Tkgs 2026 Sec 4 T2 WA Question Paper

TANJONG KATONG GIRLS’ SCHOOL WEIGHTED ASSESSMENT TWO SECONDARY FOUR CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052 Term 2 Week 5 2026 Candidates answer on the Question Paper. 40 minutes READ THESE INSTRUCTIONS FIRST Write your index number and name on all the work you hand in. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 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 30. This document consists of 10 printed pages. For Examiner’s use

Tanjong Katong Girls’ School 2 4052/S4WA2/2026 Mathematical Formulae Compound interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of 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 sin sin sin == Acbcba cos 2 222 −+= Statistics Mean = f fx   Standard deviation = 22fx fx ff  − 

Tanjong Katong Girls’ School [Turn over 3 4052/S4WA2/2026 1 (a) Show that   3 4 8 3 6433 x y x y   . [1] (b) Hence, simplify   1 63 2484 8 813 xxy y             and leave your answer in positive index form. Answer ……………………………… [2] 2 Mandy deposited $150 000 in a 5-year investment plan. For the first two years, it offers a simple interest rate of 4% per annum. After two years, the accumulated sum will enjoy a compound interest of 5% per annum, compounded quarterly for 3 years. Show that the amount of interest she will receive at the end of 5 years is about $38 000 (rounded to the nearest thousand). [4]

Tanjong Katong Girls’ School 4 4052/S4WA2/2026 3 The diagram shows the positions of the points X, P and Q where 4 2PQ =  is represented in the grid below. (a) Y is the point such that PQXY is a parallelogram. (i) Mark and label the point Y on the grid above. [1] (ii) Express PY  as a column vector. Answer PY  =………………………… [1] (b) Find QX  . Leave your answer in 2 significant figures. Answer QX  =………………..… units [1] Q X P

Tanjong Katong Girls’ School [Turn over 5 4052/S4WA2/2026 4 (a) Two fair dice with sides numbered 1 to 6 are thrown at the same time. Find the probability that both dice show the same number. Answer ……………………………… [1] 4 (b) The table below shows the results of a survey in which 60 students were asked whether they played video games every day during the school holidays and whether they had trouble sleeping at night. Played video games Daily Not daily Trouble sleeping 46 2 No trouble sleeping 8 4 Two students were selected at random from the whole group of students. Find the probability that (i) at least one student had trouble sleeping at night. Answer ……………………………… [2] (ii) neither of them played video games daily nor had trouble sleeping. Answer ……………………………… [1]

Tanjong Katong Girls’ School 6 4052/S4WA2/2026 5 A little girl has 9 coins in her pocket. She has one 10-cent coin, two 50-cent coins and six $1 coins. To pay for a drink which costs $1.50, she randomly takes out a coin from her pocket. If the coin is a 10-cent coin, it is put back into the pocket. Then, she takes out the next coin. (a) Complete the Tree Diagram. [1] (b) Given that the first coin is a 50-cent coin, find the probability that the second coin is a $1-coin. Answer ……………………………… [1] (c) Find the probability that she will have enough to pay for her drink after randomly taking out a coin twice. Answer ……………………………… [2] 1st coin 2nd coin 10-cent 10-cent 50-cent 50-cent 10-cent $1 1 8 5 8 ( ) 2 3 1 8 $1 1 9 2 9 2 3 ( ) 50-cent 50-cent 10-cent $1 $1 1 8 3 4 1 4

Tanjong Katong Girls’ School [Turn over 7 4052/S4WA2/2026 6 On a weekday, 180 cars travelled passed a certain point on a street. The speed of each car was recorded. The cumulative frequency curve below shows the speed, x km/h, and the number of cars whose speed is less than or equal to x km/h. Speed, x (km/h)

Tanjong Katong Girls’ School 8 4052/S4WA2/2026 (a) Given the following frequency table, calculate an estimate of the mean and standard deviation. Speed (x km/h) 35 40x  40 45x  45 50x  50 55x  55 60x  60 65x  Frequency 16 24 44 60 28 8 Answer Mean=………………km/h [1] Standard deviation = ………………..…km/h [1] (b) Use the curve to estimate (i) the median speed, Answer …………………………km/h [1] (ii) the interquartile range. Answer …………………………km/h [1] (c) The kth percentile speed is 47 km/h. Write down the value of k. Answer k = …………………………… [1] (d) A car is picked at random from the 180 cars. The probability that the car travels more than y km/h is 7 15 . Find y. Answer y = …………………………… [2]

Tanjong Katong Girls’ School [Turn over 9 4052/S4WA2/2026 (c) On a weekend, another 180 cars travelled passed the same point on the street. The speed of each car was recorded. The box-and-whisker plot below shows the speed of the cars on the weekend. (i) Draw the box-and-whisker plot on the same grid below to illustrate the speeds of 180 cars on the weekday. [2] (ii) Make one comment comparing the speeds of the cars on the weekday and the weekend. Answer ………………………………………………………………………………………. ………………………………………………………………………………………. ……………………………………………………………………………….……[1] (iii) If the speed of one car was incorrectly recorded and its speed was updated to 90 km/h in the dataset collected on the weekday, which of the value(s) in the five-number summary of the box-and-whisker plot will change? Based on the change(s), describe briefly what will happen to the lengths of the whiskers and the length of the box. Answer ………………………………………………………………………………………. ……………………………………………………………………………………[1] Speed (x km/h) weekday weekend 30

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