Find the matrix X if, X=B2 – 4B. At A construct an angle of 600 such that AC = 5 cm. ∠ed ∆CMO, we have OM2 = OC2 – CM2 = 132 – 52 = 169 – 25 = 144 0M = [latex]\sqrt{144}[/latex] = 12cm Hence, distance between the two chords NM = NO + OM = 5 + 12 = 17 cm. The product of their ages in years is 550. The rates of interest for two successive years are 12% and 15% respectively. Partager : 7 points exercice 1 1. a. Parmi les 13 519 dossiers, il y a 12 919 dossiers de foyers allocataires habitant la métropole. Hence, the mode of the given data is 46. [4] (b) In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. The time given at the head […] Hence, age of Vivek is 25 years and age of Amit is 22 years. Solution : (a) Minimum balance for the month Jan., 2016 = ₹ 5600 Minimum balance for the month Feb., 2016 = ₹ 4100 Minimum balance for the month Mar., 2016 = ₹ 4100 Minimum balance for the month Apr., 2016 = ₹ 2000 Minimum balance for the month May, 2016 = ₹ 8500 Minimum balance for the month June, 2016 = ₹ 10000 Total = ₹ 34300 Principal = ₹ 34300 Rate = 6% p.a. What is the probability that the card drawn is : [3] (i) a vowel (ii) a consonant (iii) none of the letters of the word median? (iii) Join the points A, B, C, D, D’, C’,B’ and A in order, so as to form a closed figure. Write down the equation of the line of symmetry of the figure formed. (ii) Find the equation of the line through G and parallel to AC. Attempt all questions from Section A and any four questions from Section B. Annales Maths Bac ES : tous les sujets et corrigés du Bac 2017 de mathématiques série ES, Obligatoire et Spé Maths, pour s'entraîner pour le bac 2021. [3] Solution : Let assumed mean (a) = 35 (b) Here PQ, is a tangent of the circle at A . The time given at the head of this Paper is the time allowed for writing the answers. (b) P(1, – 2) is a point on the line segment A(3, – 6) and B(x, y) such that AP : PB is equal to 2 : 3. مواضيع وحلول الدورة الاستثنائية. Each person must have 16 n? If the two ships are on the opposite sides of the light house, find the distance between the two ships. Join OA and OC. Thus, BD is a diameter of the circle. (a) A page from a savings bank account passbook is given below: [5] (i) Calculate the uterest for the 6 months from January to June 2016, at 6% per annum. ICSE Maths Previous Year Question Paper 2017 Solved for Class 10 General Instructions : Answers to this Paper must be written on the paper provided separately. A boy is asked to draw a card from the box. Ile mathématiques > maths bac > Bac 2017. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. 4. Draw angle bisector of ∠ABC, which is the required locus of the points equidistant from BA and BC. Construct the locus of : [4] (i) points equidistant from AB and AC. If the radius of the circle is 13 cm, find the distance between the two chords. [3] (i) Prove ∆PQR ~ ∆SPR (ii) Find the length of QR and PS (iii) [latex]\frac{\text { area of } \Delta \mathrm{PQR}}{\text { area of } \Delta \mathrm{SPR}}[/latex] (c) Mr. Richard has a recurring deposit account in a bank for 3 years at 7.5% p.a. It consists of a circle and two semi-circles each of which are of radius 5 cm. Question 3. Find : (i) VAT paid by the shopkeeper to the government. He further gives an off-season discount of 5% on the discounted price. 5. [3] Solution : (a) Here, b is the mean proportion between a and c. (b) Given equation is : 4x2 – 5x – 3 =0 By using quadratic formula, we obtain, (c) Here, O is the centre of the given circle of radius 13 cm. Sales tax (under VAT) is charged at the rate of 12% at every stage. 3. (b) A conical tent is to accommodate 77 persons. Answers to this Paper must be written on the paper provided separately. ∴ Coordinates of the centroid G of the ∆ABC are : G(2, 1) Here, line ‘l’ is drawn through G(2, 1) and parallel to the line AC. Time = [latex]\frac{1}{12}[/latex] year (b) (E) On graph , (ii) B’(- 2, 3), C’(- 1, 1), D’(- 2, 0) (iii) Equation of the line of symmetry is x = O, Question 8. The wholesaler allows a discount of 10% to the shopkeeper. (c) Prove that: [3] Solution : (a) Here, ∠DAE = 70° ∴ ∠BAD = 180° ∠DAE [a linear pair] = 180° – 70° = 110° ABCD is a cyclic quadrilateral ∴ ∠BCD + ∠BAD = 180° ∠BCD + 110° = 180° ⇒ ∠BCD = 180° – 110° = 70° Since angle subtended by an arc at the centre of a circle is twice the angle subtended at the remaining part of the circle. ∠ed ∆ANO, we have ON2 = 02 AN2 = 132 – 122 = 169 – 144 = 25 ON= [latex]\sqrt{25}[/latex] = 5cm Similarly, in it. List price of air conditioner = 45000 Discount = 10% Thus, VAT paid by the shopkeeper to the government = ₹ (5130 – 4860) = ₹ 270 Total amount paid by the customer = ₹ (42750 + 5130) = ₹ 47880, Question 9. 7. In ∆ACB, ∠ACB = ∠CAB = 30° Hence, ∆ABC is an isosceles triangle. (a) In the figure given, O is the centre of the circle. NESA 2017 HSC Mathematics General 2 Marking Guidelines . This time is to be spent in reading the question paper. Find the amount she must pay at the end of the second year to clear her debt. (a) If b is the mean proportion between a and c, show that: [3] (b) Solve the equation 4x2 – 5x – 3 = 0 and give your answer correct to two decimal places. Bac ST2S Remplacement Métropole 2017. Name the images as B’, C’, D’ respectively. Sujet Métropole 2017 Obligatoire et Spécialité. 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(a) Calculate the mean of the following distribution using step deviation method. (ii) If the account is closed on 1st July 2016, find the amount received by the account holder. (b) Given : QP = 8 cm, PR = 6 cm and SR = 3 cm In ∆PQR and ∆SPR ∠QPR = ∠PSR (given) ∠QRP = ∠SRP (common) ∴ ∆PQR ~ ∆SPR (by AA similarity rule) Since ∆PQR ~ ∆SPR. (ii) the lower quartile wage of workers. (ii) the total price to be paid by the customer for the computer set. Partager : Corrigé Bac ES-L Obligatoire et spécialité Remplacement Métropole 2017. Find matrix C where C is a 2 by 2 matrix. Question 1. Baccalauréat Mathématiques ES-L Obligatoire et spécialité Remplacement Métropole 2017 . (c) Here, number of students are 10 i.e., even number of observations. [4] (c) The marks of 10 students of a class in an examination arranged in ascending order is as follows : [3] 13, 35, 43, 46, x, x + 4, 55, 61, 71, 80 If the median marks is 48, find the value of x. Since ON⊥AB and 0M ⊥CD. Now, from the graph, we obtain: (i) median wage of the workers = ₹ 605 (ii) lower quartile wage of workers = ₹ 550 (iii) Number of workers who earn more than ₹ 625 daily = 80 – 50 = 30. ∴ M, O and N are collinear and M, N are mid-points of CD and AB. (c) Solve the following inequation and represent the solution set on a number line. ∴ Slope of the line l = Slope of the line AC [latex]\frac{-2-3}{3+1}[/latex] = [latex]\frac{-5}{4}[/latex] y – 1 = [latex](\begin{matrix} -5 \\ 4 \end{matrix}[/latex]) (x – 2) 4y – 4 = – 5x + 10 5x + 4y = 14. Now, in rt. Give your answer correct to three significant figures. ∠BAQ = 300. Question 2. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Hence, construct a circle touching the three sides of the triangle internally. Omission of essential working will result in the loss of marks. [4] (b) The daily wages of 80 workers in a project are given below Use a graph paper to draw an ogive for the above distribution. Join BC to get ∆ABC. If he gets ₹ 8325 as interest at the time of maturity, find : [3] (i) The monthly deposit (ii) The maturity value. ∴ ∠CAB = ∠BAQ = 300 Again, ∠PAC = 180° – ∠CAQ = 180°- 30°- 30° = 120° Also, AD is angle bisector of ∠PAC ∴ ∠PAD = ∠CAD = 600 Since angles in the corresponding alternate segment are equal ∴ ∠ADB =∠BAQ = 300 and ∠DBA = ∠PAD = 60° Also, angles in same segment are equal ∴ ∠DCA = ∠DBA = 600 and ∠ACB = ∠ADB = 30° Now, ∠DCB = ∠DCA + ∠ACB = 600 + 300 = 90° We know that angle in a semi-circle is right angle. Find the area of the shaded region. LDAE = 700. Total number of persons accommodated = 77 Volume of air required for each person = 16 m3 Volume of the conical tent = 77 × 16 = 1232 m3 Radius of the tent = 7 m Let h be the height of the conical tent, Using componendo and dividendo, we have [Using componendo and dividendo], Question 7. [3] (i) Find the coordinates of the centroid G of the triangle. (iii) the number of workers who earn more than ₹ 625 daily. Also, find his yield percent, to the nearest whole number. شهادة البكالوريا 2017 المواضيع و التصحيحات . Corrigé Bac S Métropole 2017 Obligatoire et Spécialité . Find the coordinates of B. You will not be allowed to write during the first 15 minutes. Solution: (a) Let Vivek’s age be x years ∴ Amit’s age = 47 – x Also, product of their ages = 550 ∴ x(47 – x) = 550 47x – x2 = 550 ⇒ x2 – 47x + 550 =0 ⇒ x2 – 25x – 22x + 550 = 0 ⇒ x(x – 25) – 22(x – 25) = 0 ⇒ (x – 25)(x – 22)= 0 ⇒ x = 25 or x = 22 Since Vivek is elder brother of Amit. [3] (c) Sixteen cards are labelled as a, b, c … m, n, o, p. They are put in a box and shuffled. Ile mathématiques > maths bac > Bac 2017. (b) Here, radius of a circle and two semi-circles = 5 cm Length of the rectangle = 5 + 10 + 5 = 20 cm Breadth of the rectangle = 10 cm Now, area of the shaded part = Area of rectangle – 2 × Area of circle (c) Given inequation is : Solution set on number line, SECTION B [40 Marks] Attempt any four questions from this Section, Question 5. Join them free hand to get the required ogive. Correction_Bac-physique-Math_2017.pdf - Google Drive ... Sign in Partager : Voir la correction. Since AB is angle bisector of ∠CAQ. Solution : Market value of a share = ₹ 60 Face value of a share = ₹ 50 Rate of dividend = 10% Total income = ₹ 450 If income is 5, then investment = ₹ 60 If income is 1, then investment = [latex]\frac{60}{5}[/latex] = ₹ 12 If income is 450, then investment = ₹ 12 × 450 = ₹ 54O0 Thus, total investment is ₹ 5480 ∴ Yield percent = [latex]\frac{450}{5400}[/latex] ×100 = 8.33 = 8 (to the nearest whole number) (c) Total number of cards = 16 (i) Number of vowels = 4 (a, e, i, o) Probability = [latex]\frac{4}{16}[/latex] = [latex]\frac{1}{4}[/latex] (ii) Numberofeonsonant = 16 – 4 = 12 Probability = [latex]\frac{12}{16}[/latex] = [latex]\frac{3}{4}[/latex] (iii) Probability (none of the letters of the word median) = [latex]\frac{10}{16}[/latex] = [latex]\frac{5}{8}[/latex], Question 6. Thus, the monthly deposit is ₹ 2000 The maturity value = ₹ 36 × 2000 + ₹ 8325 = ₹ 72000 + ₹ 8325 = ₹ 80325. She repays ₹ 33000 at the end of the first year. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area. There was a problem previewing this document. (a) The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. [3] Solution: (a) Let p(x) = 16x3 – 8x2 + 4x + 7 and g(x) = 2x + I Put 2x + 1 = 0 ⇒ x = – [latex]\frac{1}{2}[/latex], Hence, 1 is subtracted from p(x), so that g(x) is a factor of p(x). Question 29 (b) Criteria Marks • Provides correct solution 3 • Makes significant progress towards correct solution 2 • Makes progress towards correct solution 1 . AB and CD are two parallel chords, such that AB = 24 cm and CD = lo cm. Partager : Voir la correction. Let the two angle bisectors intersect each other in I. (a) The sum of the ages of Vivek and his younger brother Amit is 47 years. [3] Solution : (b) Here, A = [latex]\begin{bmatrix} 1 & 3 \\ 3 & 4 \end{bmatrix}[/latex] and B = [latex]\begin{bmatrix} -2 & 1 \\ -3 & 2 \end{bmatrix}[/latex] Now, A2 = AA B2 = BB Again, 5C = A2 – 5B2, (c) Principal = ; 50000 Time =1 year Rate = 12%. Find giving suitable reasons, the measure of: [4] (i) ∠BCD (ii) ∠BOD (iii) ∠OBD, (b) A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle. (a) The catalogue price of a computer set is 42000. (C) The printed price of an air conditioner is ₹ 45000/-.

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