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8. Translate into English:
a. Es werde Licht!
Der Fährmann setzte mich über.
schon lange thun sollen.
Vom Flegel zwischen die Steine,
Dem Hungrigen schmeckt's allzeit gut. 9. Translate into English prose :
Sie sollen ihn nicht haben,
Time : two hours.
1. What is the greatest weight which can be contained exactly both in 6 tons 3 cwt. 1 qr. and in 58 cwt. ? 2. Find tbe value of 2 11
7 18 of 1 7 49
3. Multiply 3.1416 by 3.0109, correct to four places ; and find
1 the value of correct to one part in a thousand.
871 4. An employer finds that it costs £3 15s. to get a certain job done by a workman whom he pays at the rate of 5s. a day. The next time the job has to be done he puts a second man on in addition to the first. The new man works half as fast again as the other, but has to be paid 78. a day. How much does the job cost this time ? 5. A man invests £5,000 in 3% stock at 93}: and £3000 in 3.1 % stock at par.
Find his income, to the nearest penny. 6. A sells tea to B, making a profit of 9 % on what he gave for it; B sells to C at a profit of 10 %; C sells to D at ls 11d. per lb., and makes a profit of 20 % How much per cwt. did A pay. for the tea, to the nearest penny ? 7. A certain sum of money is put out at 5 % compound interest. The interest earned in the third year is greater than that gained in the second by £52 10s. What is the sum ? 8. If one metre is equal to 39.37 inches, find to one part in a thousand the area in square centimetres of a circle of 10 inches radius.
2.23 x 2. What number must be added to x +
x in order
3 2 that the sum may be divisible by 2x2 3 ? 3. Find the value of (a + b) (b + c) (c + a) (a - b) (6 - c)
a). 4. Find the factors of p?
q + 2
gaz + 2 (pr - 98);
1 56 + 10 x - x?; 2y2
7 6. At two stations, A and B, on a line of railway, the prices of .coals are £p per ton and £q per ton respectively. If the distance between A and B be d miles, and the rate for the carriage of coal be £r per ton per mile, find the distance from A of a station at which it makes no difference to a consumer whether he buys coals from A or from B.
Having found a formula, assume any numerical values you please for the quantities denoted by the above symbols, and verify the formula. 7. A man has 40 shots at a target. Each time he makes a bullseye he receives a shilling from his friend A ; each time he misses the target he pays A sixpence. If he puts a shot on the target which misses the bullseye, he neither pays nor receives. The number of times he does this last is greater by five than the number of times he makes bullseyes. On the whole he loses Is. 6d. How many bullseyes does he make?
Time : two hours.
1. Prove that the greater angle of every triangle is subtended by the greater side or has the greater side opposite to it.
ABC is a triangle having an obtuse angle at A. AB is produced through B to any point D, and AC is produced through C to any point E.
Prove that DE is greater than BC. 2. If a straight line falling on two other straight lines makes the alternate angles equal to one another, prove that the two straight fines are parallel.
Through the extremities of a line AB two given parallel lines are drawn. Draw two oth parallel through A and B which will intersect these so as to form a rhombus.
3. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 4. Two quadrilaterals, ABCD, EFGA, are such that AB is equal and parallel to EF, BC is equal and parallel to FG, CD is equal and parallel to GH. Prove that DA is equal and parallel to HE. 5. Divide a given straight line into two parts, so that the rectangle contained by the whole and one part shall be equal to the square on the other. 6. The straight line AB is bisected at C. With C as centre a circle of any radius is described. Prove that the sum of the squares on the lines joining any point on this circle to A and B has the same value, no matter what the position of the point on the circle.
Time : two hours. 1. Describe a method of finding the area of an irregularly shaped figure. The diameter of a circle as measured by a scale is 10.6 cms., the measurement being taken to the nearest m.m.
What is the degree of accuracy of this measurement, and if the area be calculated from the observed reading, taking T as 3:1416, to what degree of accuracy is the area known? 2. Define density and specific gravity. How would you determine the density of a liquid ?
Find the mass of steam which will fill a spherical vessel 1 ft. diameter, the density of steam being •16 lbs. per cubic ft. 3. Describe the experiment of the cartesian diver. Under what conditions will the diver fail to rise ? 4. Define coefficient of linear and coefficient of cubical expansion.
The density of copper at 0° C is 8.95, what is its density at 50° C if its cubical expansion per degree = .0002 ? 5. What is Newton's Law of cooling ? · Explain how the specific heat of a liquid may be found by the method of cooling. 6. I)efine latent heat of vaporization. 16.5 grms. of steam at 100° C are passed into 460 grms. of water at 20° C, and the temperature rises to 40° C. Find the latent heat of steam at 100° C, stating clearly the reasons for each step in your work.
7. Define Young's Modulus and Hooke's Law. Describe an experiment on the bending of beams to prove the relation between the bending force and the amount of bending.
What is meant by permanent set and limit of elasticity ? 8. State the law of the parallelogram of forces, Hence show that no matter how many forces act on a particle, they may be replaced by a single force which will produce the same effect.
Time : two hours.
[N.B.-Candidates are expected to write formulae and equations
1. State how you would prepare oxygen gas, and give an account of its properties. Explain fully the change which takes place when electric sparks are passed for some time through oxygen gas. 2. Explain the meaning of the terms acid, base, salt, neutralisation. How can you ascertain whether a solution is acid, alkaline, or neutral ? 3. Given some potassium nitrate, sulphuric acid, and ammonia, how would you prepare nitrous oxide gas ? Make a sketch of the apparatus you would use for the preparation and collection of the gas. 4. What do you understand by the terms hard and soft, as applied to water. How would you purify some water containing ammonia and salt in solution !
5. How would you prepare a solution of sulphurous acid? Explain its use as a bleaching agent. 6. What is meant by the term destructive distillation? Give an account of the chief products resulting from the destructive distillation of coal. 7. What is Marsh gas, and how is it prepared ? Write an account of its properties.