مواضيع وحلول الدورة الاستثنائية. [4] Hence, solve for a and b given (b) How much should a man invest in 50 shares selling at 60 to obtain an income of 450, if the rate of dividend declared is 10%. 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? This time is to be spent in reading the question paper. 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. This time is to be spent in reading the question paper. [3] Solution : Let assumed mean (a) = 35 (b) Here PQ, is a tangent of the circle at A . Bac ST2S Remplacement Métropole 2017. ∴ M, O and N are collinear and M, N are mid-points of CD and AB. Ile mathématiques > maths bac > Bac 2017. Hence, age of Vivek is 25 years and age of Amit is 22 years. The rates of interest for two successive years are 12% and 15% respectively. [3] (i) Find the coordinates of the centroid G of the triangle. The wholesaler allows a discount of 10% to the shopkeeper. of air to breathe. S is a point on the side QR of ∆PQR such that ∠PSR = ∠QPR. 6. Hence, the mode of the given data is 46. 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. Hence, construct a circle touching the three sides of the triangle internally. Omission of essential working will result in the loss of marks. Find the matrix X if, X=B2 – 4B. ∴ 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. Partager : Corrigé Bac ES-L Obligatoire et spécialité Remplacement Métropole 2017. (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. 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. You will not be allowed to write during the first 15 minutes. Let the two angle bisectors intersect each other in I. In ∆ACB, ∠ACB = ∠CAB = 30° Hence, ∆ABC is an isosceles triangle. Find the coordinates of B. (a) Calculate the mean of the following distribution using step deviation method. Sujet Métropole 2017 Obligatoire et Spécialité. Question 4. If he gets ₹ 8325 as interest at the time of maturity, find : [3] (i) The monthly deposit (ii) The maturity value. Solution: (a) Let PQ be the light house of height 60m, A and B are the two ships on the opposite sides of the light house, such that: ∠PAQ = 60°, ∠PBQ = 45° In rt ∠ed ∆PQB, we have. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. Partager : Voir la correction. Attempt all questions from Section A and any four questions from Section B. Find the amount she must pay at the end of the second year to clear her debt. [4] (b) PQR is a triangle. (a) The sum of the ages of Vivek and his younger brother Amit is 47 years. [3] (c) If [latex]\frac{7 m+2 n}{7 m-2 n}[/latex] = [latex]\frac{5}{3}[/latex] , use properties of proportion to find : (i) m : n (ii) [latex]\frac{m^{2}+n^{2}}{m^{2}-n^{2}}[/latex] Solution : (a) Steps of Construction : 1. AB and CD are two parallel chords, such that AB = 24 cm and CD = lo cm. Question 10. . Give your answer correct to three significant figures. (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. 3. ∠ed ∆ANO, we have ON2 = 02 AN2 = 132 – 122 = 169 – 144 = 25 ON= [latex]\sqrt{25}[/latex] = 5cm Similarly, in it. If the radius of the circle is 13 cm, find the distance between the two chords. [latex]\frac{\mathrm{PQ}}{\mathrm{QB}}[/latex] = tan 45° = 1 ⇒ PQ =QB = 60 m In rt ∠ed ∆PQA, we have Now, AB = AQ + QB = 60 + 34.6 = 94.6m Hence, the distance between the two ships is 95 m (nearest to whole number). Find matrix C where C is a 2 by 2 matrix. Answers to this Paper must be written on the paper provided separately. (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. ∠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. شهادة البكالوريا 2017 المواضيع و التصحيحات . He further gives an off-season discount of 5% on the discounted price. She repays ₹ 33000 at the end of the first year. Find : (i) VAT paid by the shopkeeper to the government. The time given at the head of this Paper is the time allowed for writing the answers. (b) Use a graph paper for this question (Take 2 cm =1 unit on both x and y axis) [5] (i) Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0). [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. Give your answer correct to the nearest whole number. (b) A conical tent is to accommodate 77 persons. Section A [40 marks] (Answer all questions from this Section). 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. 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. [4] (c) AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. You will not be allowed to write during the first 15 minutes. [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. 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. Since AB is angle bisector of ∠CAQ. (ii) Find the equation of the line through G and parallel to AC. (b) The cumulative frequency distribution for the given data is : Plot the points (450, 2), (500, 8), (550, 20), (600, 38), (650, 62), (700, 75), (750, 80). (c) Here, number of students are 10 i.e., even number of observations. (ii) If the account is closed on 1st July 2016, find the amount received by the account holder. (b) Here, AP : PB = 2 : 3, therefore, P divides AB in the ratio 2 : 3 Thus, coordinates of P are: Also, coordinates of P are P(1, – 2) Hence, coordinates of B are B ( – 2, 4). 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. [3] (c) Sixteen cards are labelled as a, b, c … m, n, o, p. They are put in a box and shuffled. Find their ages. [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. (C) The printed price of an air conditioner is ₹ 45000/-. Draw angle bisector of ∠ABC, which is the required locus of the points equidistant from BA and BC. Each person must have 16 n? Question 11. Join them free hand to get the required ogive. [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). (Use a scale of 2 cm = ₹ 50 on x-axis and 2 cm = 10 workers on y-axis. However, sales tax at 8% is charged on the remaining price after the two successive discounts. Corrigé Bac S Métropole 2017 Obligatoire et Spécialité . Ile mathématiques > maths bac > Bac 2017. Partager : 7 points exercice 1 1. a. Parmi les 13 519 dossiers, il y a 12 919 dossiers de foyers allocataires habitant la métropole. The shopkeeper gives a discount of 10% on the listed price. The intended marks for questions or parts of questions are given in brackets. Find: [3] (i) the amount of sales tax a customer has to pay. [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%. ∴ ∠OBD =∠ODB Thus, ∠OBD = [latex]\frac{1}{2}[/latex] (180° – ∠BOD) = [latex]\frac{1}{2}[/latex] (180° – 140°) = [latex]\frac{1}{2}[/latex] × 40° = 20° (b) A(-1, 3), B(4, 2) and C(3, -2) are the vertices of ∆ABC. Thus, the observations are 13, 35, 43, 46, 46, 50, 55, 61, 71, 80. Write down the equation of the line of symmetry of the figure formed. The time given at the head […] ∴ ∠BOD = 2∠BCD = 2 × 70° = 140° In ∆OBD, OB = OD = radii of same circle. Hence, find the mode of the given data Solution : Hence, amount of sales tax is ₹ 2872.80 and total price to be paid by the customer for the computer set is ₹ 38782.80. Question 29 (b) Criteria Marks • Provides correct solution 3 • Makes significant progress towards correct solution 2 • Makes progress towards correct solution 1 . (c) Solve the following inequation and represent the solution set on a number line. Retrying... Retrying... Download (ii) Reflect points B, C, D on the y-axis and write down their coordinates. [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. ∠BAQ = 300. [4] (b) In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. (ii) the lower quartile wage of workers. (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. 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. 7. Use your ogive to estimate: (i) the median wage of the workers. Draw a line segment AB = 7 cm. 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. Construct the locus of : [4] (i) points equidistant from AB and AC. 4. At A construct an angle of 600 such that AC = 5 cm. A boy is asked to draw a card from the box. (ii) ABC is an isosceles triangle. Also, find his yield percent, to the nearest whole number. Through I, draw ID⊥AB. [3] (b) In the given figure ABCD is a rectangle. Since ON⊥AB and 0M ⊥CD. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area. Baccalauréat Mathématiques ST2S Remplacement Métropole 2017 . All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. (a) Evaluate without using trigonometric tables, [3] sin228° + sin262° + tan238° – cot252° + sec230° (b) If A = [latex]\begin{bmatrix} 1 & 3 \\ 3 & 4 \end{bmatrix}[/latex] and B = [latex]\begin{bmatrix} -2 & 1 \\ -3 & 2 \end{bmatrix}[/latex] and A2 – 5B2 = 5C. (iii) the number of workers who earn more than ₹ 625 daily. (a) What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor? 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. (ii) points equidistant from BA and BC. (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. If the two ships are on the opposite sides of the light house, find the distance between the two ships. ∴ ∠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. Join OA and OC. NESA 2017 HSC Mathematics General 2 Marking Guidelines . (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. Question 3. (a) In the figure given, O is the centre of the circle. It consists of a circle and two semi-circles each of which are of radius 5 cm. With I as centre and radius = ID draw a circle which touches all the sides of the ∆ABC internally. (ii) The total amount paid by the customer inclusive of tax. Sales tax (under VAT) is charged at the rate of 12% at every stage. (a) The catalogue price of a computer set is 42000. Partager : Voir la correction. Correction_Bac-physique-Math_2017.pdf - Google Drive ... Sign in ∴ 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. 2. Draw angle bisector of ∠BAC, which is the required locus of the points equidistant from AB and AC. (a) Using a ruler and a corrpass construct a triangle ABC in which AB = 7 cm, ∠CAB = 600 and AC = 5 cm. Sample answer: Tax payable = 3572 + 0.325(86 725 – 37 000) = $19 732.63 Medicare levy = 2% × 86 725 = $1734.50 LDAE = 700. Name the images as B’, C’, D’ respectively. (c) Let the monthly deposit be ₹ x Time = 3 years or 36 months, R = 7.5%, Interest = ₹ 8325. Baccalauréat Mathématiques ES-L Obligatoire et spécialité Remplacement Métropole 2017 .

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