Grade_8_Maths_Term_1_23-24.pdf

PAWAR PUBLIC SCHOOL, BHANDUP. Class Subject Term Marks Date Duration No. of printed sides VIII Mathematics 1 80...

PAWAR PUBLIC SCHOOL, BHANDUP. Class Subject Term Marks Date Duration No. of printed sides VIII Mathematics 1 80.09.2023 2 𝟏⁄𝟐 hrs. 4 Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of any essential working will result in loss of marks. The intended marks for questions or parts of the questions are given in the brackets [ ]. Geometrical figures in the Paper are not drawn to scale. Section A (40 marks) Attempt all questions from this Section Question 1 −1 (a) Write the additive inverse and the multiplicative inverse of ( ) 8 (b) Identify the adjoining polygons as convex or concave: (c) Solve: 4 = 5 y 3 2y 3 10 −5 (d) Find the value of : m ÷ n + 2, if m = 13 and n = 143 Question 2 (a) Simplify using identities: (103)2 – (97)2 (b) Find the cube root of: (– 27) × (– 3375) (c) The adjoining histogram shows the number of literate females in the age group of 10 to 40 years in a town: (i) Write the age group in which the number of literate females is the highest. (ii) What is the class width? (iii) What is the lowest frequency? Page 1 of 4 PPSB/23-24/8/MATH/T1 (d) Find the smallest natural number by which 5808 should be multiplied to make it a perfect square. Also find the square root of the resulting number. Question 3 (a) Name the property of rational numbers used in the following: −5 1 −6 (i) ( 7 ) − (7) = ( 7 ), is a rational number −9 −9 −9 (ii) ( 11 ) + 0 = ( 11 ) = 0 + ( 11 ) 1 (b) Find the cube of: (−1 4) (c) Find the measure of angle 𝑥 marked in the quadrilateral PQRS. (d) The adjoining pie chart shows the different sports liked by students of grade 8. If there are total 200 students in grade 8, find the: (i) number of students who like cricket. (ii) ratio of number of students who like tennis to number of students who like cricket. Question 4 (a) Evaluate: 8𝑚𝟑 + 3𝑚𝟐 − (8𝑚𝟐 − 4 + 2𝑚) (b) The students of a class arranged a trip. Each student contributed as many rupees as the number of students in the class. If the total contribution is 1156, find the strength of the class. 9 1 (c) Find the value of 𝑝 in the given equation: =1 40−(7−3𝑝) 2 (d) The marks scored by 20 students in a test are given below: 54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57. Taking classes as 40-50, 50-60 -------80-90 prepare a frequency distribution table and also answer the following question: How many students scored less than 60 marks? Page 1 of 4 PPSB/23-24/8/MATH/T1  Section B (40 marks) Attempt any four questions from this Section Question 5 1 (a) Brijmohan earns 28,000 per month. He spends on rent. From the remaining money he 4 2 spends on food and saves the remaining money. How much money he saves per month? 7 (b) Find the square root of 92.16 using division method. (c) (i) Using identities evaluate: (p – 3) (p + 4) (ii) Find the value of (106)2 using a suitable identity. Question 6 (a) Find the smallest natural number by which 3087 must be divided to make it a perfect cube. What is the cube root of the resulting number? (b) From the sum of 15𝑚𝟐 n – 17𝑚𝑛 + 8𝑚𝑛𝟐 and 13𝑚𝟐 n – 9𝑚𝑛𝟐 – 15𝑚𝑛, subtract 12𝑚𝑛𝟐 – 21𝑚𝑛 – 14𝑚𝟐 n −2 3 (c) (i) Insert two rational numbers between and 7 14 −6 2 (ii) Represent and on the same number line. 5 5 Question 7 (a) Find the measure of each interior angle of a regular decagon. Also find the measure of its corresponding exterior angle. 3 4 7 (b) If p = ,q= and r = , then verify that (p + q) + r = p + ( q + r ). 2 5 12 (c) Find the solution set of the following inequation and represent it on the number line: 6x – 5 < 13, x ∈ W Question 8 (a) Chandrika’s mother is thrice as old as Chandrika. After 11 years, she’ll be twice as old as her daughter. What are their present ages? (b) Answer the following: (i) Look at the units place and state with reason whether 98762 can be a perfect square or not? (ii) What will be the units place of the cube of 87? (iii) Identify the type of polynomial: 6a𝟑 – 3a𝟐 + 7a ÷ b (c) HOPE is a parallelogram. Find the measure of angles x, y and z. Page 1 of 4 PPSB/23-24/8/MATH/T1 Question 9 (a) The length of a rectangle is 2cm less than thrice its breadth. If the perimeter of the rectangle is 100cm, then find the length and breadth of the rectangle. (b) (i) Express 36 as the sum of consecutive odd numbers. (ii) Check whether (8, 9, 14) is a Pythagorean triplet. (c) The number of hours, spent by Suraj on different activities on a working day, is given below: Activities Sleep School Home Play Others Total No. of hours 8 7 4 2 3 24 Draw a pie graph representing this data. Question 10 (a) ABCD is a rhombus. If m A = 1300, then find: (i) value of x (ii) m D (b) Given below is the frequency distribution of the heights of 50 students of a class: Class Interval 140 – 145 145 – 150 150 – 155 155 – 160 160 – 165 Frequency 8 12 18 10 5 Draw a histogram representing the above data. (c) Do as directed: 3 (i) Find the value of: √35937 𝑚5 (ii) Find the cube of: 1.2 𝑛7 Page 1 of 4 PPSB/23-24/8/MATH/T1