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4) 52,320 X 0.6375 + 127,460 X 0.9625 = £ 33,354 + £ 122,680 5s = £ 156,034.25 Average rate = £ 156,034.25 ⟦line⟧ £ 52,320 + £ 127,460 = £ 156,034.25 ⟦line⟧ £ 179,780 = £ 0.8679 = £ 1 17s 4 1/4 d to nearest farthing
IJA 2550
Exams, Shamash Secondary School
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These are exam materials from the Shamash Secondary School in Baghdad. They include fourth year exams in arithmetic, trigonometry, and algebra, 1954 and 1957-1970, with handwritten answer keys. There are handwritten notes for one undated English exam. Included are final, mid-year, monthly, quarterly, and conditional exams as well as some monthly quizzes.
AI en Translation, Pages 226-250
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Shamash Secondary School Final Examination, May, 1967. Subject: Arithmetic & Trigonometry Date: 17/5/1967 Class: 4th Year Secondary. Time: 8:00 - 10:30 a.m. ⟦line⟧ Answer five questions which must include questions 2 & <del>5</del> 3. 1. (a) How much stock is obtained by investing £2,286 in a 4½ per cent stock at 95¼? After receiving the first annual dividend on this stock, it is immediately resold at 98. Calculate the total gain on the transaction. (b) I have a watch which gains six minutes in every true hour. I put the watch right at 8.30 a.m. What is the latest time indicated by the watch at which I must set out to catch a train which leaves at 10.25 a.m. if it takes me 15 minutes to walk to the station ? 2. Following a storm, water is pumped out of a flooded area through a pipe of 8 in. diameter at the rate of 1,000 gallons per minute. Taking 1 cu.ft. as 6¼ gallons and <del>⟦illegible⟧</del> π as 22/7 , calculate: (a) the speed in ft. per sec. at which the water is passing through the pipe. (b) how many tons of sediment will be pumped out in two days if it is known that the flood water contains ½ oz. of sediment in every cu.ft. of water. 3. A merchant bought 15 tons of potatoes from a farmer at £18 per ton. (a) He sold 4 ton 12 cwt of the potatoes in 1 cwt bags at £1 5s. per bag. The additional cost to the merchant in selling the potatoes in this way was 6s. 3d. per ton. (b) He sold 15 cwt retail at 4d. per lb for which he incurred additional labour costs of £5 10s. (c) He sold the remainder of the potatoes in bulk at £20 per ton. Calculate: (i) the merchant's total costs, including the initial cost of the potatoes, cost of selling the potatoes in bags, and additional labour cost for the retail sales. (ii) the total amount the merchant received from his sales. (iii) the merchant's profit calculated as a percentage, correct to 2 significant figures, of his total costs. 4. A borough is divided into two districts whose rateable values are respectively £52,320 and £127,460. The rate in the first district is 12s. 9d. in the £, and in the second district it is 19s. 3d. in the £. Find the average rate for the whole borough to the nearest farthing. (cont'd.p.2)..
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(cont'd.).. -p.2- Arith. & Trig. 17/5/67 4th Year Secondary. ⟦line⟧ 5. ABC is a triangle with AB = AC = 100 ft. and the angle BAC is 70°. At A is a vertical pole AO = 80 ft. high. Calculate: (i) the length of BC, (ii) the angle of elevation of the top of the pole from B, (iii) the angle of elevation of the top of the pole from the mid-point of BC. 6. A, B and C are three points on a coastline which runs from north to south; B is south of A and C is 1000 yards south of B. A boat is moving in a straight line towards C and when it is at a point P which is 2000 yd. from A on a bearing of (N.60.E.) its bearing from B is ( N.38E.). Calculate: (a) the distance from P to the nearest point X on the coastline. (b) the distance AB. (c) the bearing of P from C. ⟦line⟧
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Shamash Secondary School Final Examination, May, 1967. Subject: Arithmetic & Trigonometry Date: 17/5/1967 Class: 4th Year Secondary. Time: 8:00 - 10:30 a.m. ⟦line⟧ ⟦2 3⟧ Answer five questions which must include questions 2 & 5. 1. (a) How much stock is obtained by investing £2,286 in a 4½ per cent stock at 95¾? After receiving the first annual dividend on this stock, it is immediately resold at 98. Calculate the total gain on the transaction. (b) I have a watch which gains six minutes in every true hour. I put the watch right at 8.30 a.m. What is the latest time indicated by the watch at which I must set out to catch a train which leaves at 10.25 a.m. if it takes me 15 minutes to walk to the station ? 2. Following a storm, water is pumped out of a flooded area through a pipe of 8 in. diameter at the rate of 1,000 gallons per minute. Taking 1 cu.ft. as 6¼ gallons and π as 22/7 , calculate: (a) the speed in ft. per sec. at which the water is passing through the pipe. (b) how many tons of sediment will be pumped out in two days if it is known that the flood water contains ½ oz. of sediment in every cu.ft. of water. 3. A merchant bought 15 tons of potatoes from a farmer at £18 per ton. (a) He sold 4 ton 12 cwt of the potatoes in 1 cwt bags at £1 5s. per bag. The additional cost to the merchant in selling the potatoes in this way was 6s. 3d. per ton. (b) He sold 15 cwt retail at 4d. per lb for which he incurred additional labour costs of £5 10s. (c) He sold the remainder of the potatoes in bulk at £20 per ton. Calculate: (i) the merchant's total costs, including the initial cost of the potatoes, cost of selling the potatoes in bags, and additional labour cost for the retail sales. (ii) the total amount the merchant received from his sales. (iii) the merchant's profit calculated as a percentage, correct to 2 significant figures, of his total costs. 4. A borough is divided into two districts whose rateable values are respectively £52,320 and £127,460. The rate in the first district is 12s. 9d. in the £, and in the second district it is 19s. 3d. in the £. Find the average rate for the whole borough to the nearest farthing. (cont'd.p.2)..
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(cont'd.).. -p.2- Arith. & Trig. 17/5/67 4th Year Secondary. ⟦line⟧ 5. ABC is a triangle with AB = AC = 100 ft. and the angle BAC is 70°. At A is a vertical pole AO = 80 ft. high. Calculate: (i) the length of BC, (ii) the angle of elevation of the top of the pole from B, (iii) the angle of elevation of the top of the pole from the mid-point of BC. 6. A, B and C are three points on a coastline which runs from north to south; B is south of A and C is 1000 yards south of B. A boat is moving in a straight line towards C and when it is at a point P which is 2000 yd. from A on a bearing of (N.60.E.) its bearing from B is ( N.38E.). Calculate: (a) the distance from P to the nearest point X on the coastline. (b) the distance AB. (c) the bearing of P from C. ⟦line⟧
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Shamash Secondary School Final Examination, May, 1967. Subject: Arithmetic & Trigonometry Date: 17/5/1967 Class: 4th Year Secondary. Time: 8:00 - 10:30 a.m. ⟦line⟧ Answer five questions which must include questions 2 & ⟦3⟧ 5. 1. (a) How much stock is obtained by investing £2,286 in a 4½ per cent stock at 95¼? After receiving the first annual dividend on this stock, it is immediately resold at 98. Calculate the total gain on the transaction. (b) I have a watch which gains six minutes in every true hour. I put the watch right at 8.30 a.m. What is the latest time indicated by the watch at which I must set out to catch a train which leaves at 10.25 a.m. if it takes me 15 minutes to walk to the station ? 2. Following a storm, water is pumped out of a flooded area through a pipe of 8 in. diameter at the rate of 1,000 gallons per minute. Taking 1 cu.ft. as 6¼ gallons and π as 22/7, calculate: (a) the speed in ft. per sec. at which the water is passing through the pipe. (b) how many tons of sediment will be pumped out in two days if it is known that the flood water contains ½ oz. of sediment in every cu.ft. of water. 3. A merchant bought 15 tons of potatoes from a farmer at £18 per ton. (a) He sold 4 ton 12 cwt of the potatoes in 1 cwt bags at £1 5s. per bag. The additional cost to the merchant in selling the potatoes in this way was 6s. 3d. per ton. (b) He sold 15 cwt retail at 4d. per lb for which he incurred additional labour costs of £5 10s. (c) He sold the remainder of the potatoes in bulk at £20 per ton. Calculate: (i) the merchant's total costs, including the initial cost of the potatoes, cost of selling the potatoes in bags, and additional labour cost for the retail sales. (ii) the total amount the merchant received from his sales. (iii) the merchant's profit calculated as a percentage, correct to 2 significant figures, of his total costs. 4. A borough is divided into two districts whose rateable values are respectively £52,320 and £127,460. The rate in the first district is 12s. 9d. in the £, and in the second district it is 19s. 3d. in the £. Find the average rate for the whole borough to the nearest farthing. (cont'd.p.2)..
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(cont'd.).. -p.2- Arith. & Trig. 17/5/67 4th Year Secondary. ⟦line⟧ 5. ABC is a triangle with AB = AC = 100 ft. and the angle BAC is 70°. At A is a vertical pole AO = 80 ft. high. Calculate: (i) the length of BC, (ii) the angle of elevation of the top of the pole from B, (iii) the angle of elevation of the top of the pole from the mid-point of BC. 6. A, B and C are three points on a coastline which runs from north to south; B is south of A and C is 1000 yards south of B. A boat is moving in a straight line towards C and when it is at a point P which is 2000 yd. from A on a bearing of (N.60.E.) its bearing from B is ( N.38E.). Calculate: (a) the distance from P to the nearest point X on the coastline. (b) the distance AB. (c) the bearing of P from C. ⟦line⟧ ⟦illegible⟧ ⟦illegible⟧ 19.7767 ft. ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧
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Solution to Arithmetic + Trig Exam. Mid-year Exam., Jan., 29th 1967 4th Year. ⟦Diagram of a right-angled triangle with hypotenuse 24 ft, angle 52, height a, base b⟧ a = 24 sin 52 = 24 x 0.7880 = 18.912 ft b = 24 cos 52 = 24 x 0.6157 = 14.7768 ft. 18.912 - 2 = 16.912 ft sin θ = 16.912 / 24 = 0.7047 ∴ θ = 44° 48' ⟦Diagram of a right-angled triangle with hypotenuse 24, angle θ, height 16.912, base b'⟧ b' : 24 cos 44° 48' = 24 x 0.7096 = 17.0304 17.0304 14.7768 ⟦line⟧ 2.2536 ft ⟦line⟧ 2.25 ft.
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2. (i) tan θ = 6/20 = 0.3000 ∴ θ = 16° 42' 63. 60' 58 42 16 18" 47 x = 20 tan 47° 18' = 20 x 0.8920 = 19.84 ft 20 x 1.0837 19.84 + 6 = 25.84 ft 21.674 6 27.674 (ii) 8 x 50 = 400 ft² 400 cot 27 = 400 x 1.9626 = 785.04 ft² ⟦illegible⟧
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Solution to Mid-year exam. in Arithmetic ⟦illegible⟧ 4th Year, ⟦February⟧ Jan., 29th 1967 (a) +32,000 / 540,000 = £ 0.8 or 16 s (b) £ 63 x 0.8 = £ 50.4 or £ 50 8 s (c) 540,000 / 240 = £ 2250 4 Let radius of whole roll = r inches π r² - 9 π = 4800 x 12 x 1/120 = 480 π r² = 480 + 9 π r² = 480/π + 9 = 480/3.1416 + 9 = 152.79 + 9 = 161.79 r = 12.72 inches. 5) 990 x 20 / 27 1/2 = 990 x 20 x 2 / 55 = 720 (£ 1) shares 720 x 32 s = £ 720 x 1.6 = £ 1,152 he realized from the sale 1152 x 20 / 9 = 2560 (10 s) shares he bought Change of income: Income from (£ 1) shares = 720 x 10 / 100 = £ 72 " " (10 s) = 2560/2 x 5/100 = £ 64 Income decreased by £ 72 - £ 64 = £ 8
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6) 6000 : 4000 = 3 : 2. At end of 1st year B's profit = 1400 / 5 X 2 = £ 560 At beginning of 2nd year B's capital = £ 4,560 At end " " " B's profit = 1584 X 4,560 / 10,560 = £ 684 At beginning of 3rd year B's capital = £ 4,560 + £ 684 = £ 5,244 At the end of 3rd year B's profit = (1639 15s) 5,244 / 11,244 = £ 764.75 At the end of 3rd year B's capital is £ 5,244 + £ 764.75 = £ 6008.75 or £ 6008 15s - ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧
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Salwa Ezra Sweigh (11) Shamash Secondary School Mid-Year Exam. January, 1967 Subject: Arith. & Trig. Date: Jan. 29, 1967 Class: 4th Year Secondary. Time: 8:30 - 10:30 a.m. ⟦line⟧ Answer five questions which must include question 2. 1. A ladder, 24 ft. long, makes an angle of 52° with the ground and leans against a vertical wall. If the top of the ladder slips down 2 ft., how far will the foot of the ladder move ? 2. (i) The point C is 6 ft. above level ground and 20 ft. measured horizontally from a vertical pole AB where B is at ground level. If the angle ACB = 64°, calculate the length of AB. (ii) A vertical wall of length 50 ft. and height 8 ft. runs due N and S. Find the area of the shadow of the wall cast on level ground by the sun shining from the W at an elevation of 27°. 3. The total rateable value of a town is £540,000 and it is estimated that the necessary expenditure for 1959 will amount to £432,000. Calculate: (a) The rate in the £ which must be charged to meet the 1959 expenditure. (b) The rates to be paid on a house whose rateable value is £63. (c) The amount produced by a penny rate. 4. A length of 4800 ft. of paper is wrapped on a wooden cylinder of radius 3 in.; the thickness of the paper is 1/120 in. Find the radius of the whole roll to 1/100 in. 5. A man invested £990 in (£1) shares, paying 10%, at 27s. 6d.; he sold the shares at 32s. and invested the proceeds in (10s.) shares, paying 5%, at 9s. How many (10s.) shares did he buy and what was the change of his annual income ? 6. Two partners A, B started with capitals of £6000, £4000 respectively. The profits at the end of each year are divided in proportion to their capitals invested in the business at the beginning of the year. A withdrew his profits at the end of each year, while B left his in the business. The profits for the first 3 years were £1400, £1584, £1639 15s. respectively. What was B's capital at the end of 3 years? ⟦line⟧
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Let x be the amount invested in £. 2 3/4% Stock purchased = £ (x * 100) / 95 3 1/2% Stock purchased = £ ( (100 x / 95) - 900). Since his income remained the same (100 x / 95) * (2 3/4 / 100) = ( (100 x / 95) - 900) * (3 1/2 / 100) x / 95 * 11/4 = ( (x / 95) - 9) 7/2 = 7x / 2 * 95 - (7 * 9 * 100) / (2 * 95) ⟦line⟧ <del>⟦illegible⟧</del> <del>⟦illegible⟧</del> 7x / 2 * 95 - 11x / 4 * 95 = (7 * 900) / (2 * 95) 14x - 11x = 7 * 1800 3x = 7 * 1800 x = 7 * 600 = £ 4200 1.5 x = 7 * 855 x = (7 * 855 * 2) / 3 = £ 3990 285 14 ⟦line⟧ 1140 285 ⟦line⟧ 3990 ⟦line⟧ ⟦line⟧ Now the correct clock would ⟦illegible⟧ after 120 ⟦illegible⟧ days of correct time The first clock will therefore read 1 hr ⟦illegible⟧ + 6 hours ⟦illegible⟧ The slower clock will read the
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Download (a) (i) Area of surface of sphere = 4 π r² (ii) Volume of sphere = 4/3 π r³ (iii) Area of curved surface of a cone = π r l (iv) Volume of a cone = 1/3 π r² h (v) Area of trapezium = (a+b) h / 2 (b) Volume of bar = 15" x 9" x 8" cubic inches Net volume (after allowing for 10% loss = 15 x 9 x 8 x 9 / 10 cubic inches Volume of a sphere = 4/3 x 3.142 x 27/8 = 1.571 x 9 cubic inches. No. of spheres = 15 x 9 x 8 x 9 / 10 x 9 x 1.571 = 68 spheres Wt. of 68 spheres = 320/1728 x 68 x 1.571 x 9 = 5474.935 / 12 = 456 lb to nearest lb. 205 17 ⟦line⟧ 1435 205 ⟦line⟧ 3485 1.571 ⟦line⟧ 3485 24395 17425 3485 ⟦line⟧ 5474.935 456.2 12 ) 5474.935 67 74 29 Left / Abandoned Between 4 p.m Friday and noon the following Wednesday = there ⟦are⟧ 4 5/6 days The fast clock gains 3 x 4 5/6 = 14 1/2 minutes The slow " loses 2 1/2 x 4 5/6 = 12 1/12 " Difference between them = 14 1/2 + 12 1/12 (1) = 26 7/12 minutes Difference per day = 5 1/2 minutes The two clocks will show the same time again when the difference between them has become 12 hours or 12 x 60 = 720 min 720 / 5 1/2 = 720 x 2 / 11 = 130 10/11 days. 11 ) 1440 The fast clock gains 3 minutes per day It will gain 3 x 130 10/11 minutes in 130 10/11 days = 4320 / 11 minutes = 392 8/11 minutes = 6 hours and 32 8/11 minutes Now the correct clock would <del>show</del> read after 130 10/11 days of correct time 1 hr 49 1/11 min p.m The fast clock will therefore read 1 hr 49 1/11 min. + 6 hours 32 8/11 min = 8 hours 21 9/11 minutes p.m The slow clock will read the same.
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Left blank ③ 21 s 10 d + 9 s = 30 s 10 d or 30 5/6 s = 185/6 s Cost per year = £ 44 x 185 / 6 x 20 Average cost per week = £ 44 x 185 / 6 x 20 x 52 = 11 x 37 / 6 x 52 = 1.3045 = £ 1 6 s 1 d Income from investment = £ 3300 x 2.5 / 100 = £ 82.5 Garage rent = 7.5 x 52 / 20 = £ 19.5 Total expenditure = £ 126 + £ 19.5 = £ 145.5 £ 145.5 - £ 82.5 = £ 63 net expenditure He saves £ 44 x 185 / 6 x 20 = £ 67 5/6 = £ 67 5/6 - £ 63 = £ 4 5/6 = £ 4 100/6 s = £ 4 16 2/3 s = £ 4 16 s 8 d ⟦illegible⟧ ⟦illegible⟧ after 150 days of ⟦illegible⟧ ⟦illegible⟧ The first ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧ ⟦illegible⟧ The are two clocks, one of which gains 2 minutes, while the other loses 2 1/2 minutes each day. They are set right at 4 o'clock on Friday afternoon. What is the difference between them at noon on the following Wednesday? In how many days from the time they are set <del>at noon on the</del> right will they both show ⟦the same⟧ time? ⟦What⟧ what ⟦will⟧ that time be? Two clocks are set right simultaneously at 12 noon; one of which loses 6 sec. in hour, and the other gains 3 sec. in 50 min. (a) How long will it be before the minute hands are again in the same direction? (b) What will then be the time am. or P.m. by each clock? (c) When will both clocks simultaneously indicate correct time? 240
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SHAMASH SECONDARY SCHOOL Final Examination, May 1966 Subject: Arithmetic & Trigonometry Date: 18.5.1966 Class: 4th Year Secondary Time: 8:00-10:30 a.m. ⟦line⟧ Attempt five questions only including question (4). 1. A person, having bought a certain amount of 2¾% stock at 95, afterwards sold it, and with the proceeds bought 3½% stock. He obtained £900 less stock than before, but his income was unchanged. How much money did he originally invest? (20 marks) 2. A house holder owns his house which has a rateable value of £44 on which the annual rates are charged at 21s 10d in the £1. He also has to pay an annual property tax at the rate of 9s in the £ on an assessment of £44. Calculate, correct to the nearest penny, the average cost per week of the total of these charges, taking a year as 52 weeks. He subsequently sells his house for £3300, which sum he invests at the rate of 2½% per annum free of tax, and moves into a flat which he rents at £126 per annum. He has however to rent a garage for his car at 7s 6d per week. Find how much per annum he saves by the change. (20 marks) 3. (a) A watch was 5 minutes fast at 9 a.m. on Monday, and 10 minutes slow at 12 noon on the following Wednesday. Find when it was exactly right, assuming that it lost time uniformly. Note: (9 a.m. and 12 noon are correct time). (10 marks) (b) Two clocks sound the first stroke of 12 o'clock at the same instant; one clock allows an interval of 20 secs. between each stroke and the next, and the other allows 25 secs. How many strokes of the slower clock remain after the quicker one has finished striking, and what time will elapse between the 12th stroke of the quicker one and the following stroke of the slower one? (10 marks) 4. (a) A solid consists of a hemisphere, radius 8 cm., joined to a cone of the same base-radius and height 6 cm., so that the plane surfaces coincide. Find (i) the volume, (ii) the total area of the surface of the solid. (Give answer to 3 significant figures). (10 marks) (b) A sphere of radius 3 in. is filed down into the greatest possible cube; find the volume of the material removed. (Give answer to 4 significant figures). (10 marks) 5. Find the difference between the perimeters of a regular pentagon and a regular hexagon, each of which has an area of 24 square inches. (20 marks) 6. In response to an S O S call from a ship at A, another ship at B, 175 miles due east of A, starts toward A at a speed of 12 miles per hour. At the same time a third ship at C, which is 186 miles from B in a direction bearing ⟦30⟧° 15' west of north, also starts for A at a speed of 16 miles per hour. Which ship will reach A first, and how long will it take ? (20 marks) ⟦line⟧
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SHAMASH SECONDARY SCHOOL Final Examination, May 1966 Subject: Arithmetic & Trigonometry Date: 18.5.1966 Class: 4th Year Secondary Time: 8:00-10:30 a.m. Attempt five questions only including question (4). 1. A person, having bought a certain amount of 2¾% stock at 95, afterwards sold it, and with the proceeds bought 3½% stock. He obtained £900 less stock than before, but his income was unchanged. How much money did he originally invest? (20 marks) 2. A house holder owns his house which has a rateable value of £44 on which the annual rates are charged at 21s 10d in the £1. He also has to pay an annual property tax at the rate of 9s in the £ on an assessment of £44. Calculate, correct to the nearest penny, the average cost per week of the total of these charges, taking a year as 52 weeks. He subsequently sells his house for £3300, which sum he invests at the rate of 2½% per annum free of tax, and moves into a flat which he rents at £128 per annum. He has however to rent a garage for his car at 7s 6d per week. Find how much per annum he saves by the change. (20 marks) 3. (a) A watch was 5 minutes fast at 9 a.m. on Monday, and 10 minutes slow at 12 noon on the following Wednesday. Find when it was exactly right, assuming that it lost time uniformly. Note: (9 a.m. and 12 noon are correct time). (10 marks) (b) Two clocks sound the first stroke of 12 o'clock at the same instant; one clock allows an interval of 20 secs. between each stroke and the next, and the other allows 25 secs. How many strokes of the slower clock remain after the quicker one has finished striking, and what time will elapse between the 12th stroke of the quicker one and the following stroke of the slower one? (10 marks) 4. (a) A solid consists of a hemisphere, radius 8 cm., joined to a cone of the same base-radius and height 6 cm., so that the plane surfaces coincide. Find (i) the volume, (ii) the total area of the surface of the solid. (Give answer to 3 significant figures). (10 marks) ⟦cold⟧ (b) A sphere of radius 3 in. is filed down into the greatest possible cube; find the volume of the material removed. (Give answer to 4 significant figures). (10 marks) 5. Find the difference between the perimeters of a regular pentagon and a regular hexagon, each of which has an area of 24 square inches. (20 marks) ⟦free⟧ 6. In response to an S O S call from a ship at A, another ship at B, 175 miles due east of A, starts toward A at a speed of 12 miles per hour. At the same time a third ship at C, which is 186 miles from B in a direction bearing ⟦3⟧°15' west of north, also starts for A at a speed of 16 miles per hour. Which ship will reach A first, and how long will it take ? (20 marks)
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SHAMASH SECONDARY SCHOOL Final Examination, May 1966 Subject: Arithmetic & Trigonometry Date: 18.5.1966 Class: 4th Year Secondary Time: 8:00-10:30 a.m. ⟦line⟧ Attempt five questions only including question (4). ⟦little⟧ 1. A person, having bought a certain amount of 2¾% stock at 95, afterwards sold it, and with the proceeds bought 3½% stock. He obtained £900 less stock than before, but his income was unchanged. How much money did he originally invest? (20 marks) 2. A house holder owns his house which has a rateable value of £44 on which the annual rates are charged at 21s 10d in the £1. He also has to pay an annual property tax at the rate of 9s in the £ on an assessment of £44. Calculate, correct to the nearest penny, the average cost per week of the total of these charges, taking a year as 52 weeks. He subsequently sells his house for £3300, which sum he invests at the rate of 2½% per annum free of tax, and moves into a flat which he rents at £126 per annum. He has however to rent a garage for his car at 7s 6d per week. Find how much per annum he saves by the change. (20 marks) ⟦independent⟧ 3. (a) A watch was 5 minutes fast at 9 a.m. on Monday, and 10 minutes slow at 12 noon on the following Wednesday. Find when it was exactly right, assuming that it lost time uniformly. Note:(9 a.m. and 12 noon are correct time). (10 marks) (b) Two clocks sound the first stroke of 12 o'clock at the same instant; one clock allows an interval of 20 secs. between each stroke and the next, and the other allows 25 secs. How many strokes of the slower clock remain after the quicker one has finished striking, and what time will elapse between the 12th stroke of the quicker one and the following stroke of the slower one? (10 marks) ⟦good⟧ 4. (a) A solid consists of a hemisphere, radius 8 cm., joined to a cone of the same base-radius and height 6 cm., so that the plane surfaces coincide. Find (i) the volume, (ii) the total area of the surface of the solid. (Give answer to 3 significant figures). (10 marks) (b) A sphere of radius 3 in. is filed down into the greatest possible cube; find the volume of the material removed. (Give answer to 4 significant figures). (10 marks) 5. Find the difference between the perimeters of a regular pentagon and a regular hexagon, each of which has an area of 24 square inches. ⟦easy⟧ (20 marks) 6. In response to an S O S call from a ship at A, another ship at B, 175 miles due east of A, starts toward A at a speed of 12 miles per hour. At the same time a third ship at C, which is 186 miles from B in a direction bearing ⟦30⟧° 15' west of north, also starts for A at a speed of 16 miles per hour. Which ship will reach A first, and how long will it take ? (20 marks) ⟦line⟧
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Shamash Secondary Mid-Year Exam. 1965-1966 Subject:: Arithmetic Date:: 1.2.1966 Class :: 4th Year, Scientific Time:: 8:30 - 10:30 ⟦line⟧ Answer all questions: 1. A dealer sells 2640 articles for £ 341 his profit being 24% of his outlay. Find the cost price of each article. If the cost price to the dealer increased by 8% and he does not change his selling price, find how many articles he must sell in order to obtain the same total profit as before ? 2.a) Compare the volume of the Moon with that of the Earth, if the diameter of the former be to the diameter of the latter as 27 to 100. Give your answer in the form of a ratio whose denomina- tor is unity. b) In order to increase the weight of a block of steel by 1 oz. a cylindrical hole ¼ in. in diameter, is drilled in the block, and the hole is then filled with lead. To what depth must the hole be drilled if steel weighs .29 lb. per cub. in. and lead weighs .41 lb. per cub. in. ? (To nearest 1 in.) 100 3. The rate in a certain town is 13s. 10d. in the £. If the rateable value is increased by 5% and the rate reduced by 6d. in the £, will the income from rates be increased or decreased, and by how much per cent ? 4. Brass is made up of copper and zinc in the proportion 5:4 by volume. If 1cc of copper weighs 8.8 gm and 1 cc of zinc weighs 7.1 gm cal- culate: (a) the weight of copper required to form brass with 50 cc of zinc, ⟦550 gm⟧ (b) the weight of copper in 1 kilogram of brass correct to the nearest gm, ⟦608 gm⟧ (c) the volume of 1 kilogram of brass correct to the nearest cc. ⟦124 cc⟧ ⟦line⟧
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⟦Solution to the⟧ Conditional Exam in Arithmetic & Trig. 4th year, 14/9/1965 1) Income ( £ 253 15 s / 101 1/2 ) 3 1/2 = £ 8.75 or £ 8 15 s Amount realised ( £ 253 15 s ) 99 / 101.5 = £ 247 10 s 2) <del>⟦illegible⟧</del> ( 3 / 2 )³ = ( 3 / 4 )³ + 1³ + x³ x = radius x³ = 27 / 8 - 27 / 64 - 1 = 216 / 64 - 27 / 64 - 64 / 64 = 125 / 64 x = 5 / 4 radius Diam: = 2 x = 10 / 4 = 2 1/2" ⟦line⟧
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⟦illegible⟧ (3) ⟦illegible⟧ original position of ladder A'B' later position AA' = 2 ft find BB' A A' 24' θ 52° B' B C AC = 24 sin 52° = 24 X 0.7880 = 18.91 ft A'C = 18.91 - 2 = 16.91 ft sin θ = A'C / A'B' = 16.91 / 24 = 0.7046 ∠ θ = 44° 48' BC = 24 cos 52° = 24 X 0.6157 = 14.78 ft. B'C = 24 cos 44° 48' = 24 X 0.7096 = 17.03 ft. B'B = 17.03 - 14.78 = 2.25 ft 1 2 3 4 5 6 5 5 5 4 1
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4/ A E B A₁ θ B₁ 42° 55° O AA₁ = OA₁ tan 42° = OB₁ tan θ (a) OB₁ = OA₁ sec 55° (b) tan θ = OA₁ / OB₁ tan 42° from (a) = (OA₁ tan 42°) / (OA₁ sec 55°) from (b) = tan 42° cos 55° = <del>0.9004 X 0.7071</del> = 0.9004 X 0.5736 = 0.5165 θ = angle of elevation = 27° 19'
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(5)
Alternative I
68 X 7 + 196 X 2 3/4 = 476 + 196 X 11/4
= 476 + 539
= 1015 d,
Alternative II
(68 + 196) x 1 1/2 d + £ 2 5 s 6 d =
264 X 3/2 d + 546 d = 942 d
Method II is cheaper by
1015 - 942 = 73 d
or 6 s 1 d
117 X 7 = 819 d
or £ 3 8 s 3 d for light
£ 5 3 s 1 d - £ 3 8 s 3 d
= £ 1 14 s 10 d for power
no of units for power is:
{ £ 1 14 s 10 d } ÷ 2 3/4 d
= 418 X 4/11 = 152 units
for power
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Shamash Secondary School Conditional Exam. Sept.1965 Subject: Arithmetic & Trigonometry Date: 14/9/1965 Class: 4th Year Secondary. Time: 8.00-10.30 ⟦line⟧ Attempt all questions. ① Find the income produced by investing £253 15s. in 3½% stock at 101½ and the amount realised by subsequently selling out at 99. ② A spherical ball of lead 3 in. in diameter is melted and recast into three spherical balls. The diameters of two of these are 1½ in. and 2 in. respectively. What is the diameter of the other ? ③ A ladder, 24ft. long, makes an angle of 52° with the ground and leans against a vertical wall. If the top of the ladder slips down 2 ft. how far will the foot of the ladder move ? 4 An aeroplane is flying horizontally due E. When it is due N. of an observer its elevation is 42°. Find its elevation when it is N. 55° E. of the observer. ⑤ A householder has two alternative methods of paying for the electric light and power that he uses during one quarter of a year. Either he pays 7d. per unit for light and 2¾d. per unit for power, or he pays 1½d. per unit for light and for power and also a quarterly charge of £2 5s. 6d. Determine which method is the cheaper, and by how much, for a quarter during which he uses 68 units for light and 196 units for power. A householder paying by the first method used 117 lighting units during a quarter, and his electricity bill for the quarter was £5 3s. 1d. Find the number of units used for power. ⟦line⟧ 240 154 12 ⟦geometric diagram of a pyramid/triangulation⟧