The City School PAF Chapter Prep Section. Mathematics. Class 8. First Term. Workbook for Intervention Classes

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1 The City School PAF Chapter Prep Section Mathematics Class 8 First Term Workbook for Intervention Classes

2 REVISION WORKSHEETS MATH CLASS 8 SIMULTANEOUS LINEAR EQUATIONS Q# tickets were sold. Adult tickets cost $8.50, children's cost $4.50, and a total of $7300 was collected. How many tickets of each kind were sold? Q#2. The sum of the numerator and denominator of a fraction is 17. If 3 is added to the numerator, the value of fraction will be 1. What is the fraction? Q#3. A man bought 8 kiwi fruits and 7 pears for $4.10 while another man bought 4 kiwi fruits and 9 pears for $3.70. What is the cost of each kiwi fruit and each pear? Q#4. Find the perimeter of the following triangle. 3y+1 2x x+y=4 2x Q#5. A shopkeeper mixed coffee powder worth $2.50 per kg with the coffee powder worth $3.50 per kg, and sold 20kg of the mixture at $2.80 per kg. Find the weight of the 2 grades of coffee powder that he mixed together. Q#6. The ratio of two sum of money is 4:3. If the larger sum of money is increased by $40, the ratio becomes 2:1. Find the sum of money. Linear Inequalities: Short questions on Linear Inequalities 1. Solve the following inequalities and illustrate the solution by number line. a) 8-6x 4x-22 b) x + 6 > 3 c) 32 9x 4 d) 12 6x>24. e) ~ 1 ~

3 f). PROFIT AND LOSS Fill in the blanks: 1. An article was bought for $32 and was sold for $30, Loss = 2. If the original price of an article is $525 and a profit of $30 is earned, then the selling price will be 3. The Cost price of an article is $40 and it s selling price is $50, then it s percentage profit is 4. Profit = Selling Price - 5. = Cost price Selling price 6. If selling price of a book is $120 and its Cost price is $100, then Profit = MCQ s: 1) 40% of 240 is a) 69 b) 96 c) 99 2) The price of a television set is decreased from $160 to $90. The shopkeeper will get a loss of a) $250 b) $70 c) $110 3) A shopkeeper earned a profit of $30 on the cost of $600. The percentage profit was a) 6% b) 3% c) 5% 4) If Sale price of an article is $32 and its original price is $30, then profit is a) $2 b) $3 c) $4 5) If 25% of a certain article is $500, then the actual price of the article is a) $1000 b) $2000 c) $3000 Questions: 1. The profit made on a refrigerator is 30% of the cost price. If the profit is $270, find: a) The Cost price b) The Selling price of the refrigerator. 2. A shopkeeper buys a radio set for $480. Find the selling price if the profit percentage is 5% ~ 2 ~

4 3. At what price must an article which cost $450 be sold in order to make a profit of 16 ½ % on the cost? 4. An article is sold for $2000 and 15% profit on the cost is made. Find the original cost of the article. 5. If a discount of 3% is given on an article marked $150, find the amount of discount given and the sale price of the article. 6. During a sale, a washing machine was sold for $440 at a reduction of 12%. Find the original price and the amount of discount given on the washing machine. 7. A shopkeeper brought an article at a cost of $1100 and sold it for $1300. Find the percentage profit on the cost. 8. An article marked $1200 was sold at a discount of 6%. Find the price at which the article was sold. Ratio, Rate and Speed Fill in the blanks: 1. The simplest form of the ratio 75: 30: 25 is 2. The formula of Speed is 3. If a boy cycles 15 km with an average speed of 5km/h, then the time taken by the boy is 4. The ratio of A : B is 5:4. If the total profit is $450, then A s share is 5. If X : Y = 7:5 and Y : Z = 3:2 then X : Y : Z = 6. If the average of a car is 120 km/h and the time taken is 3 hours, then the distance covered is 7. If a distance of 120 km is covered in 1 ½ hour, then the average speed is 8. 12% in decimal form is : 18 in its simplest form is 10. If distance covered is 224 km and average speed is 112 km/h, then time taken is MCQ s: km/h can be expressed as a) 20m/s b) 10m/s c) 5m/s 2. A piece of string of length 160cm is divided into two parts in the ratio 1: 9. The length of the smaller part is a) 4 cm b) 16 cm c) 64 cm 3. In 24 hour clock notation, 7 :05 am is ~ 3 ~

5 a) 0705 b) 2705 c) Ratio 0.8 : 0.4 in simplest form is - a) 2 :1 b) 20 : 1 c) 2 : Which of the following ratios are equivalent to the ratios of 2 girls to 3 boys? a) b) 4:9 c) 4: 6 6. The value of 2: 5 = is -- a) 2 b) 4 c) 6 7. The ratio of 5 min and 2 seconds is a) 5: 2 b) 15: 1 c) 150: 1 8. A car left town X at and arrived Town Y at The journey time is a) 6 hr 5 min b) 7 hr 45 min c) 7 hr 05 min 9. A car reached its destination on Tuesday at after completing its journey in 8 hr. The time at which the car started the journey was a) (Tues) b) (Wed) c) (Mon) 10. If the price of a book is $12, then number of books purchased with $288 is Questions: a) 14 b) 22 c) 24 1) A sum of money is divided among A: B: C in the ratio 3: 5: 9. Calculate: a) The smallest share if the largest share is $ 108 b) The total sum of money. 2) An electricity bill consists of a monthly meter rent of $ 6.50 and charges resulting from the number of units used at 2 cents per unit. In a particular month, Mr. John used 445 units. How much was his bill? 3) A bus leaves Town X at and arrives Town Y at the next day. Calculate: a) The time taken for the journey b) The average speed of the bus, given that the distance between both the towns is 651 km. 4) A bus travelled at a speed of 50 km/h for 3 hr and then at a speed of 40 km/h for further 2 hrs. Find the average speed of the whole journey. ~ 4 ~

6 5) A car travelling 72 km/h takes 6 hours to complete the journey. Find the distance covered by the car. 6) Express 40 minutes after 5: 55 pm using 24 hour clock notation. 7) The average speed of a car is 30 m/s. how many meters can the car travel in 3 minutes. 8) The cost of material, labour and administration for an advertising campaign is in the ratio 3: 5: 2. If the total cost of the campaign is $3525, find the cost of labour. 9) 784 sweets are shared among A: B: C in the ratio 3: 5: 8. How many sweets does each get? 10) A cash discount of 5% is allowed on an item which costs $40. How much money is saved if the customer decides to pay in cash? NUMBER SEQUENCE Fill in the blanks: 1. Write down the net two terms of: a) 1, 2, 4, 8, 16,,, _ b) 1, 8, 27, 64,, c) 2, 5, 8, 11,, 2. In the sequence 1,3, 5, 7,,, the nth term is 3. In the following pattern, value of p = 2 = 1 x 2 6 = 2 x 3 12= 3 x = p x (p + 1) MCQ s: 1. If the nth term of a sequence of natural numbers is 3n, then the 20 th term of the sequence is a) 20 n b) 40 n c) 60 n 2. 1 x 3, 2 x 4, 3 x 5, 4 x 6, a) 7 x 8 b) 5 x 7 c) 7 x 9 3. The nth term of the sequence 7, 13, 19, 25, 31,, is a) 7 n + 1 b) 6 n + 1 c) n 4. The next two terms of the sequence 52, 59, 66, 73,, a) 80, 87 b) 77, 79 c) 81, 86 ~ 5 ~

7 5., 12, 24, 48, 96. The value in the circle is a) 8 b) 4 c) 6 Questions: 1) The sequence of numbers 1, 5, 11, 19, 29,, can also be expressed as + 0, + 1, a) Express the 6 th term in the same form b) Calculate the value of the 100 th term. 2) The nth term of a sequence is 2 n + 1. Write down the 7 th and 8 th term of the sequence. 3) The table below shows black (B) and white tiles (W) : B W a) Follow the pattern and find the values of b) Find the formula connecting W and B. c) Using the formula, find the number of white tiles, if there are 20 black tiles. 4) Consider the following pattern: = 1 - = - a) Write down the 8 th line of the pattern. b) Using the above, find the value of - c) Find the value of = -... = - 5) Consider the sequence 5, 9, 13, 17, 21,, a) Find the 10 th term of the sequence. b) Find the nth term of the sequence c) Write the smallest term of the sequence that is greater than 100. ~ 6 ~

8 6) The table below shows the number of tables required by the number of people sitting in the restaurant: No of People No of Tables n = 0 = 0 = 0 a) Complete the table b) How many tables are required if there are 16 people? 7) In how many ways can the number 9 be written as the sum of a) 2 consecutive numbers b) 3 consecutive numbers? Fill in the blanks: SIMPLE INTEREST 1. John took loan of $20000 for 3 ½ years and paid $5880 as simple interest on the loan. Amount paid after 3 ½ years by John will be 2. If $12000 are borrowed for a year at a simple interest rate of 6%. The interest given will be 3. 3 years 4 months = 4. Simple interest on $300 at the rate of 10% per annum is 5. If a man invested $400 for a year in a bank and receives $600 at the end of the year. The interest given to him is MCQ s: 1. Mary took a loan of $700 for 5 years and paid $210 as simple interest. The rate at which simple interest taken is a. 6% b. 8% c. 12% 2. A sum of $2000 is borrowed for 5 years at 3% per annum. The simple interest paid on it will be a. $200 b. $300 c. $ months = years. a. 2 years 2 months b.2 years 4 months c. 2 years 6 months ~ 7 ~

9 Questions: 4. If the simple interest on $500 at 4% per annum is $35, then the period of loan is a. 1 year 9 months b. 1 year 10 months c. 1 year 11 months 5. Mr. Khan borrows $500 and agrees to repay $750 at the end of 4 years. The rate of simple interest charged is a. 3.5% b. 6.5% c. 12.5% 1. A man s statement of account from a bank showed $9 as one year s interest from the bank which pays 3% interest. How much money had he in the bank before the interest was added? 2. Find: a. The simple interest b. The total amount of money When Principal = $700, rate of interest = $6% and time taken = 5 years. 3. The simple interest on a certain sum of money for 26 months at 6% per annum is $1950. Find: a. The sum of money b. Amount received. 4. John invested $1000in a business for 6 months at 2% per annum and $1500 in another business for 8 months at 5% per annum. Find the total interest he will receive from both the investments. 5. Calculate the simple interest on $500 for 4 years at 7% per annum. 6. Mr. Li invests $7500 for 3 months and receives as interest. What is the rate of simple interest per annum? 7. The cost of an article is $4000. Find the interest paid on it if the rate of interest is 5% per annum. 8. The yearly interest at 4 ½ % on a certain sum of money was $36. Find the value of the yearly interest on the same amount at 6 ¼ %. 9. If the simple interest on a sum of money invested at 3 ½ % per annum for 4 years is $100, find the principal. 10. If $350 amounts to $385 at 2 ½ % per annum, find the duration of the loan. VOLUME AND SURFACE AREA Q1. Find the volume of the following right prism. 3cm 3cm 15 c m 5cm ~ 8 ~ 5c

10 Q2. A right prism is shown in the figure below. Find its volume. 6c m 5c m 3cm 5cm 10cm Q3. Find the volume and area of given right prism when, PQ is 5cm, QR is 4cm and RS is 8cm. Q S P R Q4. If volume of a triangular right prism is 1200cm 3 when it is 20cm long, then find its area. Q5. If base of a triangle is 9cm while its height is 15cm. Find the area of the base of right prism and its volume if it is 7cm long. Q6. Find the volume and surface area of the right prism shown in the diagram below. Q7. With the help of the given measurements, find the volume and surface area of the right prism. ~ 9 ~

11 Q8. What will be the volume and surface area of the given right prism? Q9. A water tank is 10m high, 15m long and 20m wide. How many liters of water is needed to fill the tank? Q10. If a room is 12m long, 5m high and 14m wide. Find the volume of air in the room. Q11. Find the volume and surface area of the cylindrical solids with radius 10cm and height 25cm. Q12. If diameter of a solid cylinder is 4m and height is 5m, find its volume and surface area. Q13. If radius of a solid cylinder is 20mm and height is 70mm then find its volume and surface area. Q14. If surface area of cylinder is 748cm 2 and radius is 7cm, then find its height and volume. Q15. A solid cylinder with diameter 20cm and height 60cm needs to be painted. What is the surface area that needs to be painted? Q16. Fill in the blanks. i. If the volume of a cylinder is 6.275m 3, then its capacity = liters. ii. If the capacity of a water tank is 6.275l, then its volume = cm 3. iii. Volume of a right prism = iv. Volume of a cylinder with radius 8cm and height 35cm is v. Surface area of a solid cylinder = Q17. Circle the correct answer. ~ 10 ~

12 i. Value of π is (a) 3.12 (b) (c) 3.41 ii. If volume is 3425cm 3 then capacity in liters is (a) 3.425l (b) 34.25l (c) 342.5l iii. Volume of a cuboid with sides 2cm, 5cm and 6cm is (a) 11cm 3 (b) 60cm 3 (c) 22cm 3 iv. If r = 10cm then circumference of a circle will be (a) cm (b) cm (c) cm CONSTRUCTION OF TRIANGLES AND QUADRILATERALS Q1. Construct ABC with AB = 9cm, BC = 6cm and ABC = 90 o. Measure and write down the size of ACB. Q2. Construct PQR with PQ = 8cm, QR = 6cm and PQR = 60 o. Measure and write down PRQ and also measure and write the length of PR. Q3. Construct a rectangle of sides 8.4cm and 9.6cm. Measure the length of the diagonals and the acute angle made by these diagonals. Q4. Construct a parallelogram PQRS with PQ = 9cm, QR = 11.5cm and Q = 80 o. Measure QS. Q4. Find the unknown values in the following. SYMMETRY ~ 11 ~

13 Q5. State whether each of the following statement is true or false. i. An equilateral triangle has rotational symmetry of order 2. ii. An equilateral triangle is an isosceles triangle. iii. A rhombus is a quadrilateral with both the diagonals as lines of symmetry. iv. A trapezium is a parallelogram. v. A rectangle with two adjacent sides equal is a square. vi. A parallelogram is a rhombus. vii. A scalene triangle has one line of symmetry. viii. A kite has one order of rotational symmetry. ix. A parallelogram with one right angle is a square. x. If a triangle has two equal sides, then it has two equal angles. Q6. Fill in the blanks. i. Sum of interior angles of a triangle is. ii. Sum of angles around a point is. iii. Sum of four angles of a quadrilateral is. iv. There are pairs of parallel opposite sides in a rhombus. v. In a square all 4 angles are angles. vi. In a rectangle sides are equal in length. vii. There is one pair of opposite sides in trapezium. viii. In a parallelogram opposite angles are. ix. A polygon with 10 sides is called. x. A heptagon has sides. ~ 12 ~

14 Q1) Simplify: a) b) c) d) e) f) g) Indices & Standard Form h) i) j) k) l) Q2) Evaluate Q3) Solve the following Q4) Simplify Q5) Express the following number in standard form where and is an integer Q6) Express the following in ordinary notation Q7) If where and is an integer. Find the value of and. ~ 13 ~

15 Q8) Given that Find the value of each of the following, giving your answer in standard form: Q9) Express the following numbers in standard form where and n is an integer. Q10) Express the following in ordinary notation. Q11) Evaluate each of the following and give your answer in the standard form where and n is an integer. Q12) If and, find the value of Q13) Given that and, find the value of, giving your answer as a fraction. Q14) Evaluate, expressing your answer in the form where and is an integer. Q15) If, evaluate and express your answer in the standard form. a) Q16) Given that, find the value of each of the following, giving your answer in standard form: a) ~ 14 ~

PRACTICE QUESTION SET ON QUANTITATIVE APTITUDE FOR SSC RECRUITMENT EXAMINATION- 2012

WWW.JAGRANJOSH.COM PRACTICE QUESTION SET ON QUANTITATIVE APTITUDE FOR SSC RECRUITMENT EXAMINATION- 2012 1. Ratio of the principal and the amount after 1 yr is 10 :12. Then the rate of interest per annum