Mathews' matriculation mathematics: being all the papers in arithmetic and algebra, set from 1844 to 1878. With answers [&c.] by E.H. Mathews

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Page 76 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Page 55 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 99 - C: (v. 7.) but if four straight lines be proportionals, the rectangle contained by the extremes is equal to that which is contained by the means : (vi.
Page 3 - ... whole population was each of these classes ? 5. What are the advantages of decimal fractions? Express as a decimal, 17359 divided by one million. Divide -00125 by 2-5. If the number of decimal places in the divisor exceed the number in the dividend, how do you proceed? Explain this, by making 2-5 the dividend and -00125 the divisor. 6. A vulgar fraction may always be considered as expressing the division of the numerator by the denominator. Explain this, and hence show how to reduce such a fraction...
Page 48 - Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth.
Page 29 - A ship sails with a supply of biscuit for 60 days, at a daily allowance of a pound a head ; after being at sea 20 days she encounters a storm in which 5 men are washed overboard, and damage sustained that will cause a delay of 24 days, and it is found that each man's daily allowance must be reduced to fivesevenths of a pound.
Page vi - Algebra : Addition, Subtraction, Multiplication, and Division of Algebraical Quantities ; Proportion ; Arithmetical and Geometrical Progression ; Simple Equations. Geometry : The First Four £ooks of Euclid, or the subjects •thereof.
Page 14 - in the common rule of subtraction. 2. Show that a number is divisible by 8 when its three last digits are divisible by 8, and only then. State and prove the criterion of divisibility by 9. 3. Distinguish between interest and discount. Find the simple interest on £3540 10».
Page 5 - Eeduce to its lowest terms ^Q. 3. Take any number consisting of six figures, and show, from the nature of our system of numeration, that it is or is not divisible by 9, according as the sum of its digits is or is not divisible by 9. 4. Which would be most productive to the state, an income tax levied at 3 per cent., or at the rate of seven pence in the . pound? Calculate the tax at the latter rate on an income of £1755 10s. 5. Explain the notation of decimal fractions. How does it affect the value...
Page 12 - Prof. HEAVISIDE. 1. What is the cost of constructing a railroad 125 miles long, at the rate of £16 per yard ? 2. What do you understand by the prime factors of a number ? How may you determine by the inspection of "the digits of a number when it is divisible by the numbers 2, 3, and 11 respectively? Find the greatest common measure of 7854 and 9768. 3. In Great Britain, the population of which is computed at 18,526,830, '5J per cent. of the population exercise the elective franchise : determine...

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