ITL Public School Summative Assessment - 1 ( ) Mathematics (Set -B) Marking Scheme

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1 ITL Public School Summative Assessment - (0-5) Mathematics (Set -B) Marking Scheme Date: Class:VIII Time: hours M.M : 90 General Instructions:. Read the question paper carefully and answer legibly.. All questions are compulsory.. The question paper consists of questions divided into four sections A, B, C and D.. Section A comprises of questions of mark each, Section B comprises of 6 questions of marks each, Section C comprises of 0 questions of marks each and Section D comprises of questions of marks each. 5. Use of calculators is not permitted. Section A Q. Q. Q. Q. Q.5 Q.6 Q.7 How many integers are there between and? No. of integers 7 If x, then find the value of x. How many numbers lie between the squares of the numbers 75 and 76? No. of numbers between the squares of n and (n + ) n Find the number of diagonals of a nonagon. No. of diagonals 7. Section B Find the sum of the multiplicative inverse and the additive inverse of. Multiplicative inverse of Sum + Solve the equation:... 5 (0.y 6) (.y ). y 0.y.y 8 y. Additive inverse of Find the smallest number by which the number 6750 should be divided to get a perfect cube. Prime factorization of Since the prime factor is not occurring in triplet, therefore 6750 should be divided by to get a perfect cube. Q.8 Construct a frequency distribution table for the data on the number of calories taken by a toddler in 0 days using intervals , and so on: 80, 85, 80, 80, 85, 86, 89, 80, 80, 86,

2 Q.9 Q.0 Q. 8, 8, 85, 8, 80, 808, 8, 85, 85, 86. Class intervals Tally marks Frequency Half mark for each class interval A welfare association collected Rs.500 as donation from the residents. If each paid as many rupees as there were residents, find the number of residents. Let number of residents x Amount paid by each resident x Total amount paid 500 x 500 x The sum of two angles of a quadrilateral is 0. The other two angles are in the ratio : 7. Find these angles. Let other two angles be x and 7x respectively. By angle sum property of a quadrilateral, we have 0 + x + 7x 60 x Hence other two angles are: x 66 and 7x 5. Section C Using the properties of rational numbers, find (by distributive property of over +) Q. Q. The sum of three positive consecutive integers is 58. What are these integers? Let the three positive consecutive integers x, x+ and x + ATQ, x + x + + x + 58 x 58 x 55/ 85 Hence the positive consecutive integers are: x 85 x + 86 x + 87 RISK and CLUE are parallelograms, K E S U 0⁰ and 80⁰. Find. O In parallelogram RISK, + 80⁰ (Co-interior angles) R I C L

3 Q. 80⁰ - 0⁰ 70⁰ In parallelogram CLUE, 80⁰. (opposite angles of parallelogram) In ESO, 80⁰ 70⁰ 80⁰ 0⁰ (by ASP of Triangle) Construct a Rectangle CAKE, where CA 7. cm and KA 5. cm. Writing properties of triangle () steps of construction (/ mark each) Q.5 Solve for x: + Q.6 Q.7 Q x x - /9 Construct a quadrilateral LIST with LI cm, ST. cm, TL.7 cm, LS 6 cm and IT 5. cm. steps of construction (/ mark each) The number of workers in various age groups in a town is given in the following table: Age group (in years) No. of persons (in 000s) Represent the above information on a histogram. Drawing the axes and writing information on them and scale () Drawing the histogram () Find the least square number, exactly divisible by each one of the numbers 8, 0, and 5. LCM of the given numbers 0 ( ) Prime factorization of 0 5 Since the prime factors, and 5 are not occurring in pairs Therefore 0 should be multiplied by 0 to get a perfect square () Hence the perfect square no. is which is divisible by all of the given nos. (/) Q.9 A farmer had enough food to feed 5 cows for 60 days. Due to unhealthy conditions, few cows died and the food lasted for 75 days. Find the number of cows that died. Let the decreased no. of cows be x As increase in the number of days will lead to the decrease in the no. of cows. Hence it is the case of inverse proportion Therefore 5 60 x 75 x Hence no. of cows died 5 Q.0 Find the least number which must be added to 760 to make it a perfect square. Also find the square root of the number so obtained.

4 Q. Q. Q. Q. Q.5 By long division method we get the no. to be added 76 to make the given no. a perfect square. Square root of the no. so obtained Section D (a) Represent 7 on the number line. 6 Plotting the nos. on the no. line with equal intervals and marking arrows on both sides ( ) Encircling the no. (/) (b) Find two rational numbers between and. Finding LCM and writing their equivalent nos. () Writing two nos. between them () One of the digits of a two digit number is twice the other digit. The sum of the original number and the number formed by reversing the digits is 99. Find the number. Let the digit at one s place be x and then the digit at ten s place x Original no. x + 0x x On interchanging the digits at the two places, new no. obtained x + 0x x ATQ, x + x 99 We get, x Hence the two digit no. x 6 or x 6 (a) Is it possible to have a regular polygon with a measure of each exterior angle as 6? Why? (b) Can it be an interior angle of a regular polygon? Explain. (a) sum of all the exterior angles of any polygon of n sides 60⁰ Therefore 6 n 60⁰ We get, n 60⁰/6⁰, which is not a natural no. Since the no. of sides of any polygon can never be a fraction hence the given situation is not possible. (b) by linear pair, we get each interior angle of the given polygon 80⁰ - 6⁰ 6⁰ 6⁰ n (n - )80⁰ Which gives n as a fraction and hence this cannot be an interior angle of the given polygon. Construct a Rhombus whose diagonals are.8 cm and 6.6 cm. Writing properties of rhombus () Constructing the rhombus () The enrolment of classes VI to IX in a school is given below: Class VI VII VIII IX Number of students Represent the above data on a pie chart. drawing table showing central angles (0.5 ) drawing the pie chart ()

5 Q.6 Q.7 A girl distributed some sweets on her birthday. The half of the sweets she had were distributed in her school and three-fourth of the remaining were distributed in the bus. The rest 0 were distributed among the poor children living in the slums. Find the number of sweets she had. What quality of the girl is depicted by this act of hers? Let the no. of sweets the girl had be x ATQ x x 0. () Writing the value depicted by this act of the girl () If.5 kg of rice contains grains of rice, find: (a) the grains contained in 6 kg of rice? (b) the quantity of rice that contains grains? This is the case of direct proportion, as the increase in the weight of rice will lead to the increase in the no. of grains (a) grains contained in 6 kg of rice (b) quantity of rice that contains grains 5 kg Q.8 Q.9 A die is thrown. Find the probability of: (a) Getting a multiple of /6 / (b) Getting a number greater than 0 (c) Getting an even number / (d) Getting a prime number / (a) The volume of a cubical box is.768 cubic meters. Find the length of a side of the box. (b) Simplify: (a) The length of the side of the box.768. m (b) Q Construct a quadrilateral PLAN with PL cm, LA 6.5cm, P 90⁰, A 0⁰, N 85⁰. Finding missing angle () each step of construction (/) Q. men can dig a pond in 5 days. (a) How many men can dig it in 5 days? (b) Four of the persons left the job before the work started. How long would the job take now? This is the case of inverse proportion, as the increase in the no. of persons will lead to the decrease in the no. of days (a) No. of men needed to do the same work in 5 days 6 (b) No. of days needed to complete the work by i.e. by 8 men 7 days.

6 SQUARES AND SQUARE ROOTS

6 SQUARES AND SQUARE ROOTS Exercise 6.1 Q.1. What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796