PRSS 2021 Sec 4E5N Prelim AM P2(1)

3 PRSS_2021_Prelim_4E5N_AMaths_P2 Answer all the questions 1 The right angled triangle PQR is such that its height, PQ is cm and the area is . Without using a calculator, find (a) the base, QR, in cm in the form of , where a and b are integers. [4]

4 PRSS_2021_Prelim_4E5N_AMaths_P2 (b) in expression, in cm2, for PR2 in the form of , where c and d are integers. [3]

5 PRSS_2021_Prelim_4E5N_AMaths_P2 2 (a) (i) Find the range of values of for which for all real values of . [3] (ii) Hence, explain the significance of the answer. [1]

6 PRSS_2021_Prelim_4E5N_AMaths_P2 (b) A cup of hot milo was left in a room to cool. The temperature at time t minutes is given by , where P and k are constants. It is given that when , , and when , . (i) Find the values of P and k. [3] (ii) Find the time t when . [2]

7 PRSS_2021_Prelim_4E5N_AMaths_P2 (iii) Explain why the minimum temperature of the cup of milo is if the cup of milo is left in the room for a very long time. [2]

8 PRSS_2021_Prelim_4E5N_AMaths_P2 3 (a) The mass, m grams, of a piece of radioactive element X after t days is recorded in the following table. t 2 4 6 8 m 5.47 3.74 2.56 1.75 (i) On the grid on page 9, by plotting ln m against t, draw a straight line to illustrate this data. [3] (ii) Use your graph to estimate the time when m is 5. [2] It is known that the correct formula connecting t and m is where B and g are constants. (iii) Use your graph to estimate values of B and g. [3]

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11 PRSS_2021_Prelim_4E5N_AMaths_P2 (b) The variables x and y are related by the equation , where a and b are constants. Explain clearly how the values of a and b could be obtained by plotting a straight line using values of x and y. [3]

12 PRSS_2021_Prelim_4E5N_AMaths_P2 4 (a) Without using a calculator, show that cosec2 75 can be expressed in the form of where a and b are both integers. [3]