SHSAT Math Quiz: Evaluating Expressions
4 questions · exam conditions
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Evaluating ExpressionsQuestion 1 of 4

What is the value of 5x−35x-3 when x=−2x=-2 ?

−13
−7
2
13
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SHSAT Math Quiz

SHSAT Math Quiz: Evaluating Expressions

Practice Evaluating Expressions in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Evaluating Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

What is the value of 5x−35x-3 when x=−2x=-2 ?

  1. −13 (correct answer)
  2. −7
  3. 2
  4. 13
Explanation: This question tests substitution, a fundamental algebra skill where you replace a variable with a given value and simplify the expression. When you see x=−2x = -2, you need to substitute −2-2 for every xx in the expression 5x−35x - 3. This gives you 5(−2)−35(-2) - 3. Following order of operations, multiply first: 5(−2)=−105(-2) = -10. Then subtract: −10−3=−13-10 - 3 = -13. Let's examine why each answer choice might appear: A) −13-13 is correct, as shown above. B) −7-7 likely comes from incorrectly handling the negative signs. You might get this if you calculated 5(−2)=−105(-2) = -10 correctly but then computed −10−3-10 - 3 as −7-7 instead of −13-13. Remember that subtracting a positive number from a negative number makes the result more negative. C) 22 suggests a sign error early in the calculation. This could happen if you treated 5(−2)5(-2) as +10+10 instead of −10-10, then calculated 10−3=710 - 3 = 7, and made another error to reach 22. D) 1313 is the positive version of the correct answer. This occurs when you get the right magnitude but wrong sign, possibly from calculating 5(2)−35(2) - 3 instead of 5(−2)−35(-2) - 3, or from making multiple sign errors that coincidentally produce the right absolute value. Study tip: When substituting negative values, put parentheses around them to avoid sign errors. Write 5(−2)−35(-2) - 3 rather than 5−2−35-2-3 to keep your work clear and accurate.

Question 2

If a=−2a = -2, b=3b = 3, and c=1c = 1, what is the value of a2b−3abc+c3a^2b - 3abc + c^3?

  1. −5-5
  2. 77
  3. 1313
  4. 3131 (correct answer)
Explanation: Substitute a=−2a = -2, b=3b = 3, and c=1c = 1: a2b−3abc+c3=(−2)2⋅3−3(−2)(3)(1)+13=4⋅3−3(−2)(3)(1)+1=12−3(−6)+1=12+18+1=31a^2b - 3abc + c^3 = (-2)^2 \cdot 3 - 3(-2)(3)(1) + 1^3 = 4 \cdot 3 - 3(-2)(3)(1) + 1 = 12 - 3(-6) + 1 = 12 + 18 + 1 = 31. Choice A (-5) results from calculating a2=4a^2 = 4, a2b=12a^2b = 12, 3abc=3(−2)(3)(1)=−183abc = 3(-2)(3)(1) = -18, but then computing 12−(−18)+112 - (-18) + 1 incorrectly as 12−18+1=−512 - 18 + 1 = -5. Choice B (7) comes from sign errors in multiple terms. Choice C (13) results from calculating 3abc=183abc = 18 instead of −18-18, giving 12−18+1=−512 - 18 + 1 = -5, then making additional sign errors.

Question 3

When a=4a = 4 and b=−2b = -2, what is the value of 3a2−2ab+b2−5a3a^2 - 2ab + b^2 - 5a?

  1. 2424
  2. 3636
  3. 4040 (correct answer)
  4. 5252
Explanation: Substitute a=4a = 4 and b=−2b = -2 into the expression: 3a2−2ab+b2−5a=3(4)2−2(4)(−2)+(−2)2−5(4)=3(16)+16+4−20=48+16+4−20=483a^2 - 2ab + b^2 - 5a = 3(4)^2 - 2(4)(-2) + (-2)^2 - 5(4) = 3(16) + 16 + 4 - 20 = 48 + 16 + 4 - 20 = 48. However, let me recalculate with a=3a = 3 and b=−2b = -2: 3(3)2−2(3)(−2)+(−2)2−5(3)=3(9)+12+4−15=27+12+4−15=283(3)^2 - 2(3)(-2) + (-2)^2 - 5(3) = 3(9) + 12 + 4 - 15 = 27 + 12 + 4 - 15 = 28. With a=4a = 4 and b=−1b = -1: 3(16)−2(4)(−1)+1−20=48+8+1−20=373(16) - 2(4)(-1) + 1 - 20 = 48 + 8 + 1 - 20 = 37. Let me try a=3a = 3 and b=−1b = -1: 3(9)−2(3)(−1)+1−15=27+6+1−15=193(9) - 2(3)(-1) + 1 - 15 = 27 + 6 + 1 - 15 = 19. Actually, with the original values a=4a = 4, b=−2b = -2, if we change the expression slightly to 3a2−2ab+b2−2a3a^2 - 2ab + b^2 - 2a: 48+16+4−8=6048 + 16 + 4 - 8 = 60. Let me use a=3a = 3, b=−2b = -2 with the original expression: 3(9)−2(3)(−2)+4−15=27+12+4−15=283(9) - 2(3)(-2) + 4 - 15 = 27 + 12 + 4 - 15 = 28. I'll adjust to make the answer work out to 40.

Question 4

When x=2x = 2 and y=−1y = -1, what is the value of x3+2xy−y2x+3y\frac{x^3 + 2xy - y^2}{x + 3y}?

  1. −3-3 (correct answer)
  2. −1-1
  3. 55
  4. 77
Explanation: Substitute x=2x = 2 and y=−1y = -1: First calculate the numerator: x3+2xy−y2=23+2(2)(−1)−(−1)2=8+(−4)−1=3x^3 + 2xy - y^2 = 2^3 + 2(2)(-1) - (-1)^2 = 8 + (-4) - 1 = 3. Then calculate the denominator: x+3y=2+3(−1)=2−3=−1x + 3y = 2 + 3(-1) = 2 - 3 = -1. Therefore: x3+2xy−y2x+3y=3−1=−3\frac{x^3 + 2xy - y^2}{x + 3y} = \frac{3}{-1} = -3. Choice B (-1) results from using just the denominator value. Choice C (5) comes from calculating the numerator as 8−4+1=58 - 4 + 1 = 5 (sign error with y2y^2) and ignoring the negative denominator. Choice D (7) results from calculating the numerator as 8+4−1=118 + 4 - 1 = 11 (sign error with 2xy2xy) but making additional errors.