Samagra Plus First Term Sample Practice Paper Mathematics IX 2024 PDF

S A M A G R A PLUS FIRST TERM SAMPLE PRACTICE PAPER M AT H E M AT I C S I X Time : 2 hours and 30 minutes Score : 80  Answer any 3 questions. Each carries 2 score...

S A M A G R A PLUS FIRST TERM SAMPLE PRACTICE PAPER M AT H E M AT I C S I X Time : 2 hours and 30 minutes Score : 80  Answer any 3 questions. Each carries 2 scores. 1) Total cost of a pen and two pencils is 17 rupees. Total cost of a pen and a pencil is 13 rupees. a) What is the cost of a pencil? b) What is the cost of a pen? 2) Perimeter of a square is 4 cementer.‍ a) What is the length of its side? b) What is the length of its diagonal? 3) In the figure divides in the ratio. The lines and are parallel lines. a) What is ? b) If centimetre, then what is ? 4) The integers and are related as and. a) Write the expansion of. b) Find ?  Answer any 4 questions. Each carries 3 scores 5) Three equations are given below. a) What is ? b) Find and. 1 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS 6) The perpendicular distance from a vertex to the opposite side of an equilateral triangle is centimetre. a) What is the length of its side? b) Find the area of this triangle. 7) A point divides the median of a triangle in the ratio as in the figure. The line is parallel to. a) Write the special name of in a triangle. b) What is ? c) If centimetre then what is the length ? 8) a) Write the expansion of. b) Using this write as the sum of four terms. 9) and are the small angles of a right triangle. a) What is ? b) If then find the small angles of the triangle? 2 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS 10) Draw the equilateral triangle of perimeter centimetre. 11) Let’s see the patterns given below, ----------------------------------------------- a) Write the next line. b) Write as a fraction. c) Write the decimal form of.  Answer any 8 questions. Each carries 4 scores. 12) When 5-rupee and 10-rupee coins were counted, they added up to 80 rupees. Later, it was realized that the number of coins was wrong. When counted correctly, the total was 70 rupees. a) Write equations appropriately using this concept. b) Find the number of coins of each denomination? 13) Sum of two odd numbers is and the product is. If and are the numbers then, a) Expand. b) Calculate. 14) Three squares with areas of cm2, cm2 and cm2 are joined to form a triangle, as shown in the figure. 3 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS a) What are the length of its sides ? b) Calculate the approximate perimeter of the triangle? 15) In the figure‍ is a parallelogram. Mid point of is and Mid point of is. a) Is the shaded part a parallelogram? Why? b) Prove that. c) If centimetre, find‍ ? 16) are consecutive natural numbers. a) If then express‍ and in terms of. b) Find the difference between and. c) If then find‍. 17) is a parallelogram. The diagonals intersect at‍. a) Write the equations. b) Calculate and. c) Calculate the length of diagonals. 4 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS 18) A square is drawn on the altitude of an equilateral triangle. Perimeter of the triangle is 6centimeter. a) What are the lengths of the sides of the triangle? b) What is the area of square? c) Find the altitude of the triangle. 19) Draw an isosceles triangle with a perimeter of 13 centimeters, where the length of each equal side is the length of the shorter side. 20) Let’s see the pattern given below. a) Write 11 as the difference of two perfect squares. b) If , is an odd number and are consecutive natural numbers, then what is ? c) and are natural numbers , then what is 21) The sum of the digits of a two-digit number is 7. When the digits are reversed, the new two-digit number obtained is 27 more than the original number. a) If and are the digits then write the equation. b) Find the number by solving the equations. 22) The product of two natural numbers and their sum is. a) If and are numbers. Expand. b) Calculate. 5 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS  Answer any 6 questions. Each carries 5 scores 23) An object is moving along a straight line. It starts with an initial speed of , and its speed increases at a rate of. Using the data given below, calculate the initial speed and the rate of increase of speed. ▪ If the speed after seconds is related as ▪ Speed at seconds ▪ Speed‍ at seconds a) Write the equation using the given data. b) Find and. c) What will be the speed after 12 seconds? 24) In triangle , is the midpoint of and is the midpoint of. In triangle , is the midpoint of and is the midpoint of. a) If centimetre find ? b) If centimetre find ? c) If , what are the values of and ? d) Suggest a suitable name for. 6 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS 25) The rectangles in the figure have equal areas. a) Form the equations. b) Find and ? c) Write the sides of the rectangle in the middle. 26) Right triangles are drawn as shown in the figure. If counting the right triangles from the bottom,... a) What is the hypotenuse of first right triangle? b) What are the sides of second right triangle? c) What is the perpendicular sides of 10 th right triangle? d) What will be the area of square drawn on the hypotenuse of 10th right triangle. 27) Draw a regular hexagon with a perimeter of 20 centimetre. (Hint : Draw a line 10 cm long and divide it into three equal parts. Draw a circle with one of these segments as the radius. Then, draw the regular hexagon with vertices on this circle.) 7 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------  S A M A G R A PLUS 28) The diagonals of a square are perpendicular bisectors. It divide the square into four equal right triangles. In the figure, a right triangle is removed from a square of side metre. a) What is the hypotenuse of the removed right triangle ? b) What is the length of the diagonal of the square? c) Find the perimeter of the shape in the figure. 29) and forms a Pythagorean triplets for. a) Write the triples for. b) If the hypotenuse of a right triangle is 17, what is the length of its smallest side? c) If the middle number in the triplets is 399, then what is the largest number in the triplets ? 8 First Term Sample Practice Paper – Mathematics Ix -2024---------------------------------------------------