NBSS EM 2024 Prelim P2 QP

1 [Turn over NAVAL BASE SECONDARY SCHOOL PRELIMINARY EXAMINATION, 2024 O Name ( ) Class MATHEMATICS 4052/02 Paper 2 22 August 2024 Candidates answer on the Question Paper. 2 hour 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. Item For examiner’s use Presentation Accuracy Units Total Parent’s Signature This paper consists of 25 printed pages and 3 blank pages. [Turn over

2 [Turn over Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of a triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = 22        −  f fx f fx rl 24 r hr 2 3 1  3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == Abccba cos2222 −+=   f fx

3 [Turn over Answer all the questions. 1 (a) Solve 23 654 xx −+ = − . Answer x = …………………………………… [2] (b) Simplify ( ) ( ) 2 2 3 3 10 p q q p rr −−  . Answer ………………………………………. [2]

4 [Turn over (c) Solve the inequality 7 2 5 191 45 xxx −++   . Answer ………………………………………. [3] (d) Simplify 2 2 2 7 9 4 81 yy y +− − . Answer ………………………………………. [3]

5 [Turn over 2 (a) Cheryl wants to open a fixed deposit account with either Bank H or Bank L for a period of 4 years. The following are the promotions offered by the two banks. Bank H Bank L Fixed Deposit Account • Minimum deposit of $10 000. • For the first $10 000, earn 0.05% simple interest per annum. • For the subsequent amount, earn 0.95% simple interest per annum. Fixed Deposit Account • No minimum amount required. • Compound interest at the rate of 0.8% per annum. (i) Cheryl deposited $30 000 into Bank H. Calculate the total amount in her account after 4 years.