Math - Sec2 - SA2 - 2023 - Broadrick Sec

71 I Name • •• • . ~,m-~4:~.,.~ ,.:;,,;· BROADRICK SECONDARY SCHOOL SECONDARY 2 G3 END-OF-YEAR EXAMINATION 2023 MATHEMATICS 4052 Section 1 Candidates answer on the Question Paper. October 2023 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Section 1 & Section 2 Answer all questions on the Question Paper. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. 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 for each section securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of the marks for this paper is 90. For Examiner's Use For Examiner's Use Question Marks Section 1 / 45 Error in Number Deducted Rounding-off Section 2 / 45 Reasoning Presentation Total ~ [Turn Over BP-69

BP-70 Answer all the questions. in this section. 1 Simplify (a) 5x-15y-3x+I0y, An.nver [l] (b) 5p-2(p+2). Answer [l] 2 . 20 2 "' Solve the equat10n -- = x + .J . x+l hmver x = ............ or........ .. ... [3] Broadrick Secondary School , End-o f-Year Exa mination 2023. Sec T-..·o G3. /1.fathema tics [Turn Over 72

73 3 Jane bought x grams of meat for 95 cents. Find an expression for the number of grams of meat that can be bought for y dollars. 4 Two similar pentagons are drawn below. All lengths are given in centimetres. 16 22.4 f (a) Find/ (b) Find g. Answer ....... ........................... . y [2) 100° 14 Annver f= .............................. 0 [I] Answer g = .......................... cm [2] Broadrick Secondary School. End-of-Year Examination 2023, Sec Two G3, !v1atbematics

74 5 A bag contains 5 blue balls , 8 green balls and 3 yellow balls. Tu i ti On (a) A ball is drawn at random. Find the probability of gettinWit A nswer (b) x yellow balls are a <led to the bag . The probability of getting a yellow ball 1 becomes- . 2 Find the value of x. [I] Ans,-ver x = ... ... ... ... ... ... ... .. . ... ... [2] 6 Five positive integers have a mean of 12, a median of 15 and a mode of 21. Find the five numbers . Answer [2] Broadrick Secondary School. End-of-Year Examination 2023. Sec Two G3. Mathemat ics [Turn Over BP-72

75 7 Ansv.:er (b) Factorise l 8b2 -32c 2 completely. Ansiver 8 By factorising the expression 4 y2 + l 2 y + 5 , explain why it is odd for all integer values ofy. Answer Broadrick Secondary School. End-of-Year Examination 2023. Sec Two G3. rvlathematics BP-73 [l] [2] [3]

9 The stem and leaf diagram shows the height of 20 plants in a nursery . Heigliit of plan ts (cm) Stem Leaf 15 2 7 8 9 9 9 16 0 0 l 2 3 4 4 5 7 17 0 6 7 Key: 15 I 2 represents 15 2 cm Find (a) the median height of the plants, AnsH'er .............. .......................... cm [ 1] (b) the mean height of the plants. Ans,·ver .. ........ .. ....... ...................... cm [2] ( c) the fraction of plants that are at most 1160 cm. Answer [l] Broadrick Seconda1y School. End-of-Year Exa mination 2023. Sec Two G3 .. Mathematics [Turn Over 76

. ·. T11ition A tnangle ABC has sides AB= 36 cm, BC= 39 cm andA t = I~ cm. A vvit 39 cm (a) Prove that triangle ABC is a right-angled triangle. Ansi1:er [2] (b) Hence, find the exact value of /\ (i) sin ABC, Ansl-1'er [l] (ii) tan A CB . AnsJver [l] Broad.rick Secondary School , End-of-Y car Examination 2023, Sec Two G3. Mathematics 77

11 k-a It is given that h = - , - 0 - . ... x--4 (a) Find h when x = - 2.75, k = -3 .5 and g = 10. Answer h = .............................. [2] (b) Express x in terms • f k, g and h. Answe r x = ......................... ... [3] Broadrick Secondary School, End-of-Year Examination 2023. Sec Two G3. Mathematics [Turn Over 78

79 12 Xis directly proportional to Y3 . It is given Y =!when X =2. 3 (a) ExpressXin tenns of Y. (b) Find the value of X when Y = ! . 6 Ansv,,1er [2] Ansiver X = ..... ........ ..... ........... [1] (c) A change in Yproduces a change in X When the value of Y is multiplied by ! the value of X changes by a factor 2 ofm . Find the value of m. Ans,-ver m = ... . . . . ... . . . . . . .. ..... ..... .. [2] Broadrick Secondary School. End-of-Year Examination 2023, Sec Two G3. Mathematic s BP-77

80 Tuitio11 13 The diagram shows the sector A, which is a third of a circle • • cm. -----... w sector A (a) Find the area of sector A. Leave: your answer in terms of 1r . A11.nver (b) A cone is fonned by joining radii OP and OR of sector A together. (i) Find the base radius of the cone cm 2 [2] Ansiver ............................... cm [2] (ii) Find the height of the cone. Ansiver ...... .......................... cm [2] End of Section I Broadrick Secondary School, End-of-Year Examination 2023. Sec Two G3. Mathematics [Turn Over BP-78