Dehiowita Education Zone Mathematics II Grade 10 2nd Term Test 2024 PDF

OL/2020/32/S-II ish¨u ysñlï weúßKs / KOg; gjpg;GhpikAilaJ]/ All Rights Reserved ] දෙහිඕවිට wOHdmk l,dmh 32 S II Dehiowita Educ...

OL/2020/32/S-II ish¨u ysñlï weúßKs / KOg; gjpg;GhpikAilaJ]/ All Rights Reserved ] දෙහිඕවිට wOHdmk l,dmh 32 S II Dehiowita Education Zone 10 fY%aKsh fojk jdr mÍlaIKh - 2024 2nd Term Test - 2024.Ks;h II meh ;=khs fzpjk ;II Mathematics II Three hours wu;r lshùï ld,h- ñks;a;= 10 hs Use the additional reading time to go through the question paper, Additional Reading Time – 10 minutes select the questions and decide on the questions that you give priority to in answering. Important:  Answer 10 questions selecting 5 questions from part A and five questions from part B.  When answering the questions write the steps and the units correctly.  Each question is given 10 marks Part A Answer only 05 questions. 1. The information about the income tax percentage that is levied in a certain year is given below. Annual income Income tax percentage Initial 500 000 Tax free Next 500 000 4% Next 500 000 8% Next 500 000 12% The monthly income of a certain businessman is Rs.110 000. Expect that he receives an income of Rs.280 000 as the shop rent. Find the annual income tax he needs to pay and find what percentage of his total income is paid as income tax. [see page two OL/2020/32/S-II -2- 2. Given below is an incomplete table of values prepared to draw the graph of the function 𝑦 = 𝑥 2 − 5. 𝑥 -3 -2 -1 0 1 2 3 𝑦 4 -1 -4 -4 -1 4 (i) Find the value of y when x = 0 (ii) By taking a suitable scale draw the graph of the function Using the graph, (iii) Find the range of values of x in which the function is decreasing negatively. (iv) Find the roots of the equation 𝑥 2 − 5 = 0 (v) Write down the coordinates of the turning point of the new graph obtained by shifting the above graph by 02 units upwards along the y–axis. 3. (i) Expand (3𝑎 − 2𝑏)2 (ii) Write 1032 as a square of a binomial expression and evaluate (iii) Find the least common multiple of 4𝑥 2 − 1, 3(𝑥 − 1)2 , 2𝑥 2 − 𝑥 − 1 2 1 (iv) Simplify - 2𝑥 2 −𝑥−1 4𝑥 2 −1 4. It requires 40 pieces of 12cm and 20cm long iron rods to make a Vesak lantern. The total length of iron rods that is required is 608cm. Considering that no piece of iron rod is wasted and taking the number of 12cm long pieces as 𝑥 and 20cm long pieces as 𝑦 construct a pair of simultaneous equations. By solving the equations find separately the number of 12cm long pieces and 20cm long pieces of iron rods that are required. Find separately the maximum number of 12cm long and 20cm long pieces of wire that can be cut from an iron rod of 2m long so that no piece is wasted 5. The pie chart given below represents the information on class intervals of the marks obtained by a group of students in a Mathematics test. (60 − 100) (20 − 40) 300 (0 − 20) (40 − 60) The number of students who belong to the class interval 20 – 40 is twice the number of students who belong to the class interval 40 – 60. (i) Find the angle at the center of the sector which represents the number of students who belong to the class interval 60 – 100 (ii) If the number of students who belong to the class interval 40 – 60 is 4, find the total number of students that belong to this class interval. (iii) The class interval 60 – 100 is separated into two class intervals 60 – 80 and 80 – 100. The angle at the center of the sector which represent the marks interval 80 – 100 is 45°. Find the number of students who obtained marks within the interval 60 – 80. 6. The perimeter of triangle ABD is 64cm and the area of it is 168cm2. D AB = AD = 25cm and BCD is a semicircle. (i) Find the radius of the semi-circle 𝐸 (ii) Find the total area of ABCD (iii) Calculate the length of a side of a square in which the A 𝐵 25 𝑐𝑚 area is equal to the area of ABCD to two decimal places. MAWANELLA MATHS [see page three OL/2020/32/S-II -3- Part B Answer only 05 questions. 7. ABCD given in the figure is a parallelogram. The midpoint of AB is E. BA is produced to F such that 1 AF = 2AB 𝐷 𝐶 ' 𝐹 𝐴 𝐸 𝐵 (i) Copy the above diagram to your answer sheet and mark the given data (ii) Prove that 𝐵𝐸𝐶 ∆≡ 𝐴𝐹𝐷 ∆ (iii) Prove that FECD is a parallelogram. (iv) If 𝐸𝐵̂𝐶 = 110° and 𝐹𝐷 ̂ 𝐴 = 30° find the value of 𝐷𝐶̂ 𝐸 8. 𝐴 Pipe The rate at which water flows from pipe A is 100 𝑙 per minute. The rate at which water flows from pipe B is 40 𝑙 per minute. The rate at which water flows from pipe C is 50 𝑙 per minute. 𝐶 Pipe 650 𝑙 𝐵 Pipe The figure depicts how a tank of capacity 1000 𝑙 is processed to supply water to a cultivation plot. The tap of pipe C automatically closes for a minute after it has been opened and water flows through it in this manner. When the tank is completely filled, all the taps close simultaneously. Calculate the volume of water drained from pipe B when all the taps are opened and closed again when the tank is 650 𝑙 filled initially. 9. Out of 600 students who visited the ‘Rasa Roti’ canteen of Gnanaloka University, 250 students bought roti and 280 students bought tea. 80 of them bought both roti and tea. Others did not buy any food items and spent the time talking to their friends. Copy the Venn diagram given below in to your answer script, find the number of elements belonging to each region using the given information, and write them in the relevant regions Students who Students who bought roti bought tea (i) Find the number of students who bought roti. (ii) Find the number of students who bought tea. (iii) How many students has bought only tea? (iv) Shade the region which represents the students who bought only one of the items roti or tea. (v) Show the number of students who did not buy any of these food items as a percentage of the total number of students who came to the canteen. [see page four OL/2020/32/S-II -4- 10. (i) If log 𝑥 2 = 𝑎 and log 𝑥 3 = 𝑏 write down log 𝑥 12 in terms of 𝑎 and 𝑏 (ii) Without using the logarithmic table evaluate the following expression. log10 30 + log10 20 − log10 16 (iii)Simplify using a logarithmic table. 7.45 × 12.83 8.32 11. In the following figure PQ // CB and AC = AB = AQ. 𝑃𝐴̂𝑄 = 50° and the bisector of 𝐵𝐴̂𝑄 intersects CB at D. By giving reasons find the magnitude of the following angles 𝐴 𝑄 𝑃 > 500 𝐶 > 𝐵 𝐷 (i) 𝐴𝐵̂𝐶 (ii) 𝐵𝐷̂𝐴 (iii) 𝐵𝐴̂𝐶 (iv) 𝐵𝑄̂ 𝐴 12. In the triangle ABC, AB = AC. D and E are on AC and BC such that CD = CE. Extended DE and AB are intersected at F. If DA = DF and 𝐵𝐴̂𝐶 = 𝑎, prove that 𝐴𝐶̂ 𝐵 = 3𝑎 𝐴 𝑎 𝐷 𝐶 𝐵 𝐸 𝐹 ***