ADSS Prelim 2025 P1 [QP]

ADMIRALTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 SUBJECT : Elementary Mathematics CODE/PAPER : 4052/01 LEVEL/STREAM : Secondary 4 Express / 5 Normal (Academic) DATE : 26 August 2025 TIME : 0800h – 1015h DURATION : 2 hours 15 minutes Instructions to candidates: 1. Write your name, class and index number. 2. Answer ALL questions. 3. Calculators should be used 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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . 4. Essential workings must be shown. Omission of essential workings and illegible handwriting will result in loss of marks. DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO. ______________________________________________________________ This question paper consists of 19 printed pages including this cover page. NAME: NO: CLASS: 90

2 Mathematical Formulae Compound Interest Total amount = nrP    + 1001 Mensuration Curved surface area of a cone = lr  Surface area of a sphere = 2 4 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle ABC = Abc sin2 1 Arc length = r  , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard Deviation = 22       −     f fx f fx

3 Answer all the questions. 1 Solve the inequality 25 142 x x+ − . Answer ..………………………… [2] 2 The population of a particular animal increased from 400 at the start of January 2023 to 620 at the start of January 2025. The population increased by x % every month. Find the value of x . Answer x = ..…………………… [2] 3 Find the smallest value of x such that the lowest common multiple (LCM) of x and 15 is 45. Answer x= ..………………….. [2] 4 The box-and-whisker plot shows information of the distribution of marks of 40 students for a Mathematics examination. (a) Use the box-and-whisker plot to find the median mark. Answer ..………………………… [1] (b) Rachel says, “Approximately 40% of the students scored 40 marks or less”. Is she correct? Give a reason for your answer. ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [1] 5 The graph shows the number of unemployed workers in Country X for the last 10 years.

4 (a) State one feature of the graph that may be misleading. ……………………………………………………………………………………… ……………………………………………………………………………………… [1] (b) Explain how this feature affects the reader’s interpretation of the graph. ……………………………………………………………………………………… ……………………………………………………………………………………… [1] 6 ABC is a triangle in which angle BAC 90o= , AC 40= cm and BC 41= cm. AB is produced to M and AC is produced to N. (a) Express sine of angle MBC as a fraction. Answer ……………. ..……..…… [1] (b) Express cosine of angle BCN as a fraction. Answer ………………..………… [1] 7 Q is 25% greater than P. R is 30% smaller than Q. What is the ratio of P : R? 0

5 Answer ..………… : …………. [2] 8 Given that 138 16bb−− = , find the value of b. Answer b = …………………… [3] 9 Simplify 2 2 (2 1) 1 2 aa aa −−− . Answer ..………………………… [3] 10 A map is drawn to a scale of 1 : 200 000. (a) Find the actual distance, in km, represented by 8 cm on the map. Answer ..…………………….. km [1] (b) A town covers an area of 600 km2. Find in, cm2, the area representing the town on the map. Answer ..……………………. cm2 [2] 11 (a) Factorise 20 4ab b− .

6 Answer ..………………………… [1] (b) Factorise completely 3 2 6xy ab ay xb− − + . Answer ..………………………… [2] 12 22khc h += (a) Find c when k = 2.81 and h = 3.67. Give your answer correct to 2 significant figures. Answer c = ..…………….……… [1] (b) Rearrange the formula to make k the subject. Answer k = ..…………….……… [2] 13 (a) The sum of three angles of a quadrilateral is 285o . Find the fourth angle. Answer ……..…..……..………o [1] (b) Each interior angle of a regular polygon is 165o . Find the number of sides of this polygon. Answer ……..…..……..………… [2]

7 14 ξ = {integers x : 3 < x < 15} A = {prime numbers} B = {multiples of 3} C = {factors of 20} (a) List the elements in ( )AC  . Answer ……..…..……..………… [1] (b) Underline the correct statements from the list below. AB = {4, 5, 7, 11 }AC= 8 C 9 B [2] 15 Simplify 4 81 26 x x − − . Answer ……...……….….………... [3] 16 (a) Express 2 54y x x= + − in the form 2()y x p q= + − . Answer ……...……….….………... [2] (b) Write down the coordinates of the minimum point of the graph of 2 54y x x= + − . Answer (……...…… , .….……….) [1]

8 17 Each term in this sequence is found by adding the same number to the previous term. a, 11, b, c, 29, … (a) Find the values of a, b, and c. Answer a = …………………… b = …………………… c = …………………… [2] (b) Write down an expression, in terms of n, for the nth term. Answer …...……………………... [1] (c) Explain why the value of every term must be odd for all values of n. Answer ………………………………………………………………………………… ………………………………………………………………………………………… [1] 18 (a) Write 0.00024 in standard form. Answer ……..…..……..………… [1] (b) The distance between the Sun and Mercury is about 45.4246 10 megametres. Given that 1 megametre 610= , express this distance in metres. Leave your answer in standard form. Answer ……..…..……..………… [1] (c) Use the laws of indices to work out 50 49(5.2 10 ) (2.0 10 ) −  . Show your working and give your answer in standard form. Answer ………………………….. [2]

9 19 The diagram shows the arcs AB and CD of two circles, centre O, with radii 4 cm and 8 cm respectively. (a) Calculate the perimeter of the shaded region. Answer …………………….. cm [2] (b) Calculate the area of the shaded region. Answer …………………….. cm2 [2]

10 20 A hexagonal central stage is designed for a concert performance. It is divided into two sections. The shaded area is a raised stage, similar to the central stage, while the remaining area is a water stage. (a) Given that AB = 2 m and CD = 3.5 m, find the value of area of raised stage area of water stage . Answer ……...……….….………... [2] (b) The area of the raised stage