Revision Worksheet Mathematics PDF

The Shriram Millennium School, Noida Class: VIII Revision Worksheet: Final Examination Subject: Mathematics Syllabus–Topics Ch 2 - Exponents Ch 9 - Interest Ch 10 - Direct and inverse variation Ch 12 – Identities Ch 1...

The Shriram Millennium School, Noida Class: VIII Revision Worksheet: Final Examination Subject: Mathematics Syllabus–Topics Ch 2 - Exponents Ch 9 - Interest Ch 10 - Direct and inverse variation Ch 12 – Identities Ch 13 - Factorisation Ch 14 - Linear equations in one variable Ch 21 - Area of a trapezium and a polygon Ch 22 - Surface area, volume and capacity Ch 23 - Data handling Ch 24 - Probability Do workbook page number 27,28,29 and 30. Solve the following questions given below: 1. A die is thrown once. Find the probability of getting: (i) an even number (ii) a multiple of 3 (iii) not a multiple of 3 2. Two coins are tossed together. Find the probability of getting: (i) Exactly one tail (ii) At least one head (iii) No head (iv) At most one head 3. The shoppers who come to a departmental store are marked as: man(M), woman(W), boy(B) or girl(G). the following list gives the shoppers who came during the first hour in the morning. WWWGBWWMGGMMWWWWGBMWBGGMWWMMWW WMWBWGMWWWWGWMMWWMWGWMGWMMBGGW Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it. 4. Find the difference between the simple interest and the compound interest on ₹5000 for 2 years at 9% per annum. 5. Calculate the amount and compound interest on ₹10000 for 3 years at 9%p.a. 6. The sum of two numbers is 11 and their difference is 5. Find the numbers. 2 7. The breadth of a rectangular garden is 3 of its length. If its perimeter is 40 m, find its dimensions. VIII/ Math /2024-25 Page 1 of 4  8. Look at the bar graph given below and answer the following questions: (i) What does the bar graph show? (ii) In which subject is the student very poor? (iii) If maximum marks in each subject be 100, what is the average of his marks? (iv) On the basis of marks obtained, find the subject in which the student has special interest. 9. The diagram shows the sizes of the two equal angles in an isosceles triangle. (i) Write an equation to represent the situation (ii) Solve your equation to find the value of 𝑥. (iii) Work out the size of all three of the angles in the triangle. 10. Solve the following equations: 6𝑥+1 7𝑥−3 (i) 2 +1= 3 1 7 (ii) − = 35 10 𝑥 (iii) (𝑥 + 2)(𝑥 + 3) + (𝑥 − 3)(𝑥 − 2) − 2𝑥(𝑥 + 1) = 0 11. The ages of A and B are in the ratio 7:5. Ten years hence, the ratio of their ages will be 9:7. Find their present ages. 1 1 1 12. If 3𝑥 − 3𝑥 = 5, find: (i) 9𝑥 2 + 9𝑥 2 (ii) 81𝑥 4 + 81𝑥4 13. Find 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎, if 𝑎 + 𝑏 + 𝑐 = 9 and 𝑎2 + 𝑏 2 + 𝑐 2 = 29 14. Factorise the following completely: (i) 2𝑎3 − 50𝑎 (ii) 𝑎2 − 23𝑎 + 42 (iii) 𝑚 − 1 − (𝑚 − 1)2 + 𝑎𝑚 − 𝑎 (iv) 12(𝑎 + 𝑏)2 − (𝑎 + 𝑏) − 35 15. If 15 men can complete a piece of work in 50 days. How many days will be required to complete the work if 30 men work together? 16. A can do a bit of work in 8 days, which B alone can do in 10 days in how long. In how long both cooperating can do it? 17. Find he radius and the area of a circle whose circumference is 132 cm. VIII/ Math /2024-25 Page 2 of 4  18. The diagonals of a rhombus are 16cm and 12cm; find (i) its area (ii) length of its side 19. A parallelogram has sides 20 cm and 30cm. if the distance between its shorter side is 15cm, find the distance between its longer sides. 20. The total surface area of a cube is 216 𝑐𝑚2. Find its volume. 21. How many 3 cm cubes can be cut from a cuboid measuring 18cm X 12cm X 9cm? 22. The sum of the radius and the height of a cylinder is 37cm and the total surface area of the cylinder is 1628𝑐𝑚2. Find the height and the volume of the cylinder. 23. Evaluate using identities: 1812 − 912 24. Find the amount and the C.I. on ₹12,000 in one year at 10% per annum compounded half- yearly. 25. The cost of 15 pens is 375. Find how many pens can be bought for ₹800. 26. In a fort, 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate? 27. Find 𝑛 so that 811 ÷ 85 = 8−3 × 82𝑛−1 1 −2 1 −2 1 −2 28. Evaluate: (i) [(4) + (3) ] ÷ (5) (ii) (80 + 2−1 ) × 32 29. A survey was done on students (boys and girls) at Star High school about their favourite subject in high school. The results are shown in the double bar graph below. Use the double bar graph to interpret the following information: a) What subject is the most favourite of boys and of girls at this high school? b) Name the two subjects that are liked by girls more than boys? c) How many more boys than girls like Math as their favourite subject? d) Find the percentage of girls who like Physics as their favourite subject. 30. Choose the correct option for the following questions: (i) In a throw of a coin, the probability of getting a head is? (a) 1 1 (c) 2 1 (b) 4 (d) 2 (ii) Linear equation in one variable has _________ (a) Only one variable with (c) Only one variable with any power power 1 (b) Only one term with a (d) Only constant term variable 5 7 (iii) The value of 𝑥 for 𝑥 − 𝑥−4 𝑖𝑠 (a) 𝑥 = −10 (c) 𝑥 = 39 (b) 𝑥 = 10 (d) 𝑥 = 2 VIII/ Math /2024-25 Page 3 of 4  (iv) Assertion (A): The simple interest of ₹500 at the rate of 5% is ₹100. This interest is of the time 2 years. 𝑆𝑖𝑚𝑝𝑙𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 ×100 Reason (R): Interest Rate = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 ×𝑇𝑖𝑚𝑒 (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true (v) Assertion (A): If the diagonals of a rhombus are 8 cm and 12 cm, then the area of rhombus is given by 96 cm2. 1 Reason (R): Area of rhombus is 2 × 𝑑1 × 𝑑2 , where 𝑑1 𝑎𝑛𝑑 𝑑2 are lengths of the diagonals. (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true (vi) Statement 1: The area of a trapezium increases linearly as the height increases, assuming the parallel sides remain constant. Statement 2: The height is directly proportional to the area of the trapezium. (a) Both Statement 1 and Statement 2 are true (b) Both Statement 1 and Statement 2 are false (c) Statement 1 is true, but Statement 2 is false (d) Statement 1 is false, but Statement 2 is true (vii) Which of the following is not a case of direct variation? (a) Number of sheets are increased when their total weight is increased. (b) More quantity of petrol is required to travel more distance with a fixed speed. (c) More fees would be collected if number of students increased in a class. (d) Time taken will be less if number of workers are increased to complete the same work. (viii) In how many years will a sum of ₹3,000 yield a simple interest of ₹1,080 at 12% per annum? (a) 3 years (c) 2 years 1 1 (b) 2 2 years (d) 3 2 years (ix) The factors of 𝑎2 + 𝑏 − 𝑎𝑏 − 𝑎 are: (a) (𝑎 − 1)(𝑎 − 𝑏) (c) (𝑎 + 𝑏)(𝑎 − 1) (b) (𝑎 + 1)(𝑎 − 𝑏) (d) (𝑎 + 𝑏)2 (x) The expansion of (2𝑞 − 3𝑝)2 : (a) 4𝑞 2 + 12 𝑝𝑞 + 9𝑝2 (c) 4𝑞 2 − 6 𝑝𝑞 + 9𝑝2 (b) 4𝑞 2 − 12 𝑝𝑞 + 9𝑝2 (d) 4𝑞 2 + 6 𝑝𝑞 + 9𝑝2 VIII/ Math /2024-25 Page 4 of 4