Math - Sec2 - SA2 - 2023 - Regent Sec

REGENT SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2023 SECONDARY TWO EXPRESS NAME: INDEX NUMBER: CLASS: MATHEMATICS Paper1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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, highlighters, glue or correction fluid. Answer all questions. ---- 4052/01 29 September 2023 1 hours 15 minutes 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 with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 50. 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 your answers in degrees to one decimal place. For rc, use either your calculator value or 3.142. TARGET 50 , PARENT'S SIGNATURE 243 BP-239

Answer all questions. 1 Expand and simplify the following . (a) (2x + 1)2 2 244 (b) -x+2( x-3y) X 2-x Solve - + --== 1 . 4 3 BP~240 Ansiver ................................... [ 1] Ans11:er ........... ....... ... ... .... .... ... . [2] Answer x = ................ . .......... ... [3]

3 245 (a) 1 h . 1. 4 3x-3 So ve t e mequa 1ty x - < -- . 4 (b) Represent your solution on the number line. BP-241 Annver .. .. .... .. . ......... ..... ... [2] ----+------;~----+-------4----+------1------+---~;> X [l] (c) Hence, write down the largest prime number that satisfies the inequality. 4 Factorise completely (a) 2la 1b-7a, (b) 50-8p 2 , (c) 5ax+ 2bx-10ay-4by. Answer . . . . . . . . . . . . . . . . . . . . . . . . . . .. [ l] Answer ................................. [l] Answer ................................. [2] Answer ........ ................. ........ [2]

BP-242 5 The table below summarises th amount of time spent on a computer by a group of young children in one particular week. 246 Time (h hours) 0 <h $ 2 2<h$4 4<'156 6 <h :S: 8 8<h:S:10 Frequency 4 9 l6 13 8 Calculate an estimate of the mean time spent on a compute r that week. 6 The map of a village is drawn to a scale 1 : 350 000. (a) The length of the road on the map is 7.5 cm. Answer ............ .......... .... .. ..... h [2] Find the actual length , in kilometres, of the road. Answer ........ ..... ..................... km [2] (b) The area of a lake is 5 km2 . Calculate the area, in cm2, of the lake on the map. Answer .... . ..... ........... ... ........ .. cm2 [2]

7 247 BP~243 • • • • • • • • • • • • • • • • • n7 • • g u1t1on I I I I I I I 1 hours "l 0 1 2 3 4 5 6 ' 1V 11-1,. ,~ v Lr-. f.-J"-.. \.c.Jl·. • .. _ !'! .,~ \ . . • Nurul w~nts to fin~ out the number of hours ~er friends spend on homework dail~ She earned out a sunple survey and the dot diagram above shows the result she obtamed. (a) How many students participated in the survey? An.nver ...... ............................. [ 1] (b) How many students spend less than 2 hours on homework daily? Answer ................................... [l] (c) Nurul spends 3 hour on homework daily and she concluded that this duration is above the average number of hours her friends spent. Do you agree with Nurul? Explain your answer. Ans,ver ... ................................................................................................ .. . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. [2]

BPN244 8 The sketch shows a quadratic curve with the equation y = (l - .x)(x + 5). y B X Ir,= o -x)<x + s> (a) Find the coordinates of A and B. Answer A = ( ............. , ........ ... ) [ 1] Answer B = ( ...... ....... , ........... ) [I] (b) State the equation of the line of symmetry. An.nver .................. .... ........ .... . [1] 9 A sphere has a radius r cm and total surface area of 2430 cm2. Calculate r. Answer r = ..... .. .... ....... ... .. .. .... .... [3] 248

BP-245 10 Solve these simultaneous equations. 4x+Sy=7 3x+4y = 5 Answer x = ....................................... . y = ................................... [3] l l y is connected to x by the equation y = 2 5 . X (a) Find the value y when x = 5. An.nver y = .............................................. [l] (b) "y is directly proportional to x." Do you agree with the above statement? Explain your answer. Ans1ver ..................... ........... ................. .............................................. ......................... ............. . . ............................................................................................................................................... [l] 249

12 250 ABC is a triangle and AN is perpendicular to BC. AB= 7.2 cm. AN= 4.6 cm and angle ACN= 63° . Calculate (a) BN, (b) NC, (c) the area of triangle ABC. l Answer BN = ........................................ cm [2] Answer NC= ... .................. .................. . cm [2] Answer ........................... ................ .... cm2 [2]

13 251 3.8 cm Triangle ABC is an enlargement of triangle BDC. BP-247 ABC is an isosceles triangle with AB =AC, and D is a point on AC such that BC= BD. AB= 9.5 cm and BC= 3.8 cm. (a) Given that L.CAB = 36° , find LABC. Ansl·Ver .............. ...................... .......... 0 [2] (b) State the scale factor of the enlargement. Anslver ......... ............ ............... ........... [ 1] (c) Calculate DC. Answer ............................. ................. cm [2]

BP-248 14 The histogram summarises the widths of 50 leaves collected from a garden . 252 25 lltffti) •·:.'~ •·- ~ ..\_ " . ;. , • . ; ' ,A· 20 Frcqw-.:ncy 15 5 0----------+---------------+-1► ; 4 5 Width !cm J (a) How many leaves had a width of at least 5 cm? 6 7 Ans,ver ............... ............................... [l] (b) Find the probability that a leaf chosen at random has a width of between 3 cm and 5 cm. Ansiver .................................... .......... [2] End o1f paper