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Class 9 Saint Lawrence School, Tentoloi Half Yearly Examination 2021 Sub- Mathematics Date- 05.10.2021 Time 8am to 10am F.M - 80 -:General Instructions:1. Attempt all questions from section A and any four questions from section B. 2. All working including rough work must be clearly shown and must be done on the same sheet as the rest of the answer. 3. Omission of essential working will result in the loss of marks. 4. The intended marks for questions as parts of questions are given in brackets [ ] Section-A (40 marks) Q1). Q2). Q3). Q4). (a) Solve for x & y by substitution method. 3x - 7= & x + = 1 (b). The area of circular ring enclosed between two concentric is 286 cm2. Find the radii of the two circles given that their difference is 7 cm. (c). Factories the following. (i) (x2 - x) (4x2 - 4x - 5) - 6 (ii) a3 - a - 120 1 (a) If x=2+ , find the value of + x (b). Calculate the interest Rs 6000 in 3 years at 5% per annum compounded annually. (Without using formula) (c). In an isosceles ABC with AB=AC, the bisectors of B & C intersect each other at O. Show that : (i) OB = OC (ii) AO bisects A 1 1 1 2 2 (a) If ab + bc + ca = 0, Then find the value of :2 a bc b ac c ab (b). The ratio of incomes of two persons is 9:7 & the ratio of their expenditures is 4:3. If each of them manages to save Rs 2000 per month. Find their monthly incomes. (c). If O is any point in the interior of ABC prove that :- OA+OB+OC < AB+BC+CA 1 3 1 (a) If x2 + = 8 , Find x3 + 2 5 25 x 125 x 3 (b). The base of a triangular field is 3 times its height. If the cost of cultivating the field at the rate of Rs25 per 100m2 is Rs60,000. Find its base& the height. (c). ABCD is a parallogram.. E & F are the mid points of the sides AB & CD. Prove that AF & CE trisect the diagonal BD. SECTION-B Q5) (a) If x = 1 &y= 1 7 4 3 7 4 3 Then find the value of x2+y2 (b) If x + y =10, x2+y2=58. Then find the value of x3+y3 (c) The difference between CI & SI on Rs 6000 for 2 years is Rs 15 at the same rate of interest per year. Find the rate of interest. 3y 2x = . Then prove that 4x2 + 9y2 + 16z2 = (2x 3y +4z) (2x+3y+4z). 4z 3y (b) Factories (with process) = a3 + b3 + c 3 3abc 9 (c) A fraction becomes , if 2 is added to both the numerator and the denominator. If 3 is added to 11 5 both numerator and the denominator it becomes . Find the fraction. 6 Q6) (a) If Q7) (a) A In the figure AB = BC & AC = CD Prove that :- BAD : ADB = 3:1 B Q8) D C (b) The side of a square exceeds the side of another square by 3 cm. If the sum of the areas of the two squares is 549cm2, Find the ratio of their perimeters. (c) ABC is a triangle right angled at C. If M is the mid-point of the hypotenuse AB. 1 Then prove that CM= AB. 2 (a) Solve for x & y by cross multiplication method x y=a+b ax + by = a2 b2 (b) A sum of money is invested at compound interest payable annually. The interest in two successive years is Rs 225 & Rs 240. Find (i) The rate of interest (ii) The original sum (iii) The interest earned in the third year. (c) Prove that line segment joining the mid point of the diagonals of a trapezium is parallel to the parallel sides of the trapezium and is equal to the half of the difference of these sides. C Q9). (a) In the figure ABC is a quadrant of a circle of radius 28 cm & a semicircle is drawn with BC as the diameter. Find the area of the shaded region. A B a2 b2 c2 + + ab bc ac (c) Some amount is distributed equally among students. I f there are 8 student less everyone will get Rs. 10 more. If there are 16 students more everyone will get Rs. 10 less. What is the total amount distributed? 1 Q10) (a) Rationalize the denominator :7 3 2 (b) If the bisector of an angle of a triangle also bisects the opposite side. Prove that the triangle is isosceles. (c) Factories the following= (i) (x+4)2 5xy -20y 6y2 (ii) x4 14x2 +1 (b) If a + b + c =0, then find the value of :-
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