Ngee Ann Secondary 2025 Sec 2 EOY Mathematics

Name: ................................................................ Register no: ............... Class: ........... NGEE ANN SECONDARY SCHOOL G3 SECONDARY TWO END-OF-YEAR EXAMINATION MATHEMATICS 24 September 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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. 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 90. 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 or 3.142. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 19 printed pages and 1 blank page.

Mathematical Formulae Geometry and Measurement Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of a triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry C c B b A a sinsinsin == 2 2 2 2 cosa b c bc A= + − Statistics Mean = f fx   Standard deviation = 22fx fx ff  − 

Answer all the questions. 1 Expand and simplify ( ) ( ) 2 23 2 4 1 3x y x− − + . Answer .………………………................ [3] 2 (a) Factorise 26 15xx+− . Answer .………………………................ [1] Hence, simplify the algebraic expression 2 2 6 15 7(4 9) xx x +− − . Answer …………………………............. [2] (b)

3 A bag contains 18 coloured balls, of which 6 are red, 4 are yellow and the rest are purple. A ball is chosen at random from the bag. (a) Find the probability that either a red or yellow ball is chosen. Answer …………………………............. [1] (b) x red balls are added into the bag such that the probability of choosing a red ball becomes 2 5 . Find the value of x. Answer x = ……………………………... [3] Solve 3x− 5 2 x . Answer …………………………….. [2] (b) Represent the solution in (a) on the number line. [1] (c) Hence, state the smallest integer that satisfies the inequality 3x− 5 2 x Answer …….............................................. [1] 4 (a)

5 Rearrange the formula 24 5nm−= to make m the subject. Answer m =……………………............... [3] 6 The time taken (T minutes) to fill up a swimming pool is inversely proportional to the number of water pipes (N) used. 6 water pipes take 25 minutes to fill up the swimming pool. Find (a) an equation connecting N and T, Answer …………………………............. [2] (b) the extra amount of time needed to fill the swimming pool if two pipes are faulty and not working. Answer …………………………… mins [2]

7 The stem-and-leaf diagram shows the monthly savings of 20 students. Stem Leaf 0 2 3 4 8 1 1 2 4 4 5 2 0 1 1 4 3 1 4 6 7 9 4 2 5 (a) Find the median monthly savings. Answer $ ……………………………….. [2] (b) One of the students claims that the only modal amount students saved was $21. Is the student correct? Explain your answer. Answer …………………….................................................................................. ............................................................................................................................... ............................................................................................................................... 32 41 xx−−+ can be written as a single fraction in the form ( ) ( )( )41 a x b xx + −+ . Find the value of a and of b. Answer a = …..………, b = …………… [3] Key 1|1 means $11 8 [1]

9 The diagram shows two similar triangles ABC and XYZ. Angle 85BAC= , angle 2 26ABC y= −  and angle XYZ y= . AC = 10 cm, XZ = 7 cm, BY = 12 cm and CZ = 6 cm. Find (a) the value of y, Answer y =……………………................ [1] (b) the length of YC. Answer YC =………………………....cm [2]

10 In the figure below, triangle PQR is congruent to triangle SPM . PM = 11 cm, RM = 12.2cm and ST = 18.4 cm. Angle 75PQR= and angle 29PSM = . Find (a) the length of TM, Answer ……………………………... cm [2] (b) angle PRQ , Answer Angle PRQ= ………………… [1] (c) angle QTS . Answer Angle QTS = …………………. [2] (d) Is QR parallel to SM ? Explain your answer. Answer ………………………………………………………………………………………… ……………………………………………………………………………………… ………………………………………………………………………………………. [2] M Q P T S 11 12.2 18.4 75° 29° R

11 The diagram shows 2 strings, TM and TN, attached to the top of a building at point T. TM and TN make angles of 57 and 50 with the horizontal ground respectively. The building is y m tall, and the foot of the building is x m from M. (a) Express tan 57 in terms of x and y. Answer tan 57 = ……………………… [1] (b) Express tan 50 in terms of x and y. Answer tan 50 = ……………………… [1] (c) Using the results in parts (a) and (b), show that tan 57 tan 50 4 tan 50xx = +  Answer (d) Hence, find the height of the building. [1] Answer …………………………………… m [2]

12 The number of goals scored by a soccer team is recorded. Goals scored 0 1 2 3 4 5 Frequency 2 5 x 12 4 2 (a) If the mode is 3, find the largest possible value of x. Answer x = ……………………............... [1] (b) Find the value of x if the mean number of goals is 2.5. Answer x =……………………................ [2] 13 y is directly proportional to the square of t. When t = 6, y = 4. (a) Find an equation connecting y and t. Answer …………………………............. [2] (b) When t = 12, find (i) the value of y, Answer y = ……………………............... [1] (ii) the percentage increase in y if this value of t is increased by 50%. Answer ………………………………..% [2]