GMSS 4NA EM P1 Prelim 2024 Ans key

Candidate Name ANSWER KEY Class Index Number MATHEMATICS (SYLLABUS A) Paper 1 4045 / 01 4 Normal (Academic) Candidates answer on the Question Paper. 2 hours Setter: Ms Tan Kai Wei Monday, 5 August 2024 READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. 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 70. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. For Examiner’s Use This document consists of 18 printed pages and 2 blank pages. Geylang Methodist School (Secondary) Preliminary Examination 2024 70 [Turn Over

GMS(S)/EMath/P1/PRELIM2024/4N(A) 2 [Turn Over Mathematical Formulae Compound Interest n rP       1001amount Total Mensuration rl cone a of area Surface Curved 24 sphere a of area Surface r hr 2 3 1 cone a of Volume  3 3 4 sphere a of Volume r CabABC sin2 1 triangleof Area  radiansin is where,length Arc r radiansin is where,2 1 areaSector 2 r Trigonometry C c B b A a sinsinsin  Abccba cos2222  Statistics f fx  Mean 22 deviation Standard          f fx f fx

GMS(S)/EMath/P1/PRELIM2024/4N(A) 3 [Turn Over Answer all the questions. 1 (a) Write 0.005 625 819 correct to 4 significant figures. Ans: 0.005626 (4sf) Answer ……………..…………. [1] (b) Express 338 as a percentage. Ans: 337.5% Answer ……………..………… % [1] 2 Find the smallest integer satisfying the inequality 3 17x . 3 17x 25 3x [M1] Smallest integer = 5 [A1] Answer ……………..…………. [2] 3 (a) sin 0.6x Given that x is an obtuse angle, find x. sin 0.6x 1sin 0.6x  36.9 or 143.1 (1dp)   Since x is an obtuse angle, 143.1x . [B1] Answer x = …………..…………. [1] (b) cos135 cos y  Given that y is an acute angle, find y. 180 135y   45  y = 45 [B1] Answer y = …………..…………. [1]

GMS(S)/EMath/P1/PRELIM2024/4N(A) 4 [Turn Over 4 [B1 for 2 correct lines drawn x2] Draw an enlargement of this pentagon using a scale factor of 2. [2] 5 The first 5 terms of a number sequence are 5, 9, 13, 17, 21, … (a) Find an expression for the nth term of the sequence. nth term = 4n + 1 [B1] Answer ……………..…………. [1] (b) Find the 30th term. 30th term = 4(30) + 1 = 121 [B1] Answer ……………..…………. [1] (c) The pth term in the sequence is 249. Find p. 4 1 249n  [M1 – ECF from (a)] 4 248n 62n [A1] Answer p = ………. ..…………. [2]

GMS(S)/EMath/P1/PRELIM2024/4N(A) 5 [Turn Over 6 (a) Express 2 2 3 3 9x x   as a single fraction in its simplest form. 2 2 3 3 9x x   2 3 3 ( 3)( 3)x x x    [M1 for showing ( 3)( 3)x x  ] 2( 3) 3 ( 3)( 3) ( 3)( 3) x x x x x      2 6 3 ( 3)( 3) ( 3)( 3) x x x x x      [M1 for showing 2 6x ] 2 6 3 ( 3)( 3) x x x     2 3 ( 3)( 3) x x x    [A1] Answer ……………..…………. [3] (b) Rearrange the formula to make z the subject. 25 2x y z  25 2x y z  22 5z x y  [M1 for having 2z2 on one side] 2 5 2 x yz  5 2 x yz  [A1 including  ] Answer z = ………...…………. [2]

GMS(S)/EMath/P1/PRELIM2024/4N(A) 6 [Turn Over 7 Triangle ABC is similar to triangle XYZ. (a) Find the value of angle XYZ. 25XYZ ABC    [B1] Answer Angle XYZ = ………...…………. [1] (b) Find the value of XY. XY XZ AB AC 8 15 10 XY  [M1 or M1 awarded for finding scale factor] 10 120XY  12XY  [A1] Answer XY = ……… ………… ...…………. [2] A B C 10 cm 15 cm 35 X Y Z 25 8 cm

GMS(S)/EMath/P1/PRELIM2024/4N(A) 7 [Turn Over 8 Given that a : b = 7 : 5 and b : c = 1 1:3 2 , find a : c. b : c = 1 1:3 2 2 : 3 [M1 – converting ratio in fraction to integer] 10 :15 a : b = 7 : 5 = 14 : 10 a : c = 14 : 15 [A1] Answer ………… : ..…………. [2] 9 Factorise. (a) 315 3x x 315 3x x 23 (5 1)x x  [B1] Answer ……………..…………. [1] (b) 22 6y y  22 6y y  (2 3)( 2)y y   [B1 for each bracket x2] Answer ……………..…………. [2]

GMS(S)/EMath/P1/PRELIM2024/4N(A) 8 [Turn Over 10 The chart below shows the number of books read by each student in a year. Jane Alex Revo Faris Hayd Key: represents 20 books. (a) Who reads the most number of books? Faris [B1] Answer ……………..…………. [1] (b) Express the number of books Alex read, as a fraction of the number of books Faris read. 2 7 [B1] Answer ……………..…………. [1] (c) Explain one limitation of using pictogram to represent data. Answer It may lead to misinterpretation of data as it is difficult to represent data which are not multiples of 20. [B1] [1]

GMS(S)/EMath/P1/PRELIM2024/4N(A) 9 [Turn Over 11 A stadium is made up of one rectangle and two semi-circles as shown. The ratio of the length to the breadth of the rectangle is 5 : 3. The length of rectangle is 110 m. Calculate the area of the stadium. Breadth = 110 35  = 66m [M1] Radius = 33m Area of 2 semi-circles = 212 (33)2    = 1089 m2 [M1] Area of rectangle = 110 66 = 7260 m2 Total area = 1089 + 7260 = 10681.1944 = 10700 m2 [A1] Answer ……………..…………m 2 [3] 110

GMS(S)/EMath/P1/PRELIM2024/4N(A) 10 [Turn Over 12 ABCDE is a regular pentagon. Calculate angle BEC. Regular pentagon  all sides equal & all interior angles equal Each interior angle [(5 2) 180 ] 5     108  [M1] Triangle ABE and DEC are exactly the same and both are isosceles triangles. angle ABE = angle DEC (180 108) 2   36  [M1] angle BEC 108 36 36   36  [A1] Answer Angle BEC = ……………..………… [3] A B C D E