WorksheetsMid Year Final Review Practice
Total questions: 134
Worksheet time: 1hrs 10mins
What is the value of x0 for any nonzero x?
Undefined for any nonzero x
Equals x for any nonzero x
One for any nonzero x
Zero for any nonzero x
Rewrite x^{-a} using only positive exponents.
xaa in numerator
xa1 as a fraction
xa multiplied by a
xa in denominator
Simplify using positive exponents: 3−3 .
33 in numerator
331 as a fraction
1/3 as a simplified
3−6 in denominator
Simplify using positive exponents: 2−7⋅122 .
122/27 as a quotient
27⋅122 in numerator
27⋅1221
1221⋅27 combined
Simplify using positive exponents: 9−1⋅40⋅4−3 .
91⋅43 simplified
4^0 equals zero
9⋅431 overall result
9/43 final value
Write 27,500 in scientific notation.
0.275 × 105 shifted left
2.75 × 104 correct notation
27.5 × 10^2 adjusted form
2.75 × 10^3 standard form
Write 0.0016 in scientific notation.
16 × 10^{-5} scaled value
1.6 × 10^{-4} standard form
1.6 × 10−3 correct notation
0.16 × 10−2 equivalent form
Write 0.0000000047 in scientific notation.
4.7 × 10−8 shifted one
0.47 × 10^{-8} equivalent value
47 × 10^{-10} scaled form
4.7 × 10−9 correct notation
Convert to standard form: 2.92×10−1 .
0.292 as decimal
2.92 as units
0.0292 as decimal
29.2 as number
Convert to standard form: 5×107 .
500,000,000 as result
0.0000005 as decimal
50,000,000 as number
5,000,000 as value
Convert to standard form: 6.3×10−5 .
0.000063 exact decimal
0.0000063 shifted one
0.000630 moved right
0.063 moved left
Evaluate the square root: √81.
3 principal root
81 exact value
9 principal root
-9 principal root
Evaluate the square root: -√324.
-18 as value
18 as value
-162 as result
-9 as estimate
Evaluate the square root: √(1/4).
1/2 as value
1/4 as value
1/8 as value
2 as value
Evaluate the cube root: ∛8.
2 as value
-2 as value
4 as value
3 as value
Evaluate the cube root: ∛(-343).
7 as value
-7 as value
-49 as value
-3 as value
Evaluate the cube root: ∛1,728.
6 as cube root
8 as cube root
12 as cube root
9 as cube root
Which values are perfect squares? 20, 121, 36, 10, 18, 256, 400
36, 256, 400, 10
20, 36, 256, 400
121, 36, 256, 400
121, 36, 18, 256
Which values are perfect cubes? 64, 9, 300, 27, 512, 1, 250
64, 27, 512, 1
9, 27, 250, 1
64, 300, 1, 250
27, 512, 9, 300
Estimate √105 to the nearest tenth.
10.2 as estimate
9.8 as estimate
9.5 as estimate
10.5 as estimate
Estimate √68 to the nearest tenth.
8.0 as estimate
7.9 as estimate
8.2 as estimate
8.4 as estimate
Estimate -√236 to the nearest tenth.
-15.3 as estimate
-15.4 as estimate
-16.0 as estimate
-14.8 as estimate
Between which integers does √14 lie?
Between 2 and 3
Between 3 and 4
Between 1 and 2
Between 4 and 5
Between which integers does -√84 lie?
Between -7 and -6
Between -9 and -8
Between -8 and -7
Between -10 and -9
Between which integers does -√192 lie?
Between -15 and -16
Between -12 and -13
Between -14 and -15
Between -13 and -14
Which subset is the SMALLEST that includes −13/18?
Whole numbers
Natural numbers
Integers
Rational numbers
Classify −√289 into the smallest subset of the real numbers.
Rational numbers
Irrational numbers
Integers
Whole numbers
What is 7−2 written as a rational number?
1/49
−1/14
−1/49
1/14
Identify the smallest subset for |−15|.
Rational numbers
Integers
Whole numbers
Irrational numbers
Which statement about 7.5291 is true?
It is a rational number
It is an integer
It is irrational
It is a whole number
Classify ∛125 into the smallest subset of real numbers.
Integers
Whole numbers
Irrational numbers
Rational numbers
Evaluate π − π.
0
π
2π
1
Which subset is the smallest for −√100/20?
Integers
Irrational numbers
Whole numbers
Rational numbers
Order from least to greatest: 5/9 , 0.56 , 5.5×10−2 , 5−1 .
5−1 , 0.56, 95 , 5.5 \times 10−2
5.5×10−2 , 95 , 5−1 , 0.56
5−1 , 5.5×10−2 , 0.56, 95
5.5×10−2 , 5−1 , 5/9 , 0.56
Order from greatest to least: 144 , 1.2×102 , 3729 , 27 .
3729 , 144 , 1.2×102 , 27
1.2×10^2, 27 , 144 , 3729
27 , 1.2×102 , 144 , 3729
√144, ∛729, 27 , 1.2×102
Which set lists only irrational numbers?
√18, π, √7
π, √50, √9
π, √49, √3
√2, π, √16
Which number is NOT an integer?
0
−12
15
−3/5
Which is the correct placement: natural ⊂ whole ⊂ integers ⊂ rational ⊂ real?
True only for decimals
True statement
False statement
True only for positives
Evaluate: −2(1 • 4 − 2 ÷ 2) + (6 + 2 − 3). Choose the correct value.
−6
−4
−2
0
2
Find the value of (22÷2−2•5)2+(4−6÷6)2 .
10
14
32
256
196
Given w = 8 and v = −3, evaluate (wv2−4v)÷(2w+3v) .
8
5
6
4
7
Given a = −2 and b = 2 , evaluate ∣−10+7a∣−(15/2)b+5a3 .
−50
−42
−38
−54
−46
Simplify the expression: 10 − 2 k − 5 k + 28.
−7 k + 18
7 k − 18
−7 k + 38
−3 k + 38
7 k + 38
Simplify the expression: −3 a − 7 − 2 a + 9 a − 16.
4 a − 25
−4 a − 23
−4 a − 25
4 a − 24
4 a − 23
Combine like terms in 4 y − 2 x + 8 y − x + 14 y.
22 y − 3 x
12 y − 3 x
26 y − 3 x
22 y − x
26 y − x
Simplify the expression: 3(m − 7).
3m − 21
21 − 3m
3m + 21
m − 21
Simplify the expression: −5(2x + 7).
10x + 35
−10x + 35
10x − 35
−10x − 35
Simplify the expression: −(r − 3s).
r − 3s
r + 3s
−r − 3s
−r + 3s
Simplify the expression: −4(x − 9) + 2x − 1.
−6x + 35
−2x − 35
6x − 35
−2x + 35
Simplify the expression: −w + 8(3 − 4w) + 19w.
12 − 14w
−12 + 14w
12 + 14w
−12 − 14w
Simplify the expression: 1/2(2c + 18d) − (c − d).
d + 9d
d + 8d
c + 9d
−c + 9d
Factor the expression: 4x + 4.
x(4 + 4)
Prime
4(x − 1)
4(x + 1)
Factor the expression: 6r − 45.
3(2r − 15)
Prime
3(2r + 15)
6(r − 45)
Factor the expression: 9x − 32y.
9(x − 32y)
(9x − 32)y
(9 − 32)(x − y)
Prime
Factor the expression: 32m + 24n.
2(16m + 12n)
8(4m + 3n)
4(8m + 6n)
Prime
Solve the equation: −3n + 17 = 56.
n = 39/3
n = −39/3
n = 13
n = −13
Solve the equation: −21 = −16 + x/1.8.
x = −1.8
x = −9.0
x = −1
x = −9
Solve the equation: (m + 8)/(−2) = −19.
m = −11
m = −30
m = 11
m = 30
Solve the equation: (4/3)k + 15 = −31.
k = −34.5
k = −34
k = −69
k = 69
Solve the equation: a − 16 = 4a + 29.
a = 15
a = −15
a = −45/3
a = −15/1
Solve the equation: 8(p − 3) = 6(2p + 5).
p = 2
p = −22
p = 22
p = −2
Solve the equation: −(1/4)(20m − 8) = 4(m − 4).
m = 8
m = 0
m = −4
m = 4
Solve the equation: 2(5y − 8) = 9y − (16 − y).
y = 0
y = −24
No Solution
Infinite Solutions
Solve the equation: 3n + 6(n + 4) = 9(n − 2).
n = 2
n = −6
n = 6
n = 0
Which step correctly applies the distributive property to 8(3 − 4w)?
8 − 32w
11 − 4w
24 − 8w
24 − 32w
Four-fifths of the people invited to a wedding responded they were coming. Of those who responded, 19 did not show up. There were 121 guests at the wedding. How many people were invited?
121 invited in total
140 invited in total
175 invited in total
200 invited in total
The sum of two numbers is 58. The larger number is ten less than three times the smaller number. What are the two numbers?
14 and 44
16 and 42
18 and 40
20 and 38
Seventh and eighth graders sold tickets. Eighth graders sold fifteen more than twice the number seventh graders sold. Together they sold 486 tickets. How many did eighth graders sell?
321 tickets sold
333 tickets sold
339 tickets sold
327 tickets sold
Solve and graph the inequality: 4x + 7 ≥ −13. What is the solution set for x?
x ≥ −5
x ≤ −4
x ≤ −5
x ≥ −4
Solve and graph the inequality: m/−4 + 3 > 1. What is the solution set for m?
m < −8
m > 8
m < 8
m > −8
Solve and check possible solutions: 14 − 2k < 40. Which listed value of k is a solution?
−15 is a solution
−14 is a solution
−13 is a solution
−12 is a solution
Solve and check possible solutions: −1 + (5/2)p ≤ 9. Which listed value of p is a solution?
3 satisfies the inequality
4 satisfies the inequality
1 satisfies the inequality
2 satisfies the inequality
Translate the phrase: "Four more than the product of a number and -7 is 39."
−7n − 4 = 39
7n + 4 = 39
−7n + 4 = 39
4n − 7 = 39
Translate the phrase: "The sum of five-sixths of a number and 1 is -14."
(5/6)n + 1 = −14
(5/6)n − 1 = −14
(6/5)n + 1 = −14
5/(6n) + 1 = −14
Translate the phrase: "Seventeen less than twice a number is -49."
2n − 17 = −49
17 − 2n = −49
2n + 17 = −49
(n/2) − 17 = −49
Translate: "The quotient of a number and -3 is greater than or equal to -7."
n/−3 ≤ −7
n/−3 ≥ −7
n/3 ≥ −7
−3/n ≥ −7
Translate: "The product of a number and -5, increased by 8, is at least 53."
−5n + 8 ≥ 53
−5n − 8 ≥ 53
5n + 8 ≥ 53
−5n + 8 ≤ 53
Translate: "Fourteen more than twice a number is no more than -6."
2n − 14 ≤ −6
14 + n/2 ≤ −6
2n + 14 ≤ −6
2n + 14 ≥ −6
Solve and graph: x/3 + 17 ≤ 15. Which inequality describes the solution set?
x ≤ −6, open circle at −6
x ≥ −6, open circle at −6
x ≥ −6, filled circle at −6
x ≤ −6, filled circle at −6
Solve and graph: 23 − 4n < 19. Which inequality describes the solution set?
n ≥ 1, filled circle at 1
n ≤ 1, filled circle at 1
n > 1, open circle at 1
n < 1, open circle at 1
Simplify using the power rule: (w2)8
w10
w12
w14
w16
Simplify: (−6a4b9)2
36a^6 b^18
36a^8 b^18
−36a8b18
36a^8 b^20
Simplify: (2c−1d2)5
32c^{-5} d^{10}
10c−5d7
32c^5 d^10
2c−6d10
Add in scientific notation: 5.4×103+1.9×103
5.4×103
7.3×102
7.3×104
7.3×103
Compute: 4×106 + 2.5×107 . Write in scientific notation.
6.5×107
0.65×108
2.9×106
2.9×107
Subtract: 9.8×10−3−3×10−4
6.8×10−4
6.8×10−3
9.5×10−4
9.5×10−3
Subtract: 8×108 − 2×1010 . Express in scientific notation.
−0.8×109
−1.92×1010
−1.2×1010
−2.0×1010
Multiply in scientific notation: (7.5×107)(1.2×103)
7.5×1010
9.0×1010
8.7×1010
9.0×1011
Multiply: (9×102)(8×10−7)
7.2×10−5
7.2×10−4
6.8×10−4
9.0×10−5
Divide: (8.4×105)÷(7×101)
0.12×10^6
1.2×105
1.2×104
12×103
Compute: (1.9×10−8)÷(5×10−2)
3.8×10−7
3.8×10−9
0.38×10−6
9.5×10−7
Identify the rule: To simplify xm⋅xn , which exponent rule applies?
Quotient rule: subtract exponents
Zero rule: exponent becomes zero
Product rule: add exponents
Power rule: multiply exponents
Which expression uses the quotient rule correctly?
x7/x3=x10
x7/x3=x4
x7/x3=x3
x7/x3=x−4
Apply power of a power: (y3)4 equals what?
y1
y34
y12
y7
Which is correctly written in scientific notation?
0.45×105
4.5×104
4.5×105
45×103
Rewrite 0.0063 in scientific notation.
63×10−5
0.63×10−2
6.3×10−2
6.3×10−3
Strategize: To add 3.2×104 and 6.5×105 , what is the best first step?
Rewrite with same power of ten
Multiply mantissas directly
Subtract exponents first
Invert and divide numbers
Which set lists the domain of the relation {(-2, 6), (-5, -1), (3, 7), (-5, 0)}?
{-2, -5, 3, -5}
{-2, -5, 3}
{-2, 6, -5, -1}
{6, -1, 7, 0}
For the table x: 0, 4, 7, 10, 13 and y: -5, -5, -5, -5, -5, what is the range?
{-5}
{0, 4, 7, 10, 13}
{-5, -5, -5, -5, -5}
{-5, 0, 4, 7}
Using the vertical line test, which graph shows a function?
Graph in box 4 only
Graphs in boxes 4 and 5
Graphs in boxes 5 and 6
Graphs in boxes 4 and 6
From the table x: -3, -2, -1, 0, 1 and y: -27, -8, -1, 0, 1, is the relation a function?
No, some x have two y values
Yes, because y values repeat
No, some y have two x values
Yes, every x has one y
Given y = 9 − 1/2 x and domain { -6, -2, 8 }, which set is the range?
{ 12, 10, 5 }
{ 12, 8, -13 }
{ 12, 10, 13 }
{ -12, -10, -5 }
Which statement best describes the domain of a relation?
All possible x-values
All points on the graph
All possible y-values
All input and output pairs
A relation is a function if and only if:
Each x maps to one y
Each y maps to one x
No y values repeat
The graph passes a horizontal line test
Which slope type is represented by a line that rises left to right?
Positive slope
Negative slope
Zero slope
Undefined slope
What is the slope of the line passing through the points (−2, 4) and (−3, 9)?
1
−1
5
−5
Find the slope of the line through (7, −5) and (1, −13).
−8/6
−4/3
8/6
4/3
Compute the slope of the line through (4, −9) and (4, 1).
0
Undefined
10
−10
Determine the slope of the line passing through (7, −3) and (−9, 5).
−8/16
−1/2
8/16
1/2
A checking account balance changes from 443onFebruary1to 872 on February 7. What is the rate of change per day?
−$61.50 per day
$61.50 per day
$429 per day
$7 per day
Between February 7 ( 872)andFebruary15( 610), what is the average rate of change per day?
$8 per day
$32.75 per day
−$32.75 per day
−$262 per day
Which equation is in slope-intercept form?
x = 5y − 1
3(x − 2) = y
y = −4x + 7
2x + 3y = 9
Look at the graph labeled 27. Does it represent a linear or nonlinear function?
Constant function
Neither function
Nonlinear function
Linear function
Look at the graphs labeled 26 and 28. Which statement is true?
Both 26 and 28 are nonlinear
Graph 26 is linear; 28 is nonlinear
Graph 26 is nonlinear; 28 is linear
Both 26 and 28 are linear
Which graph best represents the line y = -x + 3 on a standard grid?
Slope −1, y-intercept −3, down-right
Slope −1, y-intercept 3, down-right
Slope 1, y-intercept −3, up-right
Slope 1, y-intercept 3, up-right
Convert 2x + y = −3 to slope-intercept form.
y = 2x + 3
y = −2x − 3
y = 2x − 3
y = −2x + 3
What is the slope of the line y = 7/5 x − 6?
7/5
6
−6
5/7
Which equation represents a vertical line?
x = −1
y = 6
y = 7/5 x − 6
y = −x + 3
Which equation represents a horizontal line?
2x + y = −3
y = 6
y = −x + 3
x = −1
Solve −x − 4y = 0 for y.
y = −4x
y = 4x
y = (1/4)x
y = −(1/4)x
What is the slope of a line passing through (0, 2) and (4, 5)
3/4
4/3
−3/4
−4/3
Write the equation of the line that passes through (0, −1) with slope −2.
y = −2x + 1
y = 2x − 1
y = −2x − 1
y = 2x + 1
If a line is parallel to y = −x + 3 and passes through (0, −4), what is its equation?
y = x + 4
y = −x + 4
y = x − 4
y = −x − 4
Convert x − y = 5 to slope-intercept form.
y = x + 5
y = −x + 5
y = −x − 5
y = x − 5
Match the following.
Add the exponents
x3⋅x6
Subtract the exponents
z4z8
Multiply the exponents
(y2)4
Selena Gomez has 397,500,000 followers on Instagram. What is the value of the exponent when this number is written in scientific notation?
Simplify
4x0
Match the following
x3(x−6)
Add the exponents
(y5)3
Multiply the exponents
x4x7
Subtract the exponents
4x2 + 7x2
Exponents stay the same
Write the number 0.00023 in scientific notation.
(a) x 10^ (b)
What is the EXPONENT when you write this number as scientific notation?
If the exponent on your power of 10 is positive, is your number larger or smaller than 10? (a)
Linear or non-linear?
Both the graph and equation are linear
Both the graph and equation are non-linear
The graph is linear
The equation is linear
It's transparent, not linear!
Which function is linear?
f(x)
h(x)
g(x)
