2025 3E SPS EOY P2 ANS

NAME FORM CLASS ACAD CLASS INDEX NO. Answers ST. PATRICK’S SCHOOL END-OF-YEAR EXAMINATION 2025 SUBJECT : Mathematics DATE : 6 October 2025 (4052/02) LEVEL : Secondary 3 Express DURATION : 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Name, Form Class, Acad Class and Index No. in the spaces at the top of the page. 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. Answer all questions. 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  , use either your calculator value of 3.142, unless the equation requires the answer in terms of  . The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90 . For Examiner’s Use Type of Penalties Question Number 90 Presentation 1 2 This paper consists of 19 printed pages including this cover page.

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP    Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 r h Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C  2 2 2 2 cosa b c bc A   Statistics Mean = fx f   Standard deviation = 22fx fx f f          

3 Answer all questions. 1 (a) Solve the equation 2( 3) 16x  . 3 4 or 3 4 7 1 x x x x       Answer x = ...………. or ………… [ 2] (b) Simplify 2 4 6 2 9 9 x x x    . 2(2 3) (2 3)( 3) 2 3 x x x x      Answer ...….……………………. [ 2] (c) Rearrange the formula 1px x p   to make p the subject of the formula. 2 2 1 1 ( 1)( 1) (1 ) ( 1)( 1) ( 1) 1 x xp p x p xp x x p x x xp x p x                Answer p = …..……………….……. [ 3]

4 2 (a) Simplify 2 3 2 1 5 (4 ) 2 a b a b , express your answer in positive index notation. 4 6 5 5 16 2 8 a b a b a b  Answer .…………….…..… ..…….…. [2] (b) The mass of a dust particle is 7.5×10−6 kg. Find the total mass of 2×108 such particles, giving your answer in standard form. 8 6 3 2 10 7.5 10 1.5 10      Answer .……………………… …. kg [1] (c) Solve the equation 5x+1 = 25