2022 STC Math Prelims P2

CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4048/2 Paper 2 23 August 2022 2 hours 30 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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 paper clips, highlighters, 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. Calculators should be used 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, unless the question requires the answers 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 is 100. This document consists of 25 printed pages. CHIJ ST. THERESA’S CONVENT PRELIMINARY EXAMINATION 2022 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 2 Mathematical Formulae Compound interest Total amount = P 1 100 n r+ Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 2π4 r Volume of a cone = hr 2π3 1 Volume of a sphere = 3π3 4 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== a2 = b2 + c2 − 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 3 Answer all the questions. 1 (a) Simplify 2 10 5 15 32a b −   . Answer …………………………… [2] (b) Express 2 2 (3 5) 5 3 y yy +−− as a single fraction in its simplest form. Answer …………………………… [2] (c) Simplify 2 2 3 108 2 5 42 x xx − +− . Answer …………………………… [3]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 4 (d) Solve the inequality 3 2 4 5 43 xx−+  . Answer …………………………… [2] (e) Solve the simultaneous equations. 4 3 5 6 5 2 xy xy −= + =− Answer x = ………… y = ………… [3]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 5 2 A bag contains 10 red balls and 8 green balls. Anna takes two balls from the bag, at random, without replacement. (a) Anna says that the probability that she takes one red ball and one green ball is 40 81 . Explain why Anna is wrong and provide the correct solution. ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ……………………………………………………………………………………….[2] (b) Anna puts back the two balls into the bag. n red balls are removed from the bag. The probability that she takes two green balls is 4 13 . Write down an equation to represent this information and show that it simplifies to 2 35 124 0nn− + = . [3] Answer

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 6 (c) Solve the equation 2 35 124 0nn− + = . Answer n = …..…… or …..…… [3] (d) Explain why one of the solutions in part (c) must be rejected. ………………………………………………………………………………………… ……………………………………………………………………………………… [1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 7 3 A, B, C and D are four points on horizontal ground. The points are connected by straight paths AB, BC, BD, AD and DC. C is due east of D. AB = 350 m, AD = 500 m and BC = 1060 m. Angle BAD = 85° and angle BDC = 103°. (a) Show that BD = 585 m, correct to 3 significant figures. [3] Answer North 85 103 A D B C 350 m 500 m 1060 m

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 8 (b) Calculate the bearing of B from C. Answer …………………  [3] (c) John is a Grab delivery partner. He cycles at an average speed of 12 km/h. He starts at point C, cycles along path CB to collect food at point B then path BA to collect food at point A, and delivers the food collected to point D. He spends 5 minutes to collect the food at each collection point. Calculate the time it takes him to complete the food delivery. Give your answer in minutes and seconds. Answer ………… minutes ………… seconds [3]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 9 4 ABCD is a trapezium with AB parallel to CD. A is the point (−1, 3) and B is the point (7, 9). 1 7AD =− . (a) Find the length of the line AB. Answer …………………………… [2] (b) Find the equation of the line CD. Answer …………………………… [4]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 2 10 (c) X is the point on AB such that area of triangle 1 area of traingle 3 AXD BXD = . (i) Find AX . Answer AX =   [2] (ii) Find the position vector of X. Answer OX =   [1]