CHIJ STC 2024 Math Prelim P1 solutions

CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/1 Paper 1 26 August 2024 2 hours 15 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 for this paper is 90. This document consists of 21 printed pages. CHIJ ST. THERESA’S CONVENT PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 2 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) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 3 Answer all the questions. 1 Calculate 5 326.4 14.8 4.6 3 24 +−  . Answer …………………….………… [1] 2 (a) Given that 6sin 5x= , find the two possible values for angle x, where 0 x 180 Answer x = ……………… or ……………… [2] (b) Convert 138 into radians. Answer ………………………… radians [1] 3 Solve 4 32x = . Answer x = ………….….……….……… [2] oo 6sin 5 5sin 6 56.4 or 123.6 (1 d.p.) x x x = = = 0.159 (3 s.f.) π138 138 2.41 rad (3 s.f.)180=   5 2 2 4 32 22 52 2 5 4 x x x x = = = =

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 4 4 Simplify (a) ( )5 2 4 3 x−− , Answer ……………………..………… [1] (b) 2 3 3 6 27x y −   . Answer ………………………………… [2] 5 A