Benchmark Review 1
A function is defined as f(x) is 2 less than five times a number x. Given this function, find f(-5).
-23
Write an expression to represent the phrase "ten times the sum of a number and twenty-five?"
10(x + 25)
Evaluate the expression.
Two times the sum of two raised to the eighth power and thirty-eight divided by three times fourteen squared.
0
Yolanda has scored 97%, 89%, 76%, 94% on her first four math tests. What is the minimum score she needs to get on her next test to have an A in the class?
94
Does this equation have one solution, no solutions, or infinite solutions?
2x - 5 = 2(x - 2)
No Solution
A gym offers a membership plan that includes a fixed monthly fee of $25 and an additional $2.50 for each class attended, x, for the first 10 classes and $1.50 for each class, y, attended beyond the first 10 classes. If you attend 12 classes this month, how much will you pay for your membership?
$53
Addison evaluated the expression ab2 + -a for a = -3 and b = -6. She says the solution is -105. Is she correct?
YES!
A mobile phone plan charges a $20 activation fee plus $4 per gigabyte of data. A customer has a budget of $100. How many gigabytes, x, can they use?
x ≤ 20
Solve the equation for m.
8(m+1/4) - 12 = 6m - 14
m = 7
Does this equation have one solution, no solutions, or infinite solutions?
-3(2x + 10) = 3(-2x + 10)
No Solution
Alex and Priya are selling lemonade to raise money for their community garden.
Alex earns $3 for every cup of lemonade he sells.
Priya also earns $3 per cup, but she received a $4 tip at the start of the day. How would the graph representing the total amount of money Priya earns differ from the graph representing Alex’s earnings?
The y-intercept of Alex's graph would be at 0 whereas the y-intercept of Priya's graph would be at 4.
A function is represented by this rule:
The cube of x, increased by 3, is y.
Select the ordered pairs that follow this rule.
A. (0,3) B. (1,4) C. (-2, -5) D. (2,11) E. (-1, 1)
A. B. C. D.
A student wrote the first step while solving an equation as shown.
Equation:
3y+(y+5)=40
Step 1:
(3y+y)+5=40
Which property justifies this step?
○ Associative property
○ Commutative property
○ Reflexive property
○ Substitution property
Associative Property
Does this equation have one solution, no solutions, or infinite solutions?
3(b - 8) = 3b - 24
Infinite Solutions
Which statements are true about the graph of y = 8 ?
A. The graph is a horizontal line.
B. The graph is a vertical line.
C. The point (0,8) is on the line.
D. The point (8,0) is on the line.
E. The slope of the line is undefined.
A. and C.
A candy shop sells fudge for $6 per pound. The shop offers a 25% discount on the total bill. A customer has $45 to spend and wants to buy x pounds of fudge.
Write an inequality to represent this situation and, using the correct arrow type, plot the possible values of x on a number line.
x≤10
The formula for the volume of a cone is V=1/3πr2h. Rearrange the formula to solve for h.
h= √ 3V/π r
Maria is building a rectangular picture frame. She already knows the width of the frame and the total amount of trim she has available for the outside edge.
Solve the perimeter formula for L to help Maria determine what the length of the frame must be.
P= 2L + 2W
L = P - 2W/2
A local gym is offering a weekend fitness class. The total cost,C, in dollars, is modeled by the function shown, where x is the number of people who sign up for the class.
C(x)=10x+40
What is the y-intercept and what does it mean in the context of the problem?
y-intercept = 40 and is the fixed cost for the set up of the fitness class.
What is the zero of this equation?
y = 3x+6
x=-2 or (-2,0)
What is the domain and range of the equation y=6x-9?
Domain - All Real Numbers
Range - All Real Numbers
A linear equation has a slope of 1/2 and passing through the point (2,3). Write the equation in point slope form.
y - 3 = 1/2(x - 2)
A linear equation has a slope of 3 and passing through the point (-4,5). Write the equation in standard form.
-3x + y - 17 = 0
What is the equation of line that is parallel to line y=x+10 and passing through the point (2, 4)?
A line parallel to
y=x+10
must have the same slope, which is 1.
Use point-slope form with point (2,4):
y−4=1(x−2)
Simplify:
y−4=x−2
y = x +2
Which is the equation for the line that is perpendicular to y = -2x + 5 and passes through the point (6 , 8)?
The given line is:
y=−2x+5
Its slope is –2.
A line perpendicular to this one must have the negative reciprocal slope:
m=1/2
Now use point-slope form with the point (6,8)
y−8=1/2(x−6)
Simplify:
y−8=1/2x−3
y= 1/2x +5