NO CALCULATOR: Which statement about the function $$y=x^2-4x-12$$ is true?

The expression $$x^2-4x-12$$ has factors $$\left(x-6\right)$$ and $$\left(x+2\right)$$ , and the function has zeros at $$x=-2$$ and $$x=6$$ .

The expression $$x^2-4x-12$$ has factors $$\left(x-6\right)$$ and $$\left(x+2\right)$$ , and the function has zeros at $$x=-6$$ and $$x=2$$ .

The expression $$x^2-4x-12$$ has factors $$\left(x-2\right)$$ and $$\left(x+6\right)$$ , and the function has zeros at $$x=-6$$ and $$x=2$$ .

The expression $$x^2-4x-12$$ has factors $$\left(x-2\right)$$ and $$\left(x+6\right)$$ , and the function has zeros at $$x=-2$$ and $$x=6$$ .

A student is solving the equation 𝟐𝟎𝒙 = 𝟒(𝒙 − 𝟖). Which describes a first step the student could use to solve the equation correctly?

The student can distribute 4 on the right side of the equation, resulting in $$20𝑥=4𝑥−32$$ .

The student can distribute 4 on the right side of the equation, resulting in $$20𝑥=4𝑥−8$$ .

The student can divide both sides of the equation by 4, resulting in $$5𝑥=𝑥−2$$ .

The student can divide both sides of the equation by 4, resulting in $$16𝑥=𝑥−8$$ .

NO CALCULATOR: Consider the equation. $$-2\left(x+9\right)=\frac{-3\left(4x+36\right)}{6}$$ What is the solution to the equation?

There are infinitely many solutions to the equation.

There is no solution to the equation.

A leatherworker makes wallets and coin purses to sell at a market for $𝟐𝟒 each. The function 𝒈(𝒙) = 𝟐𝟒(𝒙 + 𝟏𝟕) represents the total amount, in dollars, the leatherworker earns by selling 𝒙 wallets and 𝟏𝟕 coin purses. What does $$g\left(27\right)=1,056$$ represent?

The leatherworker sells 27 wallets and earns $1,056 by selling the wallets and coin purses at the market.

The leatherworker sells 27 wallets and spends $1,056 on supplies to make the wallets and coin purses.

The leatherworker sells 27 wallets and coin purses at the market and earns $1,056 by selling the wallets and coin purses at the market.

The leatherworker sells 27 wallets and coin purses at the market and spends $1,056 on supplies to make the wallets and coin purses.

Which geometric formula could represent a linear function?

circumference of a circle: $$C=2\pi r$$

area of a circle: $$A=\pi r^2$$

A cell phone battery has a charge of 𝟎% when the cell phone is plugged into a charger. The table of the function 𝒇(𝒕) models the cell phone’s battery percentage 𝒕 minutes after the cell phone is plugged into the charger. Which statement is true about the function on the interval from 𝒕 = 𝟐𝟎 to 𝒕 = 𝟖𝟎?

The average rate of change on the interval is 1.25, representing an average increase of 1.25% per minute.

The average rate of change on the interval is 0.80, representing an average increase of 0.80% per minute.

The average rate of change on the interval is 0.80, representing an average increase of 1% every 0.80 minute.

The average rate of change on the interval is 1.25, representing an average increase of 1% every 1.25 minutes.

At a concert, an advertising representative launches T-shirts into the crowd for fans to catch. The function $$f\left(x\right)=-4x^2+10x+6$$ represents the path of the T-shirt after it is launched, where f(x) is the height of the T-shirt, in feet, and x is the time, in seconds. Which of the following statements are true? Select ALL that apply.

If a fan doesn't catch the t-shirt, it will hit the ground after 3 seconds.

The t-shirt reaches a maximum height of 12.25 feet.

If a fan doesn't catch the t-shirt, it will hit the ground after 0.5 seconds.

The t-shirt reaches its maximum height after 2 seconds.

The t-shirt reaches a minimum height of 10 feet.

A function 𝒇(𝒙) represents a population of frogs. If the initial population of 𝟏𝟖 frogs triples each year for 𝒙 years after being discovered, which statement is true?

The function represents exponential growth because the population increases by a constant percent.

The function represents exponential decay because the population decreases by a constant percent.

The function represents exponential decay because the population increases by a constant percent.

The function represents exponential growth because the population decreases by a constant percent.

Consider the graphs of 𝒇(𝒙) and 𝒈(𝒙). Which statement is true?

While 𝑓(𝑥) represents a function changing by a constant percent, 𝑔(𝑥) represents a function changing by a constant rate.

Both 𝑓(𝑥) and 𝑔(𝑥) represent functions changing by a constant percent.

Both 𝑓(𝑥) and 𝑔(𝑥) represent functions changing by a constant rate.

While 𝑓(𝑥) represents a function changing by a constant rate, 𝑔(𝑥) represents a function changing by a constant percent.

Consider the relation. Which statement is true?

The relation is not a function because for some input values, there is more than one output value.

The relation is a function because for each input value, there is exactly one output value.

The relation is a function because for each output value, there is exactly one input value.

The relation is not a function because for some output values, there is more than one input value.

An item is on sale for a certain percent off the original price of the item. The expression 𝒙 − 𝟎. 𝟑𝟎𝒙 represents the sale price of the item, where 𝒙 is the original price of the item, in dollars. Which statement is true?

𝑥 is a variable, and the coefficient of the term −0.30𝑥 represents the percentage of the original price of the item that is subtracted from the original price of the item.

𝑥 is a coefficient, and the constant 0.30 represents the dollar amount that is subtracted from the original price of the item.

𝑥 is a coefficient, and the constant 0.30 represents the percentage of the original price of the item that is subtracted from the original price of the item.

𝑥 is a variable, and the coefficient of the term −0.30𝑥 represents the dollar amount that is subtracted from the original price of the item.

Which scenario represents an exponential function?

The number of tiles, 𝑁, in each layer of the pattern triples for each consecutive layer, 𝑥.

The area, 𝐴, of a rectangular floor is based on the length, 𝐿, and width, 𝑊, of the floor.

The total cost of labor, 𝑇, to tile the rectangular bathroom floor is based on an hourly rate, 𝑟.

The total cost of tiles used, 𝐶, is based on a set cost per tile, 𝑡.

23-24 Benchmark 3 Review

Authored by Samantha Leonard

Mathematics

9th Grade

CCSS covered

Used 3+ times

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

A knitter creates a price quote for a handmade blanket. Which is least likely to affect the value of the price quote?

the color of the knitting needles

the desired length of the blanket

the estimated hours it will take

the material of yarn chosen

Tags

CCSS.RI.8.2

CCSS.RL.11-12.2

CCSS.RL.7.1

CCSS.RL.8.1

CCSS.RL.9-10.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

the factor by which the value of the computer is multiplied after 1 year

B the factor by which the value of the computer is multiplied after 1.3 years

the factor by which the value of the computer is multiplied every 3 years

the factor by which the value of the computer is multiplied 3 times per year

Tags

CCSS.HSF.LE.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

(3𝑥 − 12)(3𝑥 − 12) square units

(3𝑥 − 12)(3𝑥 + 12) square units

(9𝑥 − 144)(9𝑥 − 144) square units

(9𝑥 − 144)(9𝑥 + 144) square units

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Consider the dimensions of a ceramic tile in the shape of a regular hexagon. Which expression(s) represent(s) the perimeter of the hexagon?

Tags

CCSS.7.EE.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Tags

CCSS.HSA.APR.C.4

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Lemonade is drained at a constant rate of 𝟖 fluid ounces per minute from a beverage dispenser containing 𝟑𝟗𝟐 fluid ounces of lemonade. Which equation represents the number of fluid ounces of lemonade remaining in the dispenser, 𝒚, based on the number of minutes, 𝒕, since lemonade started draining from the beverage dispenser, where 𝟎 ≤ 𝒕 ≤ 𝟒𝟗?

Tags

CCSS.HSF-BF.A.1A

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23-24 Benchmark 3 Review

A knitter creates a price quote for a handmade blanket. Which is least likely to affect the value of the price quote?

Consider the dimensions of a ceramic tile in the shape of a regular hexagon. Which expression(s) represent(s) the perimeter of the hexagon?

A home buyer takes out a mortgage loan with an initial value of $185,000 in 2021 and an annual interest rate of 3.45%. Which equation models the total value of the loan x years after 2021?

NO CALCULATOR: Consider the graph. Which function, 𝒇(𝒙), best represents the amount earned, in dollars, by an artist after selling handmade goods at an art fair for 𝒙 hours, where 𝟎 ≤ 𝒙 ≤ 𝟏𝟎?

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