Expressions
What is the term for a combination of numbers, variables, and operations?
an expression
What is the solution to the equation (x + 5 = 12)?
x = 7
What is a function?
a relation where each input has exactly one output
What symbol represents "greater than"?
>
A basketball player scores an average of 12 points per game. If she plays x games in a season and scores a total of 324 points, write and solve an equation to determine how many games she played.
x = 324/12 = 27
The player played 27 games.
Simplify the expression: 3x+4x−5
7x - 5
Solve for x: 2x−4=10.
x = 7
If f(x)=x, what is f(3)?
Translate the word sentence into an inequality: “2 less than a number is more than 8.”
x - 2 > 8
The local soccer field is rectangular. The length is 15 feet more than twice the width. If the perimeter of the field is 280 feet, create an equation to find the width of the field.
Let w be the width of the field.
The length is 2w+15
The perimeter equation is:
2w+2(2w+15)=280
Solve for w:
2w+4w+30=280
6w=250
The width of the field is 41.67 feet.
w = 250/6 = 41.67
If y=2x+3, what is the value of y when x=4?
11
What is the slope of the line represented by the equation (y = 3x + 2)?
3
What is the domain of the function
f(x) = 1 / x
all real numbers except for 0
solve:
-x / 3 > 5
x > -15
A track and field athlete runs 33 laps around the track each day. She increases her speed by 0.50.5 minutes each week for 88 weeks. If she initially ran each lap in 44 minutes, write an expression to represent her lap time after w weeks of training.
Let w be the number of weeks.
The lap time after w weeks is:
4−0.5w
Expression: 4−0.5w
Expand the expression: 2(x+5).
2x + 10
Solve the equation: 3(x−2)=12.
x = 6
What is the range of the function
f(x) = x^2
all real numbers y ≥ 0
Solve:
(4x + 6) / 7 < 2
x < 2
The school's baseball team is selling tickets for their championship game. Adult tickets cost $15 and student tickets cost $8. They need to raise at least $2000 and can seat no more than 200 people in the stands. Write a system of inequalities to represent this situation, using a for adult tickets and s for student tickets.
Money raised:
15a + 8s ≥ 2000
Seating limit:
a + s ≤ 200
Factor the expression: x2 - 9
(x-3)(x+3)
What are the solutions for the equation (x2 - 4 = 0)?
x = 2 and x = -2
If f(x)=2x+1 and g(x)=x−3, what is f(g(5))?
9
Write and solve the algebraic inequality. The product of –3 and a number is at least –24.
–3x ≥ –24; x = 8
In a swimming competition, one swimmer is 12 meters ahead of another. The second swimmer is moving 0.5 meters per second faster than the first swimmer, who is swimming at 2 meters per second. Write and solve an equation to determine how many seconds it will take for the second swimmer to catch up to the first swimmer.
The first swimmer’s distance:
d1=2t
The second swimmer’s distance (starting 12 meters behind, swimming at 2.5 m/s):
d2 = 2.5t − 12
Set them equal:
2.5t − 12 = 2t
Solve for t:
0.5t = 12
t=24
It will take 24 seconds for the second swimmer to catch up.