Algebraical Exercises and Examination Papers |
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Page 23
... consist ? EXERCISE XXXIV . 1. If a = -3 , b = 5 , c = - - 1 , find the value of 3a √3ab + 46-2bc √ † / a3 — 5b + 12c . 2. Solve the equations : XC- -2 x + 3 X- 4 ( 1 ) + = 7 . 3 4 6 2x 4y 5.x 3y ( 2 ) = 22 - 44 = 13 7 3 4 3 . Subtract ...
... consist ? EXERCISE XXXIV . 1. If a = -3 , b = 5 , c = - - 1 , find the value of 3a √3ab + 46-2bc √ † / a3 — 5b + 12c . 2. Solve the equations : XC- -2 x + 3 X- 4 ( 1 ) + = 7 . 3 4 6 2x 4y 5.x 3y ( 2 ) = 22 - 44 = 13 7 3 4 3 . Subtract ...
Page 60
... consist of ? 7. Insert 4 harmonic means between 1 and 1 8. If A varies directly as the square root of B and inversely as the cube of C , and if A = 3 when B = 256 , and C = 2 , find B when A = 24 and C : 2 and EXERCISE LXXV . 1. Find ...
... consist of ? 7. Insert 4 harmonic means between 1 and 1 8. If A varies directly as the square root of B and inversely as the cube of C , and if A = 3 when B = 256 , and C = 2 , find B when A = 24 and C : 2 and EXERCISE LXXV . 1. Find ...
Page 70
... β " B a for its roots is q ( x + 1 ) 2 = p2x . 6. If a , b , c , d be in continued proportion , prove that 1 1 1 1 1 Ъ + + : с d 1 + + = a : b . α b с 7. From a body of men consisting of 3 sergeants 70 ALGEBRAICAL EXERCISES.
... β " B a for its roots is q ( x + 1 ) 2 = p2x . 6. If a , b , c , d be in continued proportion , prove that 1 1 1 1 1 Ъ + + : с d 1 + + = a : b . α b с 7. From a body of men consisting of 3 sergeants 70 ALGEBRAICAL EXERCISES.
Page 71
Henry Sinclair Hall, Samuel Ratcliffe Knight. 7. From a body of men consisting of 3 sergeants , 8 corporals , and 12 privates , how many different parties can be formed con- sisting of 1 sergeant , 2 corporals , and 5 privates ? 8 ...
Henry Sinclair Hall, Samuel Ratcliffe Knight. 7. From a body of men consisting of 3 sergeants , 8 corporals , and 12 privates , how many different parties can be formed con- sisting of 1 sergeant , 2 corporals , and 5 privates ? 8 ...
Page 73
... consisting of 5 consonants and 2 vowels ? 8. Find the ( r + 1 ) th term of ( 1 ) ( 1 + x ) -2 , 1 ( 2 ) ( 1 + x ) 2 , ( 3 ) ( 1 − a ) , expressing each in its simplest form . EXERCISE XC . 1. Find the sixth root of 1 + 3x + 15 4 5 15 2 ...
... consisting of 5 consonants and 2 vowels ? 8. Find the ( r + 1 ) th term of ( 1 ) ( 1 + x ) -2 , 1 ( 2 ) ( 1 + x ) 2 , ( 3 ) ( 1 − a ) , expressing each in its simplest form . EXERCISE XC . 1. Find the sixth root of 1 + 3x + 15 4 5 15 2 ...
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Common terms and phrases
7th term a²+b² arithmetic means arithmetic series Binomial Theorem Cambridge cent common difference continued proportion digits equal equation x²+px+q=0 Extract the square Find the coefficient Find the greatest Find the H. C. F. Find the highest Find the lowest Find the number Find the square Find the sum Find the value five terms following equations following series fraction geometric mean geometrical progression Globe 8vo greatest term H. C. F. and L. C. M. half-crowns highest common divisor highest common factor infinity Least Common Multiple lowest common multiple mean proportional Multiply number of combinations PAGES places of decimals Prove the rule quadratic quantities quotient remainder Resolve into factors shew shillings simplest form Solve the equations Solve the following square root Subtract Sum the following Sum the series surd x²+1 x²+y²
Popular passages
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 130 - Any term may be transposed from one side of an equation to the other provided its sign be changed.
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.