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T1 Algebra Exam Review
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Terms in this set (62)
Rewrite this expression using radical notation: 3^3/4
(4√3)^3
What is an index?
3√10 - 3 is the index
What is a radicand?
√
8^2/3 + 100^1/2
14
Tou is the director working on a play and he needs to know the area of a circular stage with a radius of 7 feet. Use the formula A=3.14r^2 to find the area.
A = 153.86 ft^2
What categories do this number fall under? whole, integer, rational, irrational?
(-2)^4
integers, rational, whole
- simplified to 16
What is an integer?
numbers negative and positive (includes whole numbers)
- 0, -73, 333, -183
What is a rational number?
a number that can be written as a fraction
- 0.12, -18/5, √36
What is an irrational number?
non repeating and non terminating decimals and imperfect roots
- 0.12121212 repeating, √3, π
What is a whole number?
numbers without a fraction or decimal and is not negative
- 1, 2, 0, 173
What categories do this number fall under? whole, integer, rational, irrational
27^1/4
irrational
What categories do this number fall under? whole, integer, rational, or irrational
(1/4)^2
rational
- simplifies to 1/16
If a set is "closed," what does that mean? How can a set be not closed?
closed = when doing the listed operation, the answer has same subset as other numbers
- negative integers in addition are closed because when adding any negative integers, the answer is always a negative integer
not closed = when doing the listed operation, the answer has a different subset than the other numbers
- positive integers in subtraction are not closed because when subtracting some positive integers, the answer can be negative (like 3 - 4 = -1, a negative number)
Is this set closed or not?
positive irrational numbers in division
not closed - √50 divided by √2 would be √25, and √25 simplified is 5, which is a rational number
Is this set closed or not?
positive integers in addition
closed - when adding any positive integer, the answer is always positive and an integer
Simplify.
2(x + y - 3) - x
x + 2y - 6
Evaluate this expression when x = 2 and y = 4.
(9x - 3y)^2
36
Write an expression for this situation and then evaluate for the given value: Samuel earns $10 per hour plus $1 per suitcase he sells. Find his earnings when he works 8 hours and 20 suitcases.
10h + 1s
h = 8
s = 20
Megan has $25 to buy groceries. She has $15 worth of groceries in her cart and would like to buy some melons that cost $1.25 each. Write an equation that describes the situation, and determine how many melons Megan can afford.
15 + 1.25m = 25
8 melons (m = 8)
Is 20 a solution for 2x - 5 > 30?
yes
What is a function?
when an x-value is paired with only ONE y-value
- x-value is input and y-value is output
Which one is NOT a function?
a. (2,1), (4,3), (6,5), (8,5)
b. (2,1), (4,3), (6,5), (2,7)
b. (2,1), (4,3), (6,5), (2,7) - there are two x = 2, meaning 2 is paired twice in a mapping diagram
Given the functions f(x) = 7x - 2 and g(x) = 3x + 6, find the value of x for which f(x) = g(x)
x = 2
What is domain and range?
domain = x; range = y
Which ordered pair is an answer to y = 2x + 8?
a. (1, 10)
b. (5, 20)
a. (1, 10) - when plugging 1 in for x and 10 in for y, the answer on both sides match (10 = 10)
Which ordered pair is a solution to -5x + 3y > 12?
a. (2, 8)
b. (3, -6)
a. (2, 8) - when plugging in 2 for x and 8 for y, the answer is 14 > 12, which is true
Consider the rule y = 2x + 12 with a domain of {0, 2, 4, 6, 8}. What is not a member of the set's range?
a. 12
b. 14
c. 24
d. 28
b. 14 - when putting 0, 2, 4, 6, and 8 in for the domain (x-value), 14 is the only number that does not appear as the answer
A new car costs $15,000. Gasoline costs $4 a gallon. Which function shows the cost of the car and x gallons of gasoline?
a. f(x) = 4x - 15,000
b. f(x) = 4x + 15,000
c. f(x) = 4x
d. f(x) = 15,000
b. f(x) = 4x + 15,000
What is a solution for 0 = 9x + 81?
a. -9
b. 0
a. -9 - insert -9 in for x and the answer is 0
What is 10 > -2x + 4 simplified?
-3 < x
Evaluate and simplify the expression 15x^5/6 when x = 64.
480
The water level of a river is 34 ft, and it is dropping at a rate of 0.5 ft per day. Write an equation that represents the water level, w, after d days.
w = 34 - 0.5d
The speed limit is 65 miles per hour. Your car has an idle speed of 10 miles per hour and a maximum speed of 15 additional miles per gear. Write an inequality that represents how many gears can be engaged while obeying the speed limit.
10 + 15g ≤ 65
Find the slope of the line that has its x-intercept at 3 and its y-intercept at 4.
-4/3 - if you use the formula y2-y1/x2-x1, the answer should be -4/3
Tell whether the function y - 3 = 2x is linear.
yes, all x values are only paired with 1 y value
What is the rise and what is the run of -3/2?
-3 is the rise (going down 3) and 2 is the run (going right 2)
Find the slope of the line that has its x-intercept at -2 and its y-intercept at 7. What is the slope-intercept equation?
slope = 7/2
equation: y = 7/2x + 7
Brandon's cell phone bill is given by y = 0.15x + 5 and Lisa's cell phone bill is given by y = 0.20x + 25, where x is the number of text messages each sends in a month. Interpret the meaning of 0.15 and 0.20 in each equation.
- 0.15 is the amount that each text costs for Brandon and 0.20 is the amount that each text costs for Lisa
Solve the system of equations by substitution.
y - 2 = 4x
5y - 2x = 1
(-0.5, 0)
Solve the system of equations by elimination.
3x - 2y = 9
5x + y = 2
(1, -3)
Rewrite these inequalities in slope-intercept form.
4y ≤ 15x + 40
2y + 50 ≥ 25x
y ≤ 15/4x + 10
y ≥ 25/2x - 25
What is the y-intercept of 2x + 5y = 15?
(0,3)
What is standard form?
Ax+By=C
If f(x) = 3x - 4 and g(x) = -2x + 1, which of the following represents f(x) - g(x)?
a. h(x) = 5x - 5
b. h(x) x - 3
a. h(x) = 5x - 5
What is the solution for this problem?
5p - 8 = 1 + 5p - 9
no solution
What is the solution for this problem?
x - 10 + x = 8 + 2x - 18
infinitely many solutions
Which one is NOT a linear equation?
a. y = 6x
b. y = x + 6
c. 6y = x
d. xy = 6
d. xy = 6
Which equation is a solution of the point (1, 2)?
a. 3y + x = 7; x - y = -1
b. 2x + 2y = 2; 7x = 4y
a. 3y + x = 7; x - y = -1
Which is a solution to the system of inequalities of y > 3x - 1 and 2x + y < 1?
a. (0, 5)
b. (-2, 3)
b. (-2, 3)
Which of the following is a solution to the systems of equations 2x + 3y = 7 and 4x - 2y = -2?
a. (1/2, 2)
b. (2, 1)
a. (1/2, 2)
A 6-foot snowman is built and begins to melt, losing 6 inches of height per day. Write an equation that represents the height y (in feet) after x days and interpret what the x and y-intercepts mean in the real-world.
y = -0.5x + 6
- y int = 6 = height of the snowman originally
- x int = 12 = after 12 days, the snowman will be melted
The perimeter of a rectangle is 30 cm, and its height is 3 cm more than twice its width. Write a system of linear equations for h and w that describes the situation and solve the system to find the height and width of the rectangle.
2h + 2w = 30
h = 2w + 3
w = 4 cm
h = 11 cm
Isolate the variable b in this equation: a = bc + 2
b = (a - 2)/c
Isolate the variable a in this equation: b = ac
a = b/c
What can be used to represent a function?
ordered pairs, equation using y or f(x), graph, table, or mapping diagram
What is a coefficient?
Number infront of variable
- 3x = 3 would be the coefficient
Can an answer be found on a dashed line in a linear inequality?
no
When do you dash and shade a line in a linear inequality?
dash - no line under < >
solid - line under ≤ ≥
When do you do a solid or outlined dot when plotting numbers for an inequality?
solid - ≤ ≥
outlined - < >
What is a linear function?
function whose graph is not vertical
What is a linear equation?
any equation that can be put in standard form (Ax + By = C)
What is a positive and negative slope?
positive = slope rises left to right
negative = slope falls left to right
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