Maharashtra Board Class VIII Mathematics Sample Paper 1 Solution

Transcription

1 Maharashtra Board Class VIII Mathematics Sample Paper Solution Time: hrs Total Marks: 6 SECTION A. Correct Answer: (A) A quadrilateral with opposite sides parallel is called a parallelogram.. Correct Answer: (B) Area of a rhombus Product of lengths of diagonals. Correct Answer: (D) Circumference of the circle is c r. 4. Correct Answer: (D) The numerical information collected for a specific purpose is called raw data. 5. Correct Answer: (A) y If y x then k (a constant) x 6. Correct Answer: (A) A quadrilateral in which only one pair of opposite sides is parallel is called a trapezium. 7. Correct Answer: (D) area of a trapezium Sum of lengths of parallel sides height 8. Correct Answer: (C) Amount = Principal + Simple interest 9. Correct Answer: (A) Compound interest = Amount Principal. Correct Answer: (B) A shopkeeper may sell an article for less than the marked price for some reason. The difference between the marked price and the lowered selling price is called the discount.

2 . Correct Answer: (A) Volume of the cylinder rh. Correct Answer: (A) 4 Volume of the sphere r. The diagonals of a square are congruent. Therefore, they are of equal length. l(pr) = l(qr) but l(pr) = 8 cm (Given) Therefore, l(qr) = 8 cm 4. mpoq = 4 and chord PQ chord RS. 5. The measure of ROS is 4. SECTION B The congruent chords of the circle form congruent angles at the centre. ROS POQ mros mpoq 4 The area of a triangle = base height = cm 6. The marked price of the carpet is Rs 65. The discount is 8%. Discount on the marked price = marked price rate of discount 8 65 Rs.5 The selling price = marked price - discount = 65-5 = Rs. 598 The selling price of the carpet is Rs 598.

3 7. Here, r = 5cm; h = 4 cm The volume (V) of a cylinder = r h = cm The volume of the cylinder is cm. 8. x + 7x = x + 5x 8x = x(4x + 5) (4x + 5) = (4x + 5)(x ) 9. x 5 x x 5 x x 5 x x x 5 x x Answer: 6

4 SECTION C. Line k line l line m. Line c and line d are their transversals. by the property of three parallel lines and their transversals, l XY l YZ l PQ l QR 9 6 l QR 9l QR 6 6 lqr 9 l QR. The opposite sides of the rectangle are congruent. seg PS seg QR l(ps) = l(qr) l(ps) cm (Given) l(qr) = cm Similarly, seg PQ seg SR l(pq) = l( SR) l(pq) 8cm (Given) ls ( R) = 8 cm OR The sum of the measures of the angles of the quadrilateral is 6. ma mb mc md md 6 md 9 Now each angle of ABCD is a right angle. ABCD is a rectangle.

5 . To find the length of wire fencing around the circular place, we have to find the circumference of the circular place. The radius of the circular place = 7.7 m Circumference = r = m The length of the wire required for three rounds of fencing = circumference = m The cost is Rs 5 per metre the cost of wire 45. m in length = 545. = Rs. 76 The cost of wire Rs Number of peas Tally marks Frequency N=6 OR Number of peas Tally marks Frequency N = 4

6 5. The sale of cloth today (P) = Rs,, Increase in the yearly sale (R) = % Period (N) = years The sale of cloth after years R = P+ = + N 5 5 Rs. 46 The sale of cloth after years = Rs,,46 SECTION D 6. Let the numerator of the original fraction be x. Then its denominator is x + 5. x So the original fraction is x 5 If is added to both numerator and denominator, the numerator or the new fraction = x + and the denominator = x = x + 7. x From the given condition, x 7 x x 7 x 4 x 7 x x 7 4 x x The original fraction is. 8 OR Let the cost of a pen be Rs x. Then the cost of a notebook is Rs (x + 5). The cost of 4 pens at Rs x each = Rs 4x The cost of 5 notebooks at Rs (x + 5) each = Rs 5(x + 5) From the given condition, 4x + 5(x + 5) = 88 4x + 5x + 5 = 88 9x = 6 x = 7 and x + 5 = = The cost of one pen is Rs 7 and cost of one notebook is Rs.

7 7. For the cylindrical vessel: r = cm, h = 6 cm Volume of ice-cream in this cylindrical vessel = r h 6 4 cm For a cone R= cm, H = cm Volume of ice-cream in one cone = RH cm Number of cones that can be filled with ice-cream Volume of ice-cream in this cylindrical vessel = Volume of ice-cream in one cone cones can be filled with ice cream. 8. There is inverse proportion between the number of crates and the number of mangoes. Let the number of mangoes in each crate be x and the number of crates be y. Then x (Inverse variation) y x y k (k is a constant) When x 6, y6 66 k k 6 x y k xy 6 When x y 6 y crates are required.

8 SECTION E 9. Steps for the construction: a) Draw a segment XY of length 7.5 cm. b) Draw a ray XP at point X on one side of seg XY making an acute angle with it. c) Draw ray YQ making an acute angle of the same measure with seg XY. d) Take any convenient radius and with the tip of your compass at X, mark a point X on XP. e) With the compass on X and at the same distance as XX, mark another point X. Similarly, mark two more points X and X4. f) Keeping the radius same, mark points Y, Y, Y, Y4 on ray YQ. g) Draw the segment XY, XY, XY, XY and X4Y using your ruler. They intersect segment XY at points. Label them as L, M and N. h) The length of segments XL, LM, MN and NY is the same. OR

9 Steps for the construction: a) Draw a segment XY of length 6.5 cm. b) Draw a ray XP at point X on one side of seg XY making an acute angle with it. c) Draw ray YQ making an acute angle of the same measure with seg XY. d) Take any convenient radius and with the tip of your compass at X, mark a point X on XP. e) With the compass on X and at the same distance as XX, mark another point X. Similarly, mark point X. f) Keeping the radius same, mark points Y, Y and Y on ray YQ. g) Draw the segments XY, XY, XY and XY using your ruler. They intersect segment XY at points. Label them as A and B. h) The length of segments XA, AB and BY is the same.