PCWEST Algebra I EOI Review
Paul is selling lemonade as a fundraiser to buy a bicycle that will cost $68.00. The profit (P) Paul makes for x cups of lemonade is given by the equation below. P=0.50x - 2.50 How many cups of lemonade must Paul sell in order to purchase the bicycle.
141
Solve A=(1/2)BH for B.
B=(2A)/H
Is the data set below a relation or function? {(0, 2), (3.4, 2), (1, 2)}
It is a function beause the x's do not repeat.
What is the slope of the line below? -3x + 4y = -12
The slope is 3/4
The sign above a sweater says that it is 30% off, the sweater costs $45, how much will the sweater cost after the discount?
$31.50
Factor 2x^2 + 8x + 6
(2x + 2)(x + 3)
Factor x^2 - 3x - 10
(x + 2) (x - 5)
What is the slope formula?
(y2-y1)/(x2-x1)
Find the slope of the points (3, 1) (-1, 5)
-1
Line a and b are perpendicular, the slope of line a is 3, what is the slope of line b?
-1/3 I flip over the slope of line a and change the sign.
What is the simplified form of this expression: (2m - 3) + (m - 3) - (5m + 6)
-2m - 12
What is the sum of the expressions below? (2x^2 + 4x - 3) + (-5x^2 - 7x - 5)
-3x^2 - 3x - 8
If line c and d are parallel, the slope of line c is -4, what is the slope of line d?
-4 They are parallel, so they have the same slope.
The temperature of a gas is -76 degrees Fahrenheit. What is the temperature of the gas in Celsius? F=(9/5)C + 32
-60 degrees Celsius
What is the simplified form of this expression: (-5b - 3) + (4b - 2)
-b - 5
What is the slope of a horizontal line?
0 (zero)
A drink container is shaped like a cylinder. The height of the container is 10 centimeters and the radius is 6 centimeters. What is the approximate volume of the container? V=3.14R^2H
1,130.4 cubic centimeters
You roll a cube, what is the probability that you will roll an odd number?
1/2
You roll a cube, what is the probability that you will roll a number greater than 4?
1/3
What is the slope of a line perpendicular to y=-7x + 3?
1/7; remember to flip the slope and change the sign when finding slopes of perpindicular lines.
Evaluate |x - 4|; x = -6
10
Antonio read the first 60 pages of his book in 40 minutes. At this rate, how long should it take Antonio to read the rest of his 210 page book?
100 minutes
Evaluate (3m - 2(-n) - mn); m=3 and n=-2
11
What is the simplified form of this expression: 3x + 6y + 8x - 2y
11x + 4y
What is the x value of the system of equations below? x + y = 4 2x + 3y = -2
14
What is the value of f(5) in the equation f(x)=3x + 2
17
What is the value of f(-2) in the equation f(x)= -2x -2?
2
A drink dispenser fills cups at a rate of 2 ounces per second. Adrian has a 64-ounce cup that already contains 18 ounces of water. How long will it take the dispenser to fill the rest of Adrian's cup with water?
23 seconds
If f(x) = 2x + 1, what expression represents f(x + 2)?
2x + 5
If f(x) = x -5, what expressions represents f(2x + 1)?
2x - 4
Factor 2x^3 - 10x^2 + 8x
2x(x -1)(x-4)
What is the simplified form of (2x + 3)(x + 2).
2x^2 + x - 6
What is the y value of the system of equations below? y=x + 2 y=-x + 4
3
Translate the following phrase into an algebraic expression: the difference of 3 and a number
3 - x
The equation below shows the cost (y) of renting a ballroom for different number of hours (x). y=225 + 75x Rick paid $450 to rent the ballroom. How many hours did Rick rent the ballroom?
3 hours
Joe started saving for a car. He opened an account with $400 and saves $50 per week. He needs $2000 to buy his car. How many weeks will it take for Joe to save enough money to buy the car?
32 weeks
At a candle store, the ratio or green candles to red candles is 2 to 5. The store has 4,900 candles. How many candles are red?
3500 red candles
Sarah sold 40 tickets to talent show, she wants to set up 20% more chairs than tickets sold. How many chairs should she set up?
48 chairs
What is the slope of a line parallel to y = 4x + 3?
4; remember parallel lines have the same slope.
Simplify: (5p - 3) + (5xp - 2p + 1)
5xp + 3p -2
Matt starts with $15 and saves $10 a week. At the same time, Julie starts with $45 and saves $5 a week. In how many weeks will they have the same amount of money?
6 weeks
Translate the following phrase into an algebraic expression: the quotient of 7 and a number
7/n or 7 ÷ n
Evaluate 2x + 1; x =4
9
What is the y-value of the solution to the system of equations below? y=x + 4 y=2x -1
9
What type of line contains the points (-2, 5) and (4, 5)?
A horizontal line because the slope is 0.
What type of line contains the points (-1, 3) and (-1, 2)?
A vertical line because the slope is 0. (Your calculator will say error, divided by zero).
What numbers are your domain?
Domain is my x.
Solve C=(5/9)(F-32) for F.
F=(9/5)C + 32
What does HOY stand for?
H-horizontal line O-zero slope Y-y=a is the equation
Victor's car wash charges different prices for washing different sizes of cars. What is the independent and dependent variables?
Independent=car size Dependent = price charged
Is the data set below a relation or function? {(4.2, 1), (5, 2.2), (7, 4.8), (4.2, 0)}
It is a relation because you see an x twice, 4.2 is listed twice.
Solve V=LWH for L.
L= V/(WH)
When given a graph, how will you tell the difference between linear and nonlinear?
Linear means a straight line, nonlinear is NOT a straight line.
When given ordered pairs (x, y) or a set of data with x and y values, how will you tell if the data is linear?
Linear means a straight line, so the slope is constant. I can use my slope formula (y2-y1)/(x2-x1) to see which set of data has a constant slope. The data with a constant slope will be linear.
Is the data set below linear? {(0, 3), (1, 5), (2, 7), (3, 9)}
Linear, it has a constant slope.
John wants to know Ms. Moore's age. Ms. Moore tells him that she is ten less than four time his age. Write an equation to represent Ms. Moore's age.
M=4J-10
Find the mean, median, mode and range of the following numbers; 10, 13, 15, 9, 7
Mean: 10.8 Median: 10 Mode: None Range:8
Describe the graph of x<5
On the number line draw an open circle at 5, then shade to the left.
Describe the graph of "x is all numbers greater than or equal to - 3"
On the number line, draw a closed circle at -3, then shade to the right.
What numbers are your range?
Range is my y.
Samantha's age is ten years less than three times Bobby's age. What is the equation for Samantha's age?
S=3B-10
When a system of equations has infinite solutions, what does its graph look like?
The graph will look like a single line because the equations in the system are equivalent.
When a system of equations has no solution, what does its graph look like?
The graph will look like two parallel lines (they never intersect).
What is the mean and how do you find it?
The mean is the average of the data set. I add up all the numbers I am given and divide by the number of numbers I added up.
What is the median and how do you find it?
The median is the middle number when I put all of my data from least to greatest.
What is the mode and how do you find it?
The mode is the number that occurs most often. I look at my data and see which number is repeated the most. If no numbers are repeated, than there is no mode.
Probability is...
The number of favorable outcomes over the number of possible outcomes.
What is the range and how do you find it?
The range is the difference between the biggest and smallest number in my data. I take the biggest number and subtract the smallest number.
Given a set of data or ordered pairs, how can you tell which set is a function?
The set where the x's do not repeat are a function. In a function, the x's cannot repeat.
When you graph a system of equations where do you find the solution?
The solution to a system of equations is the point of intersection on the graph.
If two lines are perpendicular, what do you know about their slopes?
Their slopes are negative reciprocals.
If two lines are parallel, what do you know about their slopes?
Their slopes are the same.
What does VNOX stand for?
V-vertical line NO-no slope (undefined slope) X-x=a is the equation
What does f(3) mean?
What is y when x = 3?
Words to describe "-"
left, less than, minus, subtract, difference
Solve y=mx + b for m.
m=(y-b)/x
Words to describe " +"
more than, add, sum, total, combined, in all, altogether
Translate the following phrase into an algebraic expression: a number divided by 7
n/7 or n ÷ 7
Words to describe "×"
product, times, factor, multiply
Words to describe "x/y" or "÷"
quotient, per, out of, divide
Solve d=rt for t.
t=(d/r)
What is the slope of a vertical line?
undefined (no slope)
Translate the following phrase into an algebraic expression: 3 less than a number
x - 3
Solve -2x + 4 ‹ 8
x > -2; remember to flip the sign when you multiply or divide by a negative number.
10x - 3 = 17, solve for x.
x=2
3x - 8 = 4, solve for x.
x=4
Write an equation for a vertical line.
x=k, where k can be any number. Remember VNOX!
Simplify (x + 3)(x-2)
x^2 + x - 6
Write the equation of a line given the slope of 2 and the y-intercept of -3.
y = 2x -3
What is the formula for Point-Slope?
y-y1=m(x-x1) where m=slope and the point (x1, y1)
Write the equation of the line given the x-intercept of 2 and the y-intercept of -3.
y=(-3/2)x -3
Write the equation of a line given the points (-1, 4) and (7, 5).
y=(1/8)x + (33/8)
Write the equation of a line given the point (0, 3) and the slope of m=-2.
y=-2x + 3
Write an equation for a horizontal line.
y=k, where k can be any number. Remember HOY!
Write the formula for slope-intercept form.
y=mx + b m=slope and b=y-intercept
{(0, 1), (2, 4), (4, 2)}, what numbers are the domain?
{0, 2, 4} The domain are my x numbers in the ordered pair (x, y).
{(0, 1), (2, 2), (4, 3)}, what numbers are the range?
{1, 2, 3} The range are my y numbers in the ordered pair (x, y).
f(x)= -1.5x + 4 has a domain of {1, 2, 3, 4}, what is the range?
{2.5, 1, -0.5, -2} I plugged in each domain (x) and got my range (y).