilateral triangle with sides of y cm each, while another is bent to form a square with sides of 3y cm each. Find the perimeter of the square. (4 marks) y cm 3y cm 2022-2023-S1 S1 1st TERM EXAM-MATH-8 一 一 一一 、 二 二 二 二 》 心 二工 二 一一 一 十 一 一 38. In the figure, ABCD is a parallelogram with the height BH = h cm. AD and CE meet at F. The area of the shaded region is 39 cm2. (a) Find the area of CDE. (b) Find the area of ABCF. (c) Is the value of h smaller than 6? Explain your answer. (5 marks) 39. Solve the following equations. (a) x  4  2( x  1) x7 x7 (b)  4 4 3 (6 marks) 2022-2023-S1 S1 1st TERM EXAM-MATH-9 Section C: (30 marks) 40. PFC dim sum restaurant has a special offer at tea time. The menu is as follows: Menu Tea charge $5 per person Small dim sum $20 per dish Large dim sum $25 per dish (a) Assume that there are x people dining in the restaurant and ordering a dishes of small dim sum and b dishes of large dim sum. Write down the formula of the amount (C) of the payment in terms of x, a and b. (2 marks) (b) Mr. Cheung is dining in the restaurant with his 4 children. They order 5 dishes of small dim sum and 10 dishes of large dim sum. How much should he pay for the bill? (2 marks) (c) Miss Ho is dining in the restaurant with a friend. They order some large dim sum only and they need to pay $110. How many dishes of large dim sum do they order? (2 marks) (d) Now the restaurant has a New Year special offer. If the bill is more than $401, the customer can pay with credit card to get a 10% discount. Ken’s family has 6 members and they are dining in the restaurant at tea time. (i) If they order 6 dishes of small dim sum and 10 dishes of large dim sum, find the amount that they need to pay. (ii) Hence, Ken’s mother claims that if they order 2 more dishes of small dim sum, they can save $4 more. Do you agree? Explain your answer. (4 marks) 2022-2023-S1 S1 1st TERM EXAM-MATH-10 2022-2023-S1 S1 1st TERM EXAM-MATH-11  41. In a winter sale of a boutique, the selling price of a suit is $3 360. The suit is sold at a discount percentage of 30% on its marked price. (a) Find the marked price of the suit. (3 marks) (b) A profit of 40% is made by the selling price of the suit. Find the cost price of the suit. (3 marks) (c) The boutique manager claims that if the discount percentage is increased to 60%, then there will be a loss of 20% when selling the suit. Do you agree? Explain your answer. (4 marks) (a] $ 4800 cb) $ 2400 CC ) 2022-2023-S1 S1 1st TERM EXAM-MATH-12 一 2022-2023-S1 S1 1st TERM EXAM-MATH-13 42. The figure shows a vase formed by two parts. The upper part is a cube of side 6 cm. The lower part is a right prism having a uniform cross section of a trapezium of height 12 cm. Now 882 cm3 of water is poured into the vase. (a) (i) Find the volumes of the upper part and lower part of the vase respectively. (ii) Find the depth of the water in the vase. (5 marks) (b) At most how many marbles of volume 5 cm3 each can be put into the vase and immersed completely in the water such that no water overflows? Explain your answer. (2 marks) (c) If the vase is full of water, find the total surface area of the wet surface of the vase. (3 marks) 2022-2023-S1 S1 1st TERM EXAM-MATH-14  END OF PAPER 2022-2023-S1 S1 1st TERM EXAM-MATH-15