7 (iii) 7. (iv) 16. Q.2. The cube root of ( 1000) is

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1 MODEL TEST PAPER SUMMATIVE ASSESSMENT-I (Solved) Time: 3hr Max Marks: 80 General Instruction. Section A Q.. to Q.. carry mark each.. Section B Q.. to Q.0. carry marks each. 3. Section C Q.. to Q.30. carry 3 marks each. 4. Section D Q.3. to Q.35. carry 4 marks each. 5. All questions are compulsory. ========================================= Section - A Q.. The additive Inverse of 6 is (i) 6 (iii) 6 Q.. The cube root of ( 00) is (ii) (iv) 6 6 (i) (ii) (iii) 0 (iv) 0 Q.3. What is the negative of a negative rational number. (i) Negative (ii) positive Q.4. Every rational number is an integer (i) True (ii) False (iii) not always true Q.5. For an integer a, a 3 is always positive. (i) True (ii) False (iii) not always true Q.6. The sum of ab, bc, ca, ab, ca & bc is (i) ab (ii) 0 (iii) ab (iv) none of these Q.. The coefficient of m is 9mx + 4 is (i) 9 (ii) 0 (iii) 9x (iv) 9x 50

2 Q.8. The constant in x 3 is (i) (ii) (iii) 3 (iv) 3 Q.9. Product of ( a b) and ( a + b) is 5 5 (i) a + b (ii) a b (iii) a b (iv) none of these 5 4 Q.. If x = 3, which expression has a different value from the other three? (i) x + 9x (ii) x (iii) x (iv) x (x ) Section B Q.. Find the square root of Q.. Is 56 a perfect cube? Show steps. Q.3. Plot 5 and 5 on the same number line. Q.4. Is (6, 9, ) a Pythagorean triplet? (Show). Q.5. Express (x + 3y 3 ) as a trinomial. Q.6. Rohan rolls a die. What are the chances of getting a number which is even? Q.. Find the number of sides of regular polygon whose each exterior angle has a measure of Q.8. Find the measure of x. 5 B C 5 A X 0 5

3 Q.9. Find the measure of y. 60 x 9 Q.0. Solve : = 5 + x 5 9 Section C 0 y Q.. Evaluate : Q.. The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and is added to its denominator, the new number becomes /5. Find the original number. Q.3. The area of square field is m sq. Find the length of its side. 400 Q.4. The sum of rational numbers is 3. If one of the number is 9, find the other. 5 0 x + b Q.5. Solve : = a b x b a + b Q.6. The ratio of sides of a parallelogram is 3:5 and its perimeter is 48m. Find the length of the sides of the parallelogram. Q.. The volume of a cubical box is 3.84 cubic metres. Find the length of each side of the box. Q.8. Find the cube root of Q.9. Find the smallest four digit number which is a perfect square. Q.30. Find 3 rational numbers between and. Section D Q.3. Construct the histogram based on the data given below. It represents the number of miles per gallon of gasoline obtained by 40 drivers of compact cars in a large city. 5

4 Interval Frequency Answer the following questions: (i) (ii) (iii) What is the number of cars reporting mileages between 8 and 3 miles per gallon? How many cars reported mileages greater than 3 miles per gallon? What percent of the cars reported mileages from 4- miles per gallon? Q.3. Construct a quadrilateral PQRS, PQ = 5.5 cm, QR= 4 cm, RS = 4.4 cm, and PS=3. cm and P = 5 0. Q.33. Find the product of y + y = 3. y and (y y ) and verify the result for Q.34. If 4x + y = 40 and xy = 6. Find the value of x + y. Q.35. In a parallelogram ABCD, the bisectors of angle A and angle B meet at O. Find angle AOB. D C O A B ============================================ 53

5 SOLUTIONS Q.. (a) Q.. (b) Q.3. (b) Q.4. (b) Q.5. (b) Q.6. (b) Q.. (c) Q.8. (d) Q.9. (b) Q.. (b) Section-B Q = = 3 4 = = 84 Q.. Resolving 56 into prime factors We have 56= clearly in grouping the factors in triples of equal factors. We are left with two factors. Therefore 56 is not a perfect cube. Q.3. and on the number line Q.4. To form a Pythagorean Triplet, the number should be m, (m -), (m +) (m) + (m -) = (m +) = , 9, does not form a Pythagorean Triplet Q.5. (x + 3y 3 ) as a trinomial Using (a + b) = a + ab + b = (x) + (3y 3 ) + x 3y 3 = 4x + 9y 6 + xy 3 Q.6. Total numbers appearing on the dice = 6 Chances of getting even numbers on a die (, 4, 6) = 3 = 6 54

6 Q.. Total measure of all exterior angles of a polygon = Measure of each exterior Angle = 45 0 The number of exterior angles = = 8 The polygon has 8 sides Q.8. Since the sum of of the measures of exterior angles of a polygon is x = x 0 = x 0 = = 0 Q.9. Since the sum of of the measures of exterior angles of a polygon is y = y = y 0 = = 50 0 Q.0. x 9 = 5 + x By cross multiplication 9 (x 9) = 5 (5 + x ) 9x 8 = 5 5x 9x + 5x = x = 56 x = 56 => x = 4 => x = => x = 4 Q = = 3.05 Q.. Let the numerator be x. Then, the denominator = (x + 3) x 3. = (x + 3) + 5 x 3 => = => 5 (x-3) = (x+5) => 5x 5 = x + 5 x => 4x = 0 => x =5 Numerator = 5 Denominator = (5 + 3) = The required number is

7 Q.3. Let the length of one side of the square field be x metres. Area of the field = x Given:. Area of the field = m 400 x 4040 = m 400 x = 4040 => x = x = 4040 = Hence, the length of one side of the field is 0 m. Q.4. Given, Sum of rational numbers = One of the rational numbers = Let the other number = x x + 9 = x = x = + = + 9 = x + b x b Q.5. = a b a + b 3 0 By cross multiplication (x + b) (a + b) = (x b) (a b) x (a + b) + b(a + b) = x (a b) b(a b) ax + bx + ab + b = ax bx ab +b ax - ax+ bx+ bx = ab +b ab b bx = ab ab x = ab = x = a Q.6. Let one side of a parallelogram = 3x m & the other side of parallelogram = 5x m 0 56

8 Perimeter = (l + b) = (3x + 5x) = 8x = 6x m Given Perimeter = 48m 6x = 48 x = 48 x = 3 m 6 Hence the side of the parallelogram are : 3x = 3 3 = 9m 5x = 5 3 = 5m Q.. Given volume of a cubical box = 3.84 m 3 V = l 3 = l 3 = 3.84 l = = Cube root = 3 = =.4 Length of each side of the box =.4m Q.8. Cube root of = Cube root = 9 = = 6 Q.9. Smallest 4 digit no = 00 (3) 00 should be added to 00 to make it a perfect square =

4 is the smallest 4 digit number which is a perfect square. Q.30., 8 8 9,,,,, The four rational numbers are: 9,, 6, 4 Q.3. 8 6 4 INTERVAL (i) 5 cars (ii) 3 35 = => 36 39 = 3 => 40 43 = Total= +3+= (iii) The interval 4 has a frequency of 8.

9 4 is the smallest 4 digit number which is a perfect square. Q.30., 8 8 9,,,,, The four rational numbers are: 9,, 6, 4 Q INTERVAL (i) 5 cars (ii) 3 35 = => = 3 => = Total= +3+= (iii) The interval 4 has a frequency of 8. Total frequency for this survey is 40. Required percentage = = 0% Q.3. Given PQ = 5.5 cm Rough figure Construction R QR = 4cm 4.4cm R S S RS = 4.4 cm PS = 3.cm 3.cm 4cm P = 5 0 4cm 5 0 P 5.5cm Q P 5.5cm 58 Q

10 Q.33. (y + y ) (y y ) y (y y ) + y (y y ) y y 3 +y 3 y 4 y + y 3 y 4 = Given y = 3 L.H.S. y + y (y y ) (3+ 3 ) 3 (3) (3+ 9) ( 9) 8 (3 + ) = 468 R.H.S: y + y 3 y 4 Given y = => = 468 Hence proved L.H.S = R.H.S. Q.34. (x+y) = (x) + y + x + y a + b = a + b + ab (x+y) = (4x + y ) + 4xy (x+y) = (x+y) = 64 Using 4x + y= 40 and xy = 6 59

11 (x+y) = 64 => x+y = 8 Q.35. OA and O B are bisectors of angle A and angle B OAB = ½ A, OBA= ½ B In AOB, using ASP OAB + AOB + OBA = 80 ½ A + AOB + ½ B= 80 AOB = 80 ½ ( A + B) AOB = 80 ½ (80 ) [ A and B are adjacent angles of parallogram ABCD] AOB = = 90 ============================================= 60

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B) ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False: