Algebraic Expressions Test 2 – Question Answers

Algebraic Expressions Test 2 – Question Answers: This sample question paper is based on various placement exam in U.S as well asย  U.S. Standardized Tests ACCUPLACER, ACT, GED, GMAT, GRE, LSAT, MAT, MCAT, NCLEX, Praxis, SAT, etc

Algebraic Expressions Practice Test


1. Elijah has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?
๐Ÿ”˜ A. ย  \frac{3m^2}{2} ๐Ÿ”˜ B. ย  \frac{2m^3}{3}
๐Ÿ”˜ C. ย  \frac{3m^2}{5} ๐Ÿ”˜ D. ย  \frac{3m}{1}
๐Ÿ”˜ E. . ย  \frac{5m}{3}
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Answer: A ย  \frac{3m^2}{2} (area of square plot + area of triangular plot)
2. A travel agency charges $ 8 per km and levies a fixed charge of $ 50 for bus service. Write an algebraic expression for the above situation, if the bus is hired for x km.
๐Ÿ”˜ A. 3x + 40 ๐Ÿ”˜ B. 5x + 27
๐Ÿ”˜ C. 2x + 39 ๐Ÿ”˜ D. 3x + 31
๐Ÿ”˜ E. 8x + 50
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Answer: E 8x + 50 (algebraic expression (8 ร— x + 50)
3. A teacher gets paid $70 per hour. Last week he worked for 9 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
๐Ÿ”˜ A. 70(x + 9) ๐Ÿ”˜ B. x(70 + 9)
๐Ÿ”˜ C. 9 (x + 70) ๐Ÿ”˜ D. x (70 ร— 9 )
๐Ÿ”˜ E. 9 (x ร— 7 )
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Answer: A 70(x + 9) (Money paid last week 70 ร— 9 = $630 and money maid this week (70 ร— x)=$70x, total money paid $630 + 70x = 70(x + 9)
4. Liam collects 12 leaves and William collects x leaves for science project. After some time Liam loses 3 leaves and William collects 2x leaves. Which one of the following algebraic expression of the total number of leaves collected by both of them.
๐Ÿ”˜ A. 12 + 2x ๐Ÿ”˜ B. 12-9 + 3x
๐Ÿ”˜ C. 7 + 3x ๐Ÿ”˜ D. 3 + 3x
๐Ÿ”˜ E. 9 + 3x
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Answer: E 9 + 3x (Liam collected 12-3=9 leaves andย  William x + 2x =3xย  so total is 9 + 3x
5.Simplify combining like terms z2 + 13z2 โ€“ 5z + 7z3 โ€“ 15z
๐Ÿ”˜ A. 7z3 + 12z2 -20z ๐Ÿ”˜ B. 5z2 + 3z2 -11z
๐Ÿ”˜ C. 5z2 + 6z3 -10z ๐Ÿ”˜ D. 9z3 + 8z2 -6z
๐Ÿ”˜ E. 3z2 + 7z2 -13z
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Answer: A. 7z3 + 12z2 -20z
6.ย  Simplify combining like terms 5x2y โ€“ 5x2 + 3yx2 โ€“ 3y2 + x2 โ€“ y2 + 8xy2 โ€“ 3y2
๐Ÿ”˜ A. 8x2y + 8xy2 โ€“ 4x2 โ€“ 7y2 ๐Ÿ”˜ B. 4x2y + 4xy2 โ€“ 2x2 โ€“ 3y2
๐Ÿ”˜ C. 2x2y + 2xy2 ๐Ÿ”˜ D. 3x2 โ€“ 5y2
๐Ÿ”˜ E. 5xy2 โ€“ 3x2 โ€“ 2y2
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Answer: A 8x2y + 8xy2 โ€“ 4x2 โ€“ 7y2
7.ย  Add ab โ€“ 4a, 4b โ€“ ab, 4a โ€“ 4b
๐Ÿ”˜ A. 1 ๐Ÿ”˜ B. 2
๐Ÿ”˜ C. 3 ๐Ÿ”˜ D. 4
๐Ÿ”˜ E. 0
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Answer: E 0
8. What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?
๐Ÿ”˜ A. 2x + 2xy โ€“ y ๐Ÿ”˜ B. x2 + 2xy โ€“ y2
๐Ÿ”˜ C. x3 +ย  y3 ๐Ÿ”˜ D. xย + 3xy โ€“ y
๐Ÿ”˜ E. 2x + 2xy โ€“ 2y
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Answer: B x2 + 2xy โ€“ y2
9.ย  What should be subtracted from 2a + 8b + 10 to get โ€“ 3a + 7b + 16?
๐Ÿ”˜ A. 3a + 2b โ€“3 ๐Ÿ”˜ B. 6a + 2b โ€“ 1
๐Ÿ”˜ C. 6a – 3a + 6 ๐Ÿ”˜ D. 5a + b โ€“ 6
๐Ÿ”˜ E. a + 5b โ€“ 1
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Answer: D 5a + b โ€“ 6
10.ย  What should be taken away from 3x2 โ€“ 4y2 + 5xy + 20 to obtainโ€“ x2 โ€“ y2 + 6xy + 20?
๐Ÿ”˜ A. 4x2 โ€“ 3y2 โ€“ xy ๐Ÿ”˜ B. 4x โ€“ 3yย โ€“ xy
๐Ÿ”˜ C. 2x3 โ€“ 2y โ€“ xy ๐Ÿ”˜ D. 5x โ€“3y โ€“ xy
๐Ÿ”˜ E. 2x2 โ€“ 4y2
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Answer: A. 4x2 โ€“ 3y2 โ€“ xy

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