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added ages algebraical amount arithmetic means arrangement Binomial Theorem Cambridge cent coefficient common difference consisting cost cube decimals digits Divide equal exceeds EXERCISE expansion expressions Extract the square feet Find the greatest Find the H.C.F. Find the highest Find the number Find the square Find the sum Find the value five following equations four fraction geometrical progression given gives greater half highest common factor horse hour Including income increased infinity integer invested kind length less mean miles minutes Multiply number of combinations Oxford PAGES person places positive prove quantities quotient ratio Reduce remainder Resolve into factors result scale School shares shew shillings simplest form Simplify Solve the equations Solve the following square root Subtract Sum the series taken takes things third twice varies Write yards
Page 123 - Cn,r or nCr, the number of combinations of n things taken r at a time (without repetitions). The form nCr or even "C, is widely used but the notation Cn,r or C(n,r) or ( J is to be preferred. 6. Roman numeral for "hundred.
Page 138 - Any factor of an expression is a factor also of any multiple of that expression. Thus, if F represent a factor of an expression A, so that A = nF, then mA = mnF. That is, mA contains the factor F.
Page 77 - A person swimming in a stream which runs 1J miles per hour, finds that it takes him four times as long to swim a mile up the stream as it does to swim the same distance down : at what rate does he swim?
Page 131 - ... divided by the less is 2£ times the quotient of the less by the greater : find them. 3. The difference of two numbers is 15, and half their product is equal to the cube of the less number : find them. 4. The product of two numbers is 24, and their sum multiplied by their difference is 20 : find them. 5. The difference of the squares of two consecutive numbers is 17 : find them. 6. The product of two numbers is 18 times their difference, and the sum of their squares is 117: find them. 7. What...
Page 112 - Find three numbers in geometrical progression such that the sum of the first and last is 20, and the square of the mean 36.
Page 141 - Solve the equations : 1 (2) ax-by = 2a (3) у2+л-у =4, 7. The perimeter of a right-angled triangle is six times as long as the shortest side. What is the ratio of the two sides containing the right angle?
Page 134 - The expression n + \ n (n — 1) b is the sum of n terms of an arithmetical progression, of which the first term is unity and the common difference b. If we make 6 = 0, 1, 2, 3, ... we obtain expressions which are called the general terms of the 2nd, 3rd, 4th, order of polygonal numbers respectively.