2022 STC Math Prelims P2 Ans

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) Marking Scheme

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] 2 15 5 5 10 2 b a   [M1] = 6 4 4 b a [A1] 2 2 (3 5) 5 3 y yy +−− = 2 2(3 5) (3 5) yy y −− − [M1] = 22 10 5 5(2 ) or (3 5) (3 5) yy yy −− −− [A1] 2 2 3 108 2 5 42 x xx − +− = 2 3( 36) ( 6)(2 7) x xx − +− [M1] = 3( 6)( 6) ( 6)(2 7) xx xx +− +− [M1] = 3( 6) 27 x x − − [A1]

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−+  .