12 multiple-choice questions, progressively harder.
Evaluate 5−2(x+1)5 - 2(x + 1)5−2(x+1) when x=3x = 3x=3.
Solution
Correct answer: D
Substitute 333, do the parentheses, then multiply, then subtract.
5−2(3+1)=5−2(4)=5−8=−35 - 2(3 + 1) = 5 - 2(4) = 5 - 8 = -35−2(3+1)=5−2(4)=5−8=−3
The 222 multiplies the grouped sum before it is subtracted from 555.
Evaluate 3x2+23x^2 + 23x2+2 when x=3x = 3x=3.
Correct answer: A
Substitute 333, square first, then multiply, then add.
3(3)2+2=3(9)+2=27+2=293(3)^2 + 2 = 3(9) + 2 = 27 + 2 = 293(3)2+2=3(9)+2=27+2=29
The exponent applies to the 333 before the coefficient multiplies in.
Evaluate x+y2\dfrac{x + y}{2}2x+y when x=7x = 7x=7 and y=5y = 5y=5.
The fraction bar groups the whole top, so add before dividing.
(7)+(5)2=122=6\frac{(7) + (5)}{2} = \frac{12}{2} = 62(7)+(5)=212=6
So the value is 666, the average of 777 and 555.
Which expression means "a number nnn decreased by the sum of 222 and 333"?
Correct answer: B
The amount taken away is the whole sum 2+32 + 32+3, so it is grouped before subtracting.
n−(2+3)n - (2 + 3)n−(2+3)
The sum is removed from nnn as one quantity, giving n−5n - 5n−5.
Evaluate −x2-x^2−x2 when x=3x = 3x=3.
With no parentheses around xxx, the exponent acts first and the minus sign is applied afterward.
−(3)2=−(9)=−9-(3)^2 = -(9) = -9−(3)2=−(9)=−9
This is −(x2)-(x^2)−(x2), so the result is negative even though 333 is positive.
Evaluate 3+2(x−4)3 + 2(x - 4)3+2(x−4) when x=7x = 7x=7.
Substitute 777, do the parentheses, multiply, then add.
3+2(7−4)=3+2(3)=3+6=93 + 2(7 - 4) = 3 + 2(3) = 3 + 6 = 93+2(7−4)=3+2(3)=3+6=9
The grouped difference is handled before the multiplication and addition.
Evaluate 2x+3y−z2x + 3y - z2x+3y−z when x=4x = 4x=4, y=2y = 2y=2, and z=5z = 5z=5.
Correct answer: C
Substitute all three values, multiply each variable term, then combine.
2(4)+3(2)−(5)=8+6−5=92(4) + 3(2) - (5) = 8 + 6 - 5 = 92(4)+3(2)−(5)=8+6−5=9
So the value is 999.
How many terms does the expression x2+3x−2y+5x^2 + 3x - 2y + 5x2+3x−2y+5 have?
Terms are separated by +++ and −-− signs.
x2+3x−2y+5x^2 + 3x - 2y + 5x2+3x−2y+5
The four terms are x2x^2x2, 3x3x3x, −2y-2y−2y, and 555.
Evaluate x2+yx^2 + yx2+y when x=−3x = -3x=−3 and y=−2y = -2y=−2.
Substitute, squaring the negative first, then adding the negative yyy.
(−3)2+(−2)=9−2=7(-3)^2 + (-2) = 9 - 2 = 7(−3)2+(−2)=9−2=7
The square is positive, and adding −2-2−2 takes two away.
A rectangle has length LLL and width 333. Which expression gives its area?
Area is length times width, and the width is 333.
L×3=3LL \times 3 = 3LL×3=3L
So the area is 3L3L3L. The sum L+3L + 3L+3 would be a partial perimeter, not area.
A taxi charges a 333 dollar base fee plus 222 dollars per mile. Which expression gives the cost for mmm miles?
The per-mile charge is 222 dollars for each of mmm miles, which is 2m2m2m, plus the fixed 333 dollar fee.
2m+32m + 32m+3
The 2m2m2m varies with distance, while the 333 is the constant base fee.
Evaluate x2−1x+1\dfrac{x^2 - 1}{x + 1}x+1x2−1 when x=5x = 5x=5.
Substitute 555 into the top and the bottom, then divide.
(5)2−1(5)+1=25−16=246=4\frac{(5)^2 - 1}{(5) + 1} = \frac{25 - 1}{6} = \frac{24}{6} = 4(5)+1(5)2−1=625−1=624=4
The numerator and denominator are each evaluated before dividing.
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