Algebra 2: Semester 1 Final
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: Find h(8) - f(-7)
-14
Simplify the expression below: √324 - (2 - 9)^2 + 162 /3^3
-25
Simplify the expression below: √2^6 + (11 - 5^2)/ |-10-2(3)|
-3/8
Given the functions below, find b(-2) - a(12): a(x) = |13 - 2x| ; b(x) = 8x - 14
-41
Simplify the expression: [18 - (-1-7)^2] + 16/2^4
-45
Evaluate the expression below (if x = 4/9, y = 1/2, and z = 3/5): 6xy - 3z
-7/15
If 2x - 1 = 13, evaluate the expression below: -x^2 - 4x
-77
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: Find f (11/12)
-8/3
Write the equation below in standard form: y = -2/3x + 3
2x + 3y = 9
Simplify the expression: √|-x^2 - 4y^2| (if x = 3 and y = -2)
5
Write the equation below in standard form: (5/8x + 3/4y) = -1
5x + 6y = -8
Write the equation below in standard form: 8/3y = 5/6x - 2
5x - 16y = 12
Solve & graph each absolute value inequality. Write your answer in interval notation. -3-6|4x - 10| < -87
Solution: x > 6, x < -1 Interval notation: (-∞, -1) U (6, ∞)
Solve & graph each inequality. Write your answer in interval notation. 33x - 8(3x + 9) > -9
Solution: x > 7 Interval notation: (7, ∞)
Solve & graph the inequality below: |9x + 3| ≤ 21
Solution: x ≤ 2, x ≥ -8/3 Interval notation: [-8/3, 2]
Solve & graph each compound inequality. Write your answer in interval notation. 9y - 2 < 13 AND 3y - 2 > -29
Solution: y < 1.6, y > -9 Interval notation: (-9, 1.6)
Which represents the solution to the inequality below in interval notation? -1/3(21 - 9n) ≥ 4(2n - 7) - 9 A. (-∞, 6] B. (-∞, -6] C. [6, ∞) D. [-6, ∞)
A. (-∞, 6]
Solve by elimination: 18x = 12y + 7 -8y + 21 = -12x
NO SOLUTION
Solve & graph each inequality. Write your answer in interval notation. -11 - 8k ≥ 23 - (7 - 4k)
Solution: k ≤ -2.25 Interval notation: (-∞, -2.25]
Solve & graph each absolute value inequality. Write your answer in interval notation. |v - 3|/-5 > -1
Solution: v < 8, v > -2 Interval notation: (-2, 8)
Solve & graph each compound inequality. Write your answer in interval notation. 10 + 2w ≥ 22 OR 5w - 8 > -12
Solution: w ≥ 6, w > -4/5 Interval notation: (-4/5, ∞)
Solve & graph each compound inequality. Write your answer in interval notation. 7 - 3x ≤ -20 OR 5x - 6 ≤ 9
Solution: x ≥ 9, x ≤ 3 Interval notation: (-∞, 3] U [9, ∞)
Absolute value parent function
f(x) = |x|
Describe the transformation rule: f(x + h)
h shifts left units
Describe the transformation rule: f(x - h)
h shifts right units
Describe the transformation rule: f(x) + k
k shifts up units
Solve the equation below for m: 2m - n/5 = 7n
m = 18n
Solve each equation. Be sure to check for extraneous solutions. |2m+7| = 6m + 13
m = {-3/2}
Solve each equation. Be sure to check for extraneous solutions. |5n-10|/-2 = -15
n = {8, -4}
Solve each equation: If SA = 1/2 lp + B, find p
p = 2SA - 2B/l
Solve the system below: 3x - 5y + 2z = -53 x - 7y - 4z = -37 5x + 9y + 2z = 57
x = -1, y = 8, z = -5
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: If f(x) = 53, find x.
x = -13
Solve each equation: 7x-3/3 = 3x-4/8
x = 12/47
Find three consecutive odd numbers such that the sum of five times the smaller number and twice the larger number is 33 more than six times the median number.
x = 37, 39, 41
Give an example of a linear equation that is parallel to the y-axis.
x = 6
Solve each equation. Be sure to check for extraneous solutions. |-7-9x| = 2
x = {-1, -5/9}
Solve the equation below: |3x - 9| = 24
x = {-5, 11}
Find the x- and y-intercepts of the equation below. Write your answers as ordered pairs. 8y = -9x - 12
x-int: (4/-3, 0) y-int: (0, -3/2)
Find the x- and y-intercepts of the given line, then graph the line: 4y = 10x - 24
x-intercept: (12/5, 0) y-intercept: (0, -6)
Describe the transformation rule: -f(x)
reflects over x-axis
Simplify the expression: 4 + √121 - 2 • 3^3/ |-19-2(-8)|
-13
2a - b/5 = 7b. Solve for a
a = 18b
Solve the system below by substitution: 6x - y = -23 2x + 5y = -13
(-4, -1)
Solve by substitution: 2x + 3y = -35 8x - y = -23
(-4, -9)
Solve by substitution: 5x - 4y = 9 x + 7y = -6
(1, -1)
Solve the system below by elimination: x = y - 4 7x - 2y = 17
(5, 9)
Solve by elimination: 3x + 10 = 14y 8x - 7y = 34
(6, 2)
Solve the equation below: 8a - (1 + 5a) = 4(3a - 11) - 20
a = 7
Describe the transformation rule: a • f(x) when |a| > 1
vertical stretch
Simplify the expression: 10a - 5ab + 4ab (If a = 2/5 and b = -1/6)
11/3
Given the function below, find f(7): f(x) = -x^2 + 9x
14
Evaluate the expression below (if m = -4, n = 3, and p = 12): m^2n + 9p/√np
26
Solve the equation below: 5p - 8/2 = 7p + 4/6
7/2
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: Find g(-5)
86
The width of a rectangle is four less than one half the length. If the perimeter of the rectangle is 94 meters, find the area of the rectangle.
A = 442m^2
Solve & graph the compound inequality below: -4k - 3 < -7 OR 1 - k ≥ 6
Solution: k > 1, k ≤ -5 Interval notation: (-∞, -5] U (1, ∞)
Which ordered pairs represent solutions to the linear inequality below? (check all that apply) x - 4y < -12 A. (1, -8) B. (3, 5) C. (-8, -3) D. (-7, 9) E. (-12, 0) F. (-4, 2)
B, D
For each boat he sells, Mick earns $149 in addition to 2% of the purchase price of the boat as commission. If p represents the purchase price of the boat, which equation represents Mick's commission, c? A. c = 149 + 0.2p B. c = 149 + 0.02p C. p = 149 + 0.2c D. p = 149 + 0.02c
B. c = 149 + 0.02p
Which system of equations has an infinite solution? A. y = 2x -7, 2x + y = 5 B. x = 3y + 15, 12y = 4x - 60 C. 10x + 8y = -16, -5x = 4y + 28 D. y = 8, x = 8
B. x = 3y + 15, 12y = 4x - 60
Which represents the solution to the inequality below in interval notation? -3|n - 5| - 11 < -38 A. (-4, 14) B. (-14, 4) C. (-∞, -4) U (14, ∞) D. (-∞, -14) U (4, ∞)
C. (-∞, -4) U (14, ∞)
Solve & graph each inequality. Write your answer in interval notation. -5/3(9/10x + 15) < 7 - (8 - 9/2x)
Solution: x > -4 Interval notation: (-4, ∞)
Solve & graph each compound inequality. Write your answer in interval notation. m +5 > 11 OR 8 - 10m ≥ 33
Solution: m > 6, m ≤ -2.5 Interval notation: (-∞, -2.5] U (6, ∞)
Solve & graph each absolute value inequality. Write your answer in interval notation. |3n + 8| + 1 > 5
Solution: n > -4/3, n < -4 Interval notation: (-∞, -4) U (-4/3, ∞)
Which value of x is NOT in the solution to the compound inequality below? -15 ≤ 2x - 9 < 5 A. -3 B. 0 C. 4 D. 7
D. 7
Which represents the solution to the compound inequality below in interval notation? 5 - 2x > 31 AND 7x + 8 ≥ -55 A. (-13, -9] B. (-∞, -13] U [-9, ∞) C. [-9, ∞) D. No solution (crossed-out zero)
D. No solution (crossed-out zero)
Which of the following lines is perpendicular to the equation given below? -9x = 15 - 3y A. 6x + 2y - 8 = 0 B. x - 3y = -3 C. 12x - 24 = 4y D. 6y = 42 - 2x
D. y = 7 - 1/3x
Solve & graph each absolute value inequality. Write your answer in interval notation. |9 - a| ≥ 2
Solution: a ≤ 7, a ≥ 11 Interval notation: (-∞, 7] U [11, ∞)
Solve & graph the compound inequality below: 1/2a - 5 ≥ -3 OR -6a - 14 ≤ -56
Solution: a ≥ 4, a ≥ 7 Interval notation: [4, ∞)
Solve & graph the equation below: 5 - (9 - 4x)/-2 < -5
Solution: x > 3.5 Interval Notation: (3.5, ∞)
The sum of three consecutive numbers is 41 less than five times the largest number. Find the largest number.
Largest number = 19
Solve the equation below: |6w + 4| = 2w - 10
NO SOLUTION
A change jar contains nickels, dimes, and quarters, totaling an amount of $1.90. The amount of nickels is one more than twice the number of dimes. The number of quarters is one half the total number of nickels and dimes. Find the number of each coin in the change jar.
Nickels = 7 Dimes = 3 Quarters = 5
Solve each equation: 7 - 5/2(8n - 18) = 14 -10(2n -3)
No solution
Give an example of a line that is parallel and a line that is perpendicular to the given line: y = -5
Parallel: y = -3 Perpendicular: x = -1
Give an example of a line that is parallel and a line that is perpendicular to the given line: 9x + 6y = -6
Parallel: y = -3/2x + 2 Perpendicular: y = 2/3x + 2
Ben has a collection of quarters and nickels worth $5.35. If the number of nickels is five less than twice the number of quarters, find the number of each coin.
Quarters = 16 Nickels = 27
Solve & graph each compound inequality. Write your answer in interval notation. -18 ≤ 2b - 8 < -8
Solution: -5 ≤ b < 0 Interval notation: [-5, 0)
Solve & graph each inequality. Write your answer in interval notation. 11(5u - 4) - 7u ≥ 8(6u - 7)
Solution: All real numbers Interval notation: (-∞, ∞)
Aliyah bought four composition notebooks and three packs of pencils from the school bookstore and paid $10.93. Laura bought seven composition notebooks and two packs of pencils and paid $13.31. If each pencil pack contains ten pencils, what is the unit price per pencil?
Unit price/pencil = $0.179
Define variables and write equations to represent the following situations, then solve: For commission as a realtor, Michelle earns $349 plus 3% of the purchase price for each home she helps buy or sell. If she earned $8,965 in commission on a certain home, find its purchase price.
VARIABLES: p = purchase price c = commission EQUATION: 8965 = 349 + 0.03p ANSWER: p = $287, 200
Define variables and write equations to represent the following situations, then solve: On Ryan's last social studies test, there were two types of questions: true/false worth 2 points each and multiple choice questions worth 4 points each. If Ryan earned 86 points on the test and answered 18 multiple choice questions correctly, how many true/false questions did he answer correctly?
VARIABLES: t = true/false m = multiple choice EQUATION: 2t + 4m = 86 ANSWER: t = 7 (answered correctly)
Find the x- and y-intercepts of the given line, then graph the line: y = -5x - 3
x-intercept: (3/-5, 0) y-intercept: (0, -3)
Which equation has a solution of all real numbers? a. 5k - (6k - 18) = 9 - k + 17 b. 14 - 5(y + 10) = 4 - 8(y + 5) c. 6(-2w - 3) = -4(3w + 7) + 10 d. 7m - 2(2m + 3) = 8 - (3m -10)
c (0 = 0)
Solve the equation below: -2|7 - 9c| + 7 = -15
c = { 2, -4/9}
Linear parent function
f(x) = x
Quadratic parent function
f(x) = x^2
Solve each equation: 3(7-9k) + 23k = 4k - (24-k)
k = 5
Solve each equation. Be sure to check for extraneous solutions. 2-10 |k+1| = -78
k = {7, -9}
Describe the transformation rule: f(x) - k
k shifts down units
Solve & graph each compound inequality. Write your answer in interval notation. 7p + 5 ≤ -37 AND -10p < 10
p ≤ -6, p > -1 NO SOLUTION
Given the function below, if h(x) = -1, find x: h(x) = -6x + 20
x = 7/2
Solve the system below using your method of choice: 4x + 2y - 5z = 47 x - 2y + 6z = -10 9x - 7y - z = 75
x = 8, y = 0, z = -3
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: If h(x) = 39, find x.
x = {-10, 16}
Use f(x) = -4x + 1, g(x) = x^2 - 8x + 21, or h(x) = |9 - 3x| for the question below: Find g(x + 4)
x^2 + 5
Given the function below, find p(x - 1): p(x) = x^2 - 7x
x^2 - 9x + 2
Write the equation in slope-intercept form with the given information: Passes through (-8, 3) with a slope of -2
y = -2x - 13
Write a linear equation in slope-intercept form that passes through the points (-11, -5) and (1, -2).
y = 1/4x - 9/4
Write the equation in slope-intercept form with the given information: Passes through (-7, -3) and (5, 6)
y = 3/4x + 9/4
Write the equation below in SLOPE-INTERCEPT form, then graph the line: 12x = 4y - 28
y = 3x + 7
Write the equation below in SLOPE-INTERCEPT form, then graph the line: 4x - 5y = -10
y = 4/5x + 2
