Review: Chapters 1 to 11

Simplify 5a - 7x + 3b - 10c - 14a + 12y - 8x + 12a - 11x + 9b.

Simplify 2cd - a^2b + 7cd^2 - 12ab + 17ad - cd + 4c^2d.

Add 10x - 9 + 4ax - 2cd, \;-6ax - 15x + 12cd, \;10 - ax + 5cd, and -6cd + 11x - 19 - 7ax.

Add a^3 - 3 + 4a^2 - a, \;-a + 3a^2 - 5a^3, \;-3a^2 + 6a^3 - 2a + 8, \;-a - 5a^2 - 2a^3 + 5, and 2a^3 - 3a^2 + 4a - 5.

Add Ax^3 + Bx^2 + Cx and Ax^2 + Bx + C.

Add 7(a - b) - 10(c - d) + 8(x - y), \;-6(c - d) - 4(a - b) - 7(x - y), and 12(x - y) - 15(c - d) + 7(a - b). Keep each parenthesis as one quantity.

Add -2(x + y) + 3(x - y) - 4(a + b), \;8(x - y) - 9(x + y) + 4(a + b), and -(a + b) + (x - y) - 10(x + y). Keep each parenthesis as one quantity.

Add \tfrac13ax + \tfrac23ax^2 - \tfrac56a^2x^2 + a, \;\tfrac16ax^2 - ax - 9a + 2a^2x^2, and a^2x^2 + \tfrac12ax^2 - \tfrac14a.

What must be added to 2x^2 - 3xy + y^2 - 1 to give x^2 + 10xy - 9 - 5y^2?

What must be added to 3a^2y - 7ay^2 + z - 5ay to give -a^2y + 12ay^2 - ay - 15?

What must be added to -17a^2bcd^2 - 4ab^2c^2d^3 + 3abcd + ax to give 3ab^2c^2d^3 - 12?

What must be added to 27xy + 13z - 12 + ab to give 0?

(a + b) - (a - b) + 4a - (a + 3b) + c

15x - 2(12x - 16y) + xy + 3(3x - 4xy) - x

ab - (7x + 4y - 2z) + 42 + 5(5ab - x - y)

[x - (-4x + 8y + 2z) + b - 4(3x - z)] - 5b

[ab - \{-5ac + 7(d - a) + 4ca + 7d\} - 6ba] + 13a

\{5x^2 - 2[-4 - (2x^2 - 3x)] + 5\} - (x^2 + 4x - 2)

(x^4 - 4x^2y^2 + 4y^4)(x^4 + 4x^2y^2 + 4y^4)

(4x^4 - x^2 + 5)(3x^3 - x + 7)

(a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc)

(x + y)(x^6 - x^5y + x^4y^2 - x^3y^3 + x^2y^4 - xy^5 + y^6)

(5x - 9x^5 + x^2 - 4x^4 - 3x^3 + 10)(-x^3 + 3x - x^2 + 2x^4)

(3x^2 - 4y)(9x^4 + 16y^2)(3x^2 + 4y)

(a - 3b + 2c)^2

(x - y + z)^3

(x^a - y^b)(x^a + y^b)

(x^a + 2y^b + 3z^c)(x^a - 3y^b)

Divide 6a^5 - 13a^4 + 4a^3 + 3a^2 by 2a^2 - 3a^2 + a.

Divide -30a^4 - 11a^3 + 82a^2 + 12a - 48 by 3a^2 + 2a - 4.

Divide 10x^2 + 20x^3 - 11x^5 + 10x^6 - 3x^4 + 2 by -3x^2 - 2 + 2x + 5x^3.

Divide a^8 - 3a^6 + a^4 - 7a^2 + 3 by (a^2 - 1)^2.

Divide a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 7ab^4 - b^5 by (a - b)^2.

Divide (6a^2 + 5a - 6)(2a^2 - 13a + 20) by (3a - 2)(2a - 5).

Divide x^3 - 27y^3 + 64 + 36xy by x - 3y + 4.

Find y: 6y - 20 + 5y - 18 = 36y - 4 - 40y + 9

Find y: 4y - 3(6 - y) + 2 = 6(y - 2) - 13y + 24

Find y: 6y - 4(1 - 2y) + 10 = 4(2y - 5) - 4y + 1

Find y: (y + 7)(y - 11) = (y + 8)(y - 5) - 2

Find y: (y - 3)^3 = (y^2 - 6y + 9)(5 + y) - 8y^2

Find y: y^2 + a^2 - (y + 1)^2 - (a + 1)^2 = 0

Find y: 3ay + 6ac + 4b^2 = 3ab + 4by + 8bc

Find x = \dfrac{-b + \sqrt{b^2 - 4ac}}{2a} when a = 1, b = 10, c = -11.

Find x = \dfrac{-b + \sqrt{b^2 - 4ac}}{2a} when a = 5, b = -6, c = -8.

Find x = \dfrac{-b - \sqrt{b^2 - 4ac}}{2a} when a = 3, b = 5, c = -8.

Find x = \dfrac{-b - \sqrt{b^2 - 4ac}}{2a} when a = 2, b = 7, c = -22.

If f = 12, m = 18, and v = 20, find s in fs = \tfrac12 mv^2.

If a = 32.2, m = 7, t = 40, find e in e = \tfrac12 m(at)^2.

If s = \dfrac{a + b + c}{2}, find \sqrt{s(s - a)(s - b)(s - c)} when a = 3, b = 4, c = 5.

If the square of a certain number is increased by 38, the result equals the product of the next two consecutive numbers. Find the numbers.

The square of a certain odd number is 98 less than the product of the next two consecutive odd numbers. Find the numbers.

If the square of a certain odd number is increased by 47, the result equals the product of the next two consecutive even numbers. Find the numbers.

The product of two consecutive numbers is 42 less than the product of the next two consecutive numbers. Find the four numbers, smallest first.

Two people are 42 and 15 years old. In how many years will the elder be twice as old as the younger?

Two people are 36 and 16 years old. How many years ago was the older three times as old as the younger?

Two men are 52 and 21 years old. How many years from now will the older be twice as old as the younger?

Two people are 87 and 42 years old. How many years ago was the elder four times as old as the younger?

A collection of 32 quarters, dimes, and nickels is worth $3.60. There are twice as many nickels as quarters. Find the number of each.

A bullet averages 1280 feet per second. Six seconds after firing, the marksman hears it strike the target. Sound travels 1120 feet per second. Find the distance to the target in feet.

A party-game leader tells each player to add 12 to their age, multiply the sum by 3, subtract 36, and then add their age again. Each announces the result, and the leader instantly names their age. By what number does the leader divide each result?

In the 1900s United States, the percent of people under 20 exceeded the percent between 20 and 60 by 5. The percent between 20 and 60 was nine times the percent over 60. Find each percent.

The St. Gothard tunnel is 9000 feet longer than the Mont Cenis tunnel, and 1320 feet shorter than twice the Hoosac tunnel in Massachusetts. The three together are 113,760 feet long. Find each length in feet.

The first cascade of Yosemite Falls is 520 feet higher than Staubbach Falls, and 60 feet more than four times the falls of the Zambezi. The Zambezi falls are 32 feet more than twice the height of Niagara. The four heights add to 3004 feet. Find each in feet.

A cubic foot each of mercury, water, and alcohol weigh 962.2 pounds together. Alcohol weighs 11.5 pounds per cubic foot less than water, and a cubic foot of mercury weighs 32.7 pounds more than sixteen cubic feet of alcohol. Find each weight per cubic foot.

If Boston's yearly rainfall were 3 inches less, it would be one third of Neah Bay's. Boston's is 1 inch more than St. Louis's, and 1 inch less than five times San Diego's. Together the four get 219 inches. Find each in inches.

By 1910 life tables, a person of 10 may expect to live 5.39 years longer than one of 21, and 15.31 years longer than one of 45. A person of 45 may expect to live 0.94 of a year less than twice as long as one of 65. Together, one person of each age may expect 109.42 more years. How many more years may each expect?