Ahmad Ibrahim E Math Prelim 2023 with ANS

BP-3 AHMAD IBRAHIM SECONDARY SCHOOL GCE O-LEVEL PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS Name: Class: Register No.: MATHEMATICS Paper'1 Candidates answer on the Question Paper. 4052t01 1 August 2023 2 hours 15 minutes REAO 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. 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 number of marks for this paper is 90. For Examiner's Use /90 PartnerlnLeaming ,| Answer all questions. lf working is needed for any questions 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. lf 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 n, use either your calculator value or 3.142, unless the question requires the answer in terms of fi.

BP.5 I Calculate -10.53 4 8-Jre Answer all the questions. and correct your answer to 2 significant figures. Answer tll 2 Solve the eo*tion 3'-5-t=3.'46 Answer x:....... tzl 3 (a) Express 4680 as a product of its prime factors, giving your answers in index notation. Answer tll (b) The HCF and LCM of 120 and ln are 12 and 4680 respectively. Given that 12=22 x3,findthe value of z. Answer m ...... ............. t2l PartnerlnLeaming 3

BP-6 4 Evaruate [,-iX,-iI l\-- --: l- leavins vour answer as a fraction. 100 /'r-l),s) x ,l Answer tzl 5 (e) Express -.r2 +5x-7 inthe form -(x+ p)' +q . Answer O) Hence explain why there is no real solution for -x'z +5x-7 --O . Answer t2l t1l PartnerlnLeaming 4

BP-7 6 A P B PA and PB are targents to a circle, centre O. Show that triangLe AOP arLdtrrargle BOP are congnrent. Give a reason for each statement you make. Answer I2l PartnerlnLeaming 5

BP-8 7 P is directly proportional to the cube of Q. P is increased by 700%. Calculate the percentage change in p. Answer %t2) 8 A ffi of grass grows approximately 70 picometre in 1 millisecond. Estimate how much the same tuft of grass will grow in I second. Express your answer in metes expressed in standard form. [pico = l0 -12] Answer ..........................m [2] PartnerlnLeaming o

BP-9 9 Number of new BubbleTV subscribers in March and April 2023 l0 March April State one feahre of the bar graph that may be misteading and explain how this may lead to a misinterpretation. Answ* ........,.. l2l l0 Given that .r=9 is a solution of the equation 7(x'z+3*:-+5)=(l-&)x-1, find the value of [. Answer k=.....,. ............... t2l PartnerlnLeaming 7 9(] Numberofnew Soc subscribers 700 60(

BP"IO l l Simnlifo l\am - 4n- 5m +l2an 8n2 *6mn-5m2 Answer t3l 12 Forreal numbers x,yandz,it is given that x =Z=1, and y* z.yzx (a) Show that x+y+z--0. Answer (b) 't) Find the value of x for ' - ' =12 . x y+z t2) Answer x t2) PartnerlnLeaming 8

BP-11 13 (a) Solve the inequalities 5-4x <2x +1< x+8. Answer O) Represent the solution on the number line Answer (c) Write down the smallest prime number that satisfies 5-4x<2x+l<x+8 l2l t1l PartnerlnLeaming o Answer .............................tI1

BP-12 14 The diagram shows the plan of a neighbourhood pl ay arca ABCD tn the shape of a quadrilateral. It is drawn to a scale of 1 centimetre represent I kilometre. D A sandy court is located in the play area, nearer to D than to I and nearer to CD than to lD. Shade and label the region S, where the sandy court is to be located- t3l PartnerlnLeaming 10 C DA

BP-13 15 Coffee beans are packed in bags of250 g and 750 g. The number of250 g bags and 750 g bags are in the ratio I : 2. When two ofthe 750 g bags are repacked into 250 g bags, the ratio becomes 5 : 3, (a) Find the original number of 250 g bags. Answer (b) Find the total mass ofthe coffee beans in kilograms. t3l Answer ke Il 16 P and Q are two end points of a diameter of a circle with cenhe C. The coordinate ofP is (-1, 5). The coordinate of C is (3, 6), (a) Find the length ofthe diameter ofthe circle. Answer (b) Find the gradient of PQ. t2l PartnerlnLeaming 11 Answer l2l