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Algebra Word Problems Practice Questions Set 5

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Updated on Sep 26, 2011

Algebra Word Problems

Basic algebra problems ask you to solve equations in which one or more elements are unknown. The unknown quantities are represented by variables, which are letters of the alphabet, such as x or y. The questions in this set of practice problems give you practice in writing algebraic equations and using these expressions to solve problems.

  1. The quotient of 3d4 and 12d6 is
    1. 4d2.
    2. 4d8.
    3. .
    4. .
  2. The product of 6x2 and 4xy2 is divided by 3x3y. What is the simplified expression?
    1. 8y
    2. 4y
  3. If the side of a square can be expressed as a2b3, what is the area of the square in simplified form?
    1. a4b5
    2. a4b6
    3. a2b6
    4. a2b5
  4. If 3x2 is multiplied by the quantity 2x3y raised to the fourth power, what would this expression simplify to?
    1. 48x14y4
    2. 1,296x16y4
    3. 6x9y4
    4. 6x14y4
  5. Sara's bedroom is in the shape of a rectangle. The dimensions are 2x and 4x + 5. What is the area of Sara's bedroom?
    1. 18x
    2. 18x2
    3. 8x2 + 5x
    4. 8x2 + 10x
  6. Express the product of –9p3r and the quantity 5p – 6r in simplified form.
    1. –4p4r – 15p3r2
    2. –45p4r + 54p3r2
    3. –45p4r – 6r
    4. –45p3r + 54p3r2
  7. A number, x, increased by 3 is multiplied by the same number, x, increased by 4. What is the product of the two numbers in terms of x?
    1. x2 + 7
    2. x2 + 12
    3. x2 + 7x + 12
    4. x2 + x + 7
  8. The length of Kara's rectangular patio can be expressed as 2x – 1 and the width can be expressed as x + 6. In terms of x, what is the area of her patio?
    1. 2x2 + 13x – 6
    2. 2x2 – 6
    3. 2x2 – 5x – 6
    4. 2x2 + 11x –6
  9. A car travels at a rate of (4x2 – 2). What is the distance this car will travel in (3x – 8) hours?
    1. 12x3 – 32x2 – 6x + 16
    2. 12x2 – 32x2 –6x + 16
    3. 12x3 + 32x2 – 6x – 16
    4. 12x3 – 32x2 – 5x + 16
  10. The area of the base of a prism can be expressed as x2 + 4x + 1 and the height of the prism can be expressed as x – 3. What is the volume of this prism in terms of x?
    1. x3 + x2 – 13x – 3
    2. x3 + 7x2 – 13x – 3
    3. x3x2 – 11x – 3
    4. x3 + x2 – 11x – 3
  11. The dimensions of a rectangular prism can be expressed as x + 1, x – 2, and x + 4. In terms of x, what is the volume of the prism?
    1. x3 + 3x2 + 6x – 8
    2. x3 + 3x2 – 6x – 8
    3. x3 + 5x2 – 2x + 8
    4. x3 – 5x2 – 2x – 8
  12. The area of Mr. Smith's rectangular classroom is x2 – 36. Which of the following binomials could represent the length and the width of the room?
    1. (x + 6)(x + 6)
    2. (x – 6)(x – 6)
    3. (x + 6)(x – 6)
    4. x(x – 36)
  13. The area of a parallelogram can be expressed as the binomial 2x2 – 10x. Which of the following could be the length of the base and the height of the parallelogram?
    1. 2x(x2 – 5x)
    2. 2x (x – 5)
    3. (2x – 1)(x – 10)
    4. (2x – 5)(x + 2)
  14. A farmer's rectangular field has an area that can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field?
    1. (x + 1)(x + 2)
    2. (x – 1)(x – 2)
    3. (x – 1)(x + 2)
    4. (x + 1)(x + 1)
  15. Harold is tiling a rectangular kitchen floor with an area that is expressed as x2 + 6x + 5. What could the dimensions of the floor be in terms of x?
    1. (x + 1)(x + 5)
    2. (x – 1)(x – 5)
    3. (x – 2)(x + 3)
    4. (x + 2)(x + 3)
  16. The area of a rectangle is represented by the trinomial: x2 + x – 12. Which of the following binomials could represent the length and width?
    1. (x + 4)(x – 3)
    2. (x – 4)(x – 3)
    3. (x – 4)(x + 3)
    4. (x – 6)(x + 2)
  17. Katie's school has a rectangular courtyard whose area can be expressed as 3x2 – 7x + 2. Which of the following could be the dimensions of the courtyard in terms of x?
    1. (3x – 1)(x + 2)
    2. (3x – 1)(x – 2)
    3. (3x – 2)(x – 1)
    4. (3x + 2)(x + 1)
  18. The distance from the sun to the earth is approximately 9.3 × 107 miles. What is this distance expressed in standard notation?
    1. 930,000,000
    2. 93,700,000
    3. 0.00000093
    4. 93,000,000
  19. The distance from the earth to the moon is approximately 240,000 miles. What is this distance expressed in scientific notation?
    1. 24 × 104
    2. 240 × 103
    3. 2.4 × 105
    4. 2.4 × 10–5
  20. It takes light 5.3 × 10–6 seconds to travel one mile. What is this time in standard notation?
    1. 0.00000053
    2. 0.000053
    3. 5.300000
    4. 0.0000053
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