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A1 ST. FRANCIS SCHOOL, MT. POINSUR, BORIVALI (W), MUMBAI Sub: MATHEMATICS 1st ASSESSMENT EXAM 2016-17 Marks: 80 10 Class: X Time: 2 hrs Date: /08 /2016. _____________________________________________________________________________________________________ SECTION 1 Question 1 a) Divide 36,465 between A and B so that when their shares are lent out at 10% compound interest per year, the amount that A receives in 7 yrs is the same as what B receives in 5 years. (3 m) b) Solve the given inequation and graph the solution on the number line. (3 m) 2y 3 < y + 1 4y + 7, y R. c) The price of a TV set inclusive of sales tax of 9% is 13407. Find its marked price. If the sales tax is increased to 13%, how much more does the customer pay for the TV? (4 m) Question 2 a) If 8a 5b = 8a + 5b , prove that a = c. (3 m) 8c 5d 8c + 5d b d b) Using factor theorem, show that (x + 4) is a factor of (2x3 + 9x2 + x 12). Hence factorise the given expression completely. (3 m) c) The ages of A and B are in the ratio 7:8. Six years ago, their ages were in the ratio 5:6. Find their present ages. (4 m) Question 3 a) The model of a building is constructed with scale factor 1:30. (i) If the height of the model is 80 cm, find the actual height of the building in metres. (ii) If the actual volume of the tank on the top of the building is 27 m3, find the volume of the tank on the top of the model. (3 m) b) In the figure, PB and QA are perpendicular to the line segment AB. If PO = 6 cm, QO = 9 cm and the area of POB = 120 cm2, find the area of QOA. (3 m) P A O B Q 3 2 1 4 (4 m) 2x 1 c) Find x and y if + 2 4 5 = 4 2 y . Question 4 a) In the given figure, AB is a diameter of a circle with centre O and chord ED is parallel to AB and EAB = 650. Calculate: (i) EBA (ii) BED (iii) BCD. (3 m) E D C A B b) In the given figure, PQ and PR are two equal chords of a circle. Show that the tangent at P is parallel to QR. Q S R T P c) Show that equal chords of a circle subtend equal angles at the centre of the circle. (4 m) SECTION 2 Question 5 P1 Std 10 Mathematics 2015-16 (3 m) Page 1 of 2 a) Prove that: sin A + (1 + cos A) = 2 cosec A. (3 m) (1 + cos A) sin A b) The upper part of a tree broken by the wind, falls to the ground without being detached. The top of the broken part touches the ground at an angle of 360 30 at a point 5 m from the foot of the tree. Calculate: (i) the height at which tree is broken (ii) the actual height of the tree. (3 m) c) The cost of leveling a circular field at 2 per square metre is 33957. Calculate: (4 m) (i) The area of the field; (ii) the radius of the field (iii) the circumference of the field and (iv) the cost of fencing it at 2.75 per metre. Question 6 a) The marks obtained by a set of students in an examination are given below: (3 m) Marks 5 10 15 20 25 30 No of 6 4 6 12 x 4 students If the mean of the above data is 18, calculate the numerical value of x. b) Find the mean of 25 numbers, it being given that the mean of 15 of them is 18 and the mean of remaining ones is 13. (3 m) c) A bag contains 5 black balls, 7 blue balls, 4 white balls and 6 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is (i) red (ii) black or white (iii) not blue (iv) neither black nor blue. (4 m) Question 7 a) The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the step deviation method. (4 m) b) Using a graph paper, draw an Ogive for the following distribution which shows a record of the weight in kilogram of 200 students: (6 m) Weight 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 Frequenc 5 17 22 45 51 31 20 9 y Use your Ogive to estimate the following: (i) The percentage of students weighing 55 kg or more. (ii) The number of students who are (a) under weight and (b) over weight, if 55.70 kg considered as standard weight. Question 8 a) A sum invested at compound interest amounts to 6875 in 1 year and 8318.75 in 3 years. Calculate the rate percent and the sum. (3 m) b) A shopkeeper sells an article at its marked price, 7500 and charges sales tax at the rate of 12% from the customer. If the shopkeeper pays a VAT of 180; calculate the price(inclusive of tax) paid by the shopkeeper. (3 m) c) A Mathematics aptitude test of 50 students was recorded as follows: (4 m) Marks 50 60 60 70 70 80 80 90 90 100 No. of students 4 8 14 19 5 Draw a histogram for the above data using a graph paper and locate the mode. P1 Std 10 Mathematics 2015-16 Page 2 of 2
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