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Algebra - Mixed Practice (Up to Quadratic Equations)

Lesson Plans > Mathematics > Algebra > Mixed Content

Algebra - Mixed Practice (Up to Quadratic Equations)

These worksheets are an immediate follow-up to the worksheet set on factoring; the new content in these worksheets is solving quadratic equations in one variable by factoring.

Included are problems in which no rearranging of terms is needed, followed by problems in which rearranging of terms is required. The third worksheet includes a variety of word problems solvable through factoring.

In each worksheet, some linear equations are included as part of the material review, since students have a tendency to fixate on one type of problem or the other; being able to recognize which type of problem they're looking at, and then to recognize the process used to solve it, is very important.

The final worksheet is focused entirely on solving word problems. It contains a mix of linear and quadratic word problems.

Worksheet 6.1

• Distributive property and combining like terms
• Solving linear equations
• Solving quadratic equations (no rearranging)

Worksheet 6.2

• Writing expressions
• Solving linear equations
• Solving quadratic equations (with rearranging)

Worksheet 6.3

• Mixed linear and quadratic equations
• Solving word problems with quadratic equations

Worksheet 6.4

• Mixed linear and quadratic word problems

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

Mixed Practice 6.1

1. 3x2 + 2x + 5x - x2

2. 2(3x + 1) + 2x(x + 1) =

3. 1
2
x -
1
3
x2 -
1
5
x +
2
5
x2

4. 2x[3x - 5(1 - x) + 1] =

5. 5 - {4 - [3 - (2 - 1)]} =

Solve the linear equations

6. 2x + 7 = 35

7. 11x - 10 = 12

8. 2(x + 4) = 18

9. 3(2x - 1) + 5 = 54

10. 2(x + 1) = 3(x - 1) - 5

11. (x - 3)(x + 5) = 0

12. (2x - 1)(5x - 2) = 0

13. (x + 7)(2x + 1) = 0

14. x2 - 8x + 7 = 0

15. x2 - 3x - 28 = 0

16. 3x2 + 4x - 7 = 0

17. 2x2 + 8x + 8 = 0

18. x2 - 16 = 0

19. 18x2 - 2 = 0

20. 6x2 - 7x + 1 = 0

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Mixed Practice 6.2

1. The sum of a number and four less than that number =

2. Four less than the product of five and a number =

3. The difference between twice a number and half the number =

4. Five times the difference between a number and seven =

5. A price increased by half of a percent =

6. A price increased by three hundred percent =

7. The product of a number and two less than that number =

Solve the linear equations

8. 2
3
(x + 6) = 12

9. 0.2(0.1x - 0.5) = 0.42x

10. 3x +
2
5
x = 17

11. 2x2 + 9x = 11

12. 4
9
x2 - 80 = 1

13. x2 = 4x - 4

14. 2x(x + 1) = 84

15. (x - 1)(x + 5) = 72

16. 5(x + 1) = 3x(x - 2) + 15

17. (x + 1)2 + (x + 2)2 = (x + 3)2

18. 3(x - 1)2 + 4(x - 1) = 1 - x

19. 1
3
x2 + x = -
2
3

20. x2 + 8x + 8 = 2x - 1

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Mixed Practice 6.3

Solve the equations below.

1. x2 - 7x = -12

2. 4(x + 2) = 2x + 42

3. -3(x - 1) = 9

4. (x + 1)(x - 3) = 21

5. 2
3
(x + 1) = 12

6. 5x + 2(3x -
1
2
) = 65

7. 3x(x - 1) = (x + 1)(x - 2) + 42

8. 5x2 = 3x2 + 2(5x + 14)

9. 10(2x +
1
2
) = 25

10. x(x - 9) = 36

Solve the word problems

11. The product of a number and 12 more than that number is -27. What is the largest of the possible numbers?

12. The length of a rectangle is two less than its width. The area is 80. What are the rectangle's dimensions?

13. If twice a number is decreased by 7, and the result is multiplied by the number, the final result is 30. What are the possible values of the number?

14. The square of a number is equal to four times the number plus 12 more. What are the possible values of the number?

15. The height of an object off the ground after has been launched is given by the equation h = 64.4t- 16.1t2, where t is time since the launch. How many seconds long will the object's flight be? [Hint: The object's flight is over at the moment it hits the ground. You will get two t values; one of them is zero, which represents the moment the object was launched, not the time it landed]

16. In the previous problem, after how many seconds will its height off the ground be 48.3 feet? [Hint: all the numbers in the equation are multiples of 16.1; factor this number out before factoring the quadratic]

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Mixed Practice 6.4

1. A number, plus twice that number, plus fifteen, is forty-five more than the number. What is the number?

2. Two less than a number is multiplied by two more than the number, and the result is four less than seven times the number. What is the number?

3. The price of a dozen eggs \$1.80 less than the price of eighteen eggs. Assuming the same price per egg, how much does a single egg cost?

4. The profit Ellen makes (in cents) selling lemonade is
1
12
n2 -
1
3
n, where n is the number of cups she sells. How many cups does she need to sell to make a profit of \$0.33? [Hint: multiply both sides of the equation by 12, and then solve]

5. David's average score for three tests was 76. His first two scores where 70.4 and 74. What is the third score?

6. A positive number, plus twice the square of that number, is 45. What is the number?

7. Two more than a number, multiplied by three less than a number is nineteen less than the square off the number. What is the number?

8. The area of a rectangle is 88 square units. The length is five less than twice the width. What is the length of the rectangle?

9. The perimeter of a rectangle is 88 units. The length is five less than twice the width. What is the width of the rectangle?

10. Jack is five years older than Mack. Next year, the product of their ages will be 104. What is Jack's age now?

11. If a number is doubled, and the result is tripled, and then 5 is subtracted, the result is 85. What is the number?

12. Two is added to a negative number, and the result is squared. Then the number is added. The final result is 108. What is the original number?

13. A number is doubled, and the result is multiplied by two more than the number. The result is 286. What is the number?

14. The cost, in cents, of an item is 12 more than the number of items purchased. \$1.08 was spent. How much did one item cost?

15. Five times a number squared, minus that number is the product of three times the number with seven more than the number. If the number is positive, what is the number?