Dunman 2026 Prelim 4E5N A Maths P1

This document consists of 19 printed pages and 1 blank page. DUNMAN SECONDARY SCHOOL CANDIDATE NAME CLASS INDEX NUMBER PRELIMINARY EXAMINATION 2026 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/01 Paper 1 19 August 2026 2 hours 15 minutes Candidates answer on the Question Paper. READ 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 90. Calculator Model Total Marks

2 4049/01/PRELIM/4EXP/2026 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion ( ) 1 2 2 ... ...12 n n n n n r r nn n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ( ) ( ) ( )1 ... 1! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cosec 1 cotAA=+ ( )sin sin cos cos sinA B A B A B =  ( )cos cos cos sin sinA B A B A B=  ( ) tan tantan 1 tan tan ABAB AB =  sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formula for  ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + −  = 1 sin2 bc A

3 4049/01/PRELIM/4EXP/2026 [Turn over 1 Express ( ) ( ) 2 2 2 3 8 21 xx xx −− +− in partial fractions. [5]

4 4049/01/PRELIM/4EXP/2026 2 Solve the equation ( )3 9 9log 2log 3 log 4xx− = + . [5]

5 4049/01/PRELIM/4EXP/2026 [Turn over 3 Prove that ( ) 2 2 1 sin 2 tan 1cos x xx − =− . [4]

6 4049/01/PRELIM/4EXP/2026 4 A school started a weekly Math Café. In Week 1, 60 students attend the session. From Week 2 onwards, the attendance increases by 10% from that of the previous week. The venue can hold up to 150 students. If the attendance exceeds 1 50 students in a particular week, the Math Café is moved to a larger venue from the following week onwards. Determine the week in which the attendance first exceeds 150 students. [4]

7 4049/01/PRELIM/4EXP/2026 [Turn over 5 The line 3yx− =− cuts the curve 22 19x xy y− + = at the points A and B. Find the x-coordinates of these two points. [4]

8 4049/01/PRELIM/4EXP/2026 6 A right pyramid has a square base with diagonal 28+ cm. The volume of the pyramid is 10 6 2+ cm3. Without using a calculator, (a) show that the area, in cm2, of the square base is 6 4 2+ , [3] (b) find the height, in cm, of the pyramid in the form 2cd+ , where c and d are integers. [4]

9 4049/01/PRELIM/4EXP/2026 [Turn over 7 (a) Find ( ) 3d ed xxx . [2] (b) Hence find 3e dxxx . [4]

10 4049/01/PRELIM/4EXP/2026 8 A company manufactures open-top rectangular plastic storage boxes, each with a square base of side x cm and height of h cm. Each storage box has an external surface area of 432 cm2. (a) Show that the volume of the storage box is 3432 4 xx− cm3. [3] (b) Given that x can vary, find the value of x for which the volume is stationary and determine its nature. [4]