ACSBR 2023 3EXP Math EYE P1

Full Name Class Index No Class Anglo-Chinese School (Barker Road) END-OF-YEAR EXAMINATION 2023 SECONDARY THREE EXPRESS MATHEMATICS 4052 PAPER 1 1 HOUR 45 MINUTES Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name on all the work you hand in. Write in dark blue or black pen. 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  , use either your calculator value or 3.142, unless the question requires the answer 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 70. This question paper consists of 16 printed pages. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 Mathematical Formulae Compound interest Total amount 1 100 n rP=+  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 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== 2 2 2 2 cosa b c bc A= + − Statistics Mean fx f=  Standard deviation 22fx fx ff  =−   

Anglo-Chinese School (Barker Road) 3 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 1 Expand and simplify ( ) 2 23xy− . Answer ___________________________ [2] 2 The first 4 terms in a sequence are 6, 10, 14, 18, … . (a) Write down an expression, in terms of n, for the nth term, Tn, of this sequence. Answer ___________________________ [1] (b) Evaluate T11. Answer ___________________________ [1] (c) Explain why Tn is always an even number, for all values of n. Answer ________________________________________________________ ________________________________________________________ ________________________________________________________ [1]

Anglo-Chinese School (Barker Road) 4 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1 3 The population of Zimbabwe was 15.99 million with a land area of 390 745 km 2 in 2021. (a) Write 15.99 million in standard form. Answer ___________________________ [1] (b) Calculate the number of people per square kilometre, correct your answer to the nearest w