AHS 2025 S4 AM Prelim P1

© Anglican High School 2025 4049/01/Prelim/25 NAME: _______________________________ ( ) CLASS: 4 ( ) 9o ADDITIONAL MATHEMATICS 4049/01 Paper 1 22 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. Additional Material: Graph Paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this 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 the 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. 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 Examiners’ Use Question Marks Question Marks Clarity / Logic 1 8 2 9 Precision / Accuracy 3 10 4 11 Units 5 12 6 13 Total: 90 7 14 Parent’s Name & Signature: Date: This paper consists of 18 printed pages. S4 ANGLICAN HIGH SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATIONS 2025

2 © Anglican High School 2025 4049/01/Prelim/25 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for Area of ! "!" #" $++ = !" ! !! " #$ " !± != ( ) !" " ### ###!" ! !! ! ! " " !!! !#$ # # $ # $ # $ $ " !! !"# "# "#+= + + + + + +$% $% $%&' &' &' ( ) ( )( )! """ !# ## # ! !! ! "! " "!" " !! +"#==$% !&' !"#$$%& '' =+ !! !! !! "#$%&'( += !!"#$%" & "#'!!=+ !"!"!" !"#$%!$%!!"#&!"#' ±=± !"#$ % !"# !"# #&' #&'!" ! " ! "±= ! !"# !"#!"#$ % & !"# !"# !"!" !" ±±= ! !"# $ $!"# %&!!! !=!!!!! !!!! "#$!%%&'"!"#$&'"!&'" !=!=!= ! !! !"#$% "#$!!"#$ ! = !"#!! " # A B C !"#!"#!"# == !"##"A !"#$$$$ !+= !"#!"# $ %=!

3 © Anglican High School 2025 4049/01/Prelim/25 [Turn over 1 (a) Find the range of values of p for which lies entirely above the line.[4] (b) Hence, deduce, without finding the discriminant, the number of intersection points when p = 3. [1] ! !!" "=! ! !" #!" #=+

4 © Anglican High School 2025 4049/01/Prelim/25 2 By using substitution or otherwise, find the values of x for which , giving your answer where appropriate, to one decimal place. [5] !" #!! ! $!!!+=!

5 © Anglican High School 2025 4049/01/Prelim/25 [Turn over 3 A closed circular cylinder has a volume of p cm3, a radius of cm and a height h cm. Express h in the form of where p and q are integers. [4] ( )!! " " #+ ( )!! "+ !"!"+

6 © Anglican High School 2025 4049/01/Prelim/25 4 Express in partial fractions. [6] !" ! ""# $ " % !!! !! !+ ! +

7 © Anglican High School 2025 4049/01/Prelim/25 [Turn over 5 Given the curve, where k is a constant. (a) By expressing y in the form , determine the value of k and of b. [3] (b) Hence, show that the curve is always below the x-axis. [2] (iii) State the turning point of the curve and determine the nature of this point. [2] !!"!" # " #=+! !"# $!" #+!

8 © Anglican High School 2025 4049/01/Prelim/25 6 The binomial expansion of where n > 0, in ascending powers of x is Find the value of p, of n and of q. [6] ( )! ! "#+ !! "# #! !$ %%%! " ! #!!+ ++

9 © Anglican High School 2025 4049/01/Prelim/25 [Turn over 7 (a) The surface area of a solid cube is increasing at . Find the rate of increase of the volume when the length of a side is 1 cm. [4] !"#! $% &'

10 © Anglican High School 2025 4049/01/Prelim/25 (b) A curve has the equation , where . Find the gradient of the curve at the point where , leaving your answer in exact form. [4] ( )!"#$ % & '!"! != ! "!!"" !!=