Grade 6 Math Practice Test: Expressions and Equations
- Expressions and Equations
- 12 questions
- 15 minutes
This test covers exponents, the order of operations, writing and evaluating expressions, equivalent expressions, one-step equations and inequalities, and dependent and independent variables. Tip: after you solve an equation, put your answer back into the original equation to check it.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the value of 25?
Correct answer: D
25 means 2 used as a factor 5 times: 2 × 2 × 2 × 2 × 2 = 32. 10 multiplies the base by the exponent, and 25 is 52, with the base and exponent switched.
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Question 2
What is the value of 20 − 3 × 4 + 23?
Correct answer: C
Exponents first (23 = 8), then multiplication (3 × 4 = 12), then add and subtract from left to right: 20 − 12 + 8 = 16. 0 comes from adding 12 + 8 before subtracting, but addition and subtraction are done in order from left to right.
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Question 3
Which expression means “5 less than the product of 4 and n”?
Correct answer: B
The product of 4 and n is 4n, and “5 less than” that amount means 5 is subtracted from it: 4n − 5. 5 − 4n subtracts in the wrong order.
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Question 4
What is the value of 3x2 + 2 when x = 4?
Correct answer: B
Only x is squared, and exponents come first: 42 = 16. Then 3 × 16 = 48 and 48 + 2 = 50. 146 squares 3 × 4 = 12, and 26 doubles 4 instead of squaring it.
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Question 5
Which expression is equivalent to 6(2x + 5)?
Correct answer: C
The distributive property multiplies 6 by each term inside the parentheses: 6 × 2x + 6 × 5 = 12x + 30. 12x + 5 multiplies only the first term by 6.
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Question 6
Which expression is equivalent to 24a + 36?
Correct answer: A
The greatest common factor of 24 and 36 is 12, and 24a = 12 × 2a and 36 = 12 × 3, so 24a + 36 = 12(2a + 3). In 12(2a + 36) only the first term was divided by 12, so it equals 24a + 432.
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Question 7
Which expression is equivalent to 5y + 3 + 2y − 1?
Correct answer: D
Combine like terms: 5y + 2y = 7y and 3 − 1 = 2, so the expression is 7y + 2. 9y adds the constants to the y-terms, but 3 and −1 do not have a y.
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Question 8
Maria bought 7 notebooks that each cost the same amount. She paid $10.50 in all. How much did one notebook cost?
Correct answer: A
Let n be the cost of one notebook: 7n = 10.50. Divide both sides by 7 to get n = 1.50, so each notebook cost $1.50. $3.50 subtracts 7 instead of dividing by 7.
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Question 9
Solve the equation.
x4 = 9
Correct answer: D
x is divided by 4, so undo that by multiplying both sides by 4: x = 9 × 4 = 36. Check: 36 ÷ 4 = 9. 2.25 divides 9 by 4 instead of multiplying.
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Question 10
To ride a roller coaster, a person must be at least 48 inches tall. Which inequality shows the heights h, in inches, of people who may ride?
Correct answer: B
“At least 48” means 48 or more, so a person who is exactly 48 inches tall may ride: h ≥ 48. h > 48 leaves out people who are exactly 48 inches tall.
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Question 11
Which value of x makes the inequality x + 6 < 15 true?
Correct answer: A
The inequality is true when x < 9. Only 8 works: 8 + 6 = 14, and 14 < 15. For x = 9 the sum is exactly 15, which is not less than 15.
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Question 12
A shop rents kayaks. The table shows the cost c, in dollars, of renting a kayak for h hours.
Hours (h) 1 2 3 4 Cost (c) 15 30 45 60 Which statement is true?
Correct answer: C
Each hour adds $15, so c = 15h. The cost depends on the number of hours, so c is the dependent variable and h is the independent variable. c = h + 15 does not fit the table: for 2 hours it gives 17, not 30.
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