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Algebra - Mixed Practice (Up to Systems of Equations)

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Algebra - Mixed Practice (Up to Systems of Equations)

As was mentioned previously in this set of review worksheets, there are places in the traditional Algebra One course in which not all curricula organize the sequence the same way. I have seen curricula in which quadratic equations are studied before systems of equations, and I have seen curricula in which the sequence is reversed.

For this reason, these review worksheets do not cover quadratic equations, in order to help ensure they can be used widely, regardless of the curriculum you use. If you would like to have problems that review quadratics and quadratic equations, They can be found in other sections of this series; just scan down to the index to find other worksheet units.

Worksheet 8.1

  • Combining like terms
  • Solving linear equations
  • Solving systems

Worksheet 8.2

  • Writing expressions
  • Solving word problems
  • Recognizing inconsistent and indeterminate systems

Worksheet 8.3

  • Simplifying rational expressions
  • Factoring
  • Solving fractional systems

Worksheet 8.4

  • Multiplying, adding, subtracting polynomials
  • Solving word problems with systems of equations

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

Lesson by Mr. Twitchell

Handouts/Worksheets

Mixed Practice 8.1

Simplify the following expressions

  1. 3x + 2x - 3xy + 5 - 5x + xy =
     
  2. 2x - 2(x - 5) - 2x(3 - x) = 
     
  3. 5y2 - x(-3y - 2x) + y(x + y) =
     
  4. x - 3[x - 2(x + 3] + 4x] =
     
  5. x + 3y - 2{5 - x[3y + 2(-3 + y)] + 2} =

    Solve the following equations
     
  6. 2x + 3(x + 1) = 32
     
  7. 5x + 3y - 2x =27 + 3y
     
  8. 2(x + 1) + 3(x - 1) = 4(x + 12)
     
  9. 2x(x - 10) - x(x + 1) = x2 - 15
     
  10. 3
    2
    (x + 1) -
    4
    3
    (x + 1) = 17

    Solve the systems of equations. State your answer as an ordered pair.
     
  11. x + y = 12; x - y = 14
     
  12. 2x + 3y = 37; 3x - y = 6
     
  13. 2(x + y) - 10 = 30; x = 5 + y
     
  14. 2x + y = 15 + x - y; x - y = 3
     
  15. 3x + 2y = 3(x + y) - 10; x + 2y = 35
     
  16. x(x + y + 11) = 44 - x2 - xy; 3x + y = 18
     
  17. x = 3y - 25; x = 2y + 4
     
  18. x + y = 0; x - 3y = 24
     
  19. 5x + 4y = 40; 4x - 3y = 1
     
  20. x + 1 = y - 12; x = 3y

Mixed Practice 8.1: Answer Key

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Mixed Practice 8.2

Convert the following to algebraic expressions. Simplify your expression

  1. The sum of a number and five more than that number
     
  2. Two more than the product of a number with seven
     
  3. Three less than three more than a number
     
  4. Four times three more than a number
     
  5. Ten less than the product of two less than a number with two more than a number
     
  6. Five dollars more than two-thirds of the price
     
  7. Two thirds of five dollars more than the price

    Solve the word problems below
     
  8. The sum of a number and twice that number is equal to 36 more than the number. Find half of the number.
     
  9. A price is increased by 3 dollars, and then increased again by 25%. The resulting price is $24. What would the price have been if it had not been increased?
     
  10. After the temperature rose by a certain number of degrees, it was four times what it was before. If the increase in temperature was 44 degrees more than the original temperature, what was the temperature after the increase?
     
  11. A mixture is 80% olive oil and 12% water. The remaining percentage is vinegar. If there are 2.4 oz of vinegar, how much of the mixture is water?
     
  12. Half of a number, plus 15% of that number, plus that number times .07 is equal to 2448. What is 17% of the number?

    Solve the systems of equations; write indeterminate or inconsistent if they cannot be solved.
     
  13. 3x  = y + 12; 2y - 6x = -24
     
  14. 2x + y = 15; x - y = 24
     
  15. x = 5y + 10; x - 5y = 11
     
  16. 2(x + y) - x = x - y + 22; x + y = x + 3y = 43
     
  17. 3x = 6y - 20; 3(
    1
    2
    x - y) + 10 = 0
     
  18. 3x + 2y = 20; x - y = 10

Mixed Practice 8.2: Answer Key

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Mixed Practice 8.3

Simplify the following expressions

  1. 36
    48
    =
     
  2. 2x
    14
     ·
    2
    5

     
  3. 3x2
    12x
     ÷
    2
    5

     
  4. 2x
    4
    +
    10
    30

     
  5. x
    2
    - (
    x
    3
    -
    x
    4
    ) = 

    Factor the following expressions
     
  6. 2x2 - 14x
     
  7. x3y2 + xy
     
  8. x2 + 12x + 32
     
  9. 2x2 - 5x - 12
     
  10. x3 - 25x
     
  11. 16x2 - 16xy + 4y2
     
  12. x3y2 - 8x2y2 + 15xy2

    Solve the following systems of equations. Write your answers as ordered pairs.
     
  13. x
    3
    +
    y
    2
    = 8; x +
    y
    5
    = 11
     
  14. x + 1
    3
    + y = 5; x +
    y - 2
    2
    = 8
     
  15. x
    2
    +
    x
    4
    = 4;
    x
    2
    -
    x
    4
    = 1
     
  16. 12
    x
    +
    6
    y
    = 7;
    6
    x
    -
    3
    y
    =
    1
    2
     
     
  17. x2
    2x
    +
    y
    2
    = 5;
    x
    3
    +
    y2
    6y
    = 3

Mixed Practice 8.3: Answer Key

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Mixed Practice 8.4

Perform the stated operation.

  1. Add 3x2 + 2x + 1 and 2x - x2 + 4
     
  2. Add -x2 + 50x - 50 and x2 - x  - 1
     
  3. Subract 3x3 - 4x + 1 from x2 + 5x + 1
     
  4. Subtract -x + 1 from x2 + x + 1
     
  5. Multiply x3 - 2 and x - 1
     
  6. Multiply (x - 1)(x2 - 2x + 1)

    Solve each word problem.
     
  7. The sum of John's age and Don's age is 48. John is 8 years older than Don. How old will Don be in 5 years?
     
  8. A item's price is discounted by a certain amount, resulting in a price of $5.70. If three items had been purchased at the regular price, and two at the discounted price, the cost would have been $29.25. What is the cost of 5 undiscounted items?
     
  9. Bub has $12.50 in nickels and quarters. In all he has 190 coins. What is the value of all his nickels?
     
  10. A solution is 15% oil. Another solution is 20% oil. If the two solutions are mixed, there will be a total of 45 gallons of solution, containing 8 gallons of oil. How much of the first solution is there?
     
  11. The price of two bracelets and twenty earrings is $184. The price of four bracelets and 10 earrings is $128. How much does one bracelet and two earrings cost?
     
  12. Three consecutive integers add to a certain number. The first two of those integers add to 21 more than half of the sum of all three. What is the third integer?
     
  13. Two consecutive odd integers add to z.If, from z, a third of the first number is subtracted, the result is half of forty-six more than z. What are the two numbers?
     
  14. When the price of an item is increased by a certain amount, the price is 20% more than it was originally. If three of these items were sold at the original price that would be $7.20 more than purchasing two items at the inflated price. What was the original price?
     
  15. A bricklayer charges a rate which varies directly with the height of the wall, and varies directly with the length of the wall. A wall which is 4 feet tall and 18 feet long costs  $314. A wall which is 2 feet tall and 40 feet long costs $529. How much does the bricklayer charge for a wall which is one foot tall and two feet long?

Mixed Practice 8.4: Answer Key

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