Algebra 1 Benchmark #2 Review (calc)

Algebra 1 -

Benchmark #2 Review

Calculator Part

Multiple Choice

The weight of a chimpanzee, 𝒚, in pounds, 𝒙 months after birth is modeled by the equation 𝒚=𝟏.𝟓𝒙+𝟖. Which represents the equation when solved for 𝒙?

• $$x=\frac{y-8}{1.5}$$

• $$x=\frac{y+8}{1.5}$$

• $$x=1.5\left(y-8\right)$$

• $$x=1.5\left(y+8\right)$$

Multiple Choice

The graph shows the distance, 𝒚, in yards, from the start of a beach to the edge of the water as the tide changes 𝒙 hours after the distance is first recorded.

What is the average rate of change on the interval from 𝒙=𝟎 to 𝒙=𝟔?

• −60 yards per hour

• −10 yards per hour

• 60 yards per hour

• 10 yards per hour

Multiple Choice

Which statement about the function $$𝒇(𝒙)=𝒙^2−𝒙−𝟐𝟎$$ is true?

• The expression $$x^2−𝑥−20$$ has factors (𝑥−5) and (𝑥+4), and 𝑓(𝑥) has zeros at 𝑥=−5 and 𝑥=4.

• The expression $$x^2−𝑥−20$$ has factors (𝑥−5) and (𝑥+4), and 𝑓(𝑥) has zeros at 𝑥=−4 and 𝑥=5.

• The expression $$x^2−𝑥−20$$ has factors (𝑥−4) and (𝑥+5), and 𝑓(𝑥) has zeros at 𝑥=−5 and 𝑥=4.

• The expression $$x^2−𝑥−20$$ has factors (𝑥−4) and (𝑥+5), and 𝑓(𝑥) has zeros at 𝑥=−4 and 𝑥=5.

Multiple Choice

Consider the table of values for the two linear functions, 𝒇(𝒙) and 𝒈(𝒙).

For which value of 𝒙 does 𝒇(𝒙)=𝒈(𝒙) have a solution?

• -1

• 0

• 1

• 2

Multiple Choice

A cell phone company charges a flat rate for the first 𝟖 gigabytes of data used. For any additional gigabytes of data used, the cell phone company charges an additional rate per gigabyte, 𝒈. When 𝒈≥𝟖, the expression 𝟒𝟓+𝟕.𝟑𝟓(𝒈−𝟖) represents the scenario.

When 𝒈≥𝟖, which statement is true?

• The cell phone company charges $45 as the flat rate for the first 8 gigabytes and $7.35 for each additional gigabyte.

• The cell phone company charges $45 as the flat rate for the first 8 gigabytes and $8.00 for each additional gigabyte.

• The cell phone company charges $52.35 as the flat rate for the first 8 gigabytes and $7.35 for each additional gigabyte.

• The cell phone company charges $52.35 as the flat rate for the first 8 gigabytes and $8.00 for each additional gigabyte.

Multiple Choice

An artist paints a mural containing different-sized triangles. The area of each triangle is given by the function $$𝑨(𝒙)=\frac{1}{2}𝒙(𝒙−𝟑)$$ , where 𝒙 represents the base length of the triangle, in inches.

What is the area of a triangle with a base length of 𝟏𝟔 inches, represented by 𝑨(𝟏𝟔)?

• 70 square inches

• 104 square inches

• 125 square inches

• 128 square inches

Multiple Choice

Which statement about $$𝒇(𝒙)=𝒙^2+𝟓𝒙−𝟖𝟒$$ is true?

• The quadratic function factors into (𝑥−12)(𝑥+7) and has zeros at 𝑥=−12 and 𝑥=7.

• The quadratic function factors into (𝑥−12)(𝑥+7) and has zeros at 𝑥=−7 and 𝑥=12.

• The quadratic function factors into (𝑥−7)(𝑥+12) and has zeros at 𝑥=−12 and 𝑥=7.

• The quadratic function factors into (𝑥−7)(𝑥+12) and has zeros at 𝑥=−7 and 𝑥=12.

Multiple Choice

The concentration of chlorine in a swimming pool, 𝒇(𝒙), can be modeled by the equation 𝒇(𝒙)=𝟐.𝟔(𝟎.𝟗𝟕)𝒙, where 𝒙 is the time, in hours, since the chlorine was added to the pool. The table shows the approximate concentration levels over time.

Which statement is true?

• The values of 𝑓(𝑥) are negative, and for each unit increase in 𝑥, 𝑓(𝑥) decreases.

• The values of 𝑓(𝑥) are negative, and for each unit increase in 𝑥, 𝑓(𝑥) increases.

• The values of 𝑓(𝑥) are positive, and for each unit increase in 𝑥, 𝑓(𝑥) decreases.

• The values of 𝑓(𝑥) are positive, and for each unit increase in 𝑥, 𝑓(𝑥) increases.

Multiple Choice

The table shows the number of squirrels in a population 𝒙 years after the initial population is measured.

What is the average rate of change on the interval from 𝒙=𝟐 to 𝒙=𝟖?

• 26 squirrels per year

• 39 squirrels per year

• 78 squirrels per year

• 156 squirrels per year

Multiple Choice

A function 𝒇(𝒙) is defined as $$𝒇(𝒙)=\frac{𝟐^x}{8}$$ . What is the value of 𝒇(𝟒)?

• 1

• 2

• 4

• 5

Multiple Choice

Consider the linear function 𝒇(𝒙)=𝒙.

Which graph represents 𝒈(𝒙)=−𝒇(𝒙)−𝟓?

Multiple Choice

Which inequality represents the solutions to 𝟐(𝟕−𝟑𝒙)≥−𝟒(𝒙−𝟗)?

• 𝑥≤−11

• 𝑥≥−11

• 𝑥≤−5

• 𝑥≥−5

Multiple Choice

A bee flies in a straight line from one side of a garden arch to the other. The graph represents the equation $$−𝒙^2+𝟔𝒙=𝒙+𝟒$$ , which can be used to find where the bee’s path and the garden arch intersect.

What is (are) the solution(s) to the equation $$−𝒙^2+𝟔𝒙=𝒙+𝟒$$ ?

• 𝑥=1 only

• 𝑥=1 and 𝑥=4 only

• 𝑥=4 only

• 𝑥=4 and 𝑥=6 only

Multiple Choice

What is (𝟔𝒙+𝟏)(𝟕𝒙−𝟒) when simplified?

• $$42x^2-4$$

• $$42x^2-17x-4$$

• $$42x^2+17x-4$$

• $$42x^2+4$$

Multiple Choice

The table shows the relationship between the annual profit of a company in millions of dollars, 𝒇(𝒙), and the number of years, 𝒙, since the company was started.

Between which two 𝒙 values is the function most likely at a minimum value?

• between 1 and 2

• between 3 and 4

• between 4 and 5

• between 6 and 7

Multiple Choice

A student graphs the function $$𝒚=−𝒙^2+𝟏𝟔$$ . Which characteristics help the student correctly graph the function?

• The only 𝑥-intercept of the function is at (−4,0), and the 𝑦-intercept is at (0,16).

• The only 𝑥-intercept of the function is at (4,0), and the 𝑦-intercept is at (0,16).

• The 𝑥-intercepts of the function are at (−4,0) and (4,0), and the 𝑦-intercept is at (0,−16).

• The 𝑥-intercepts of the function are at (−4,0) and (4,0), and the 𝑦-intercept is at (0,16).

Multiple Choice

Consider the ceramic tile in the shape of a regular pentagon, where each side measures (𝟐𝒙−𝟔) inches.

If the perimeter of the ceramic tile, 𝑷, in inches, is represented by the equation 𝑷=𝟓(𝟐𝒙−𝟔), which represents the equation when solved for 𝒙?

• $$x=\frac{P-30}{10}$$

• $$x=\frac{P-10}{30}$$

• $$x=\frac{P+10}{30}$$

• $$x=\frac{P+30}{10}$$

Multiple Choice

The function 𝒇(𝒙)=−𝟒𝟓𝒙+𝟐𝟕𝟎 represents the total distance, in miles, a traveler is from home 𝒙 hours after beginning the trip home. What is the average rate of change over the interval from 𝒙=𝟏 to 𝒙=𝟑?

• -90 miles per hour

• -45 miles per hour

• 135 miles per hour

• 225 miles per hour

Multiple Select

Which two are the solutions to the quadratic equation $$𝟑𝒙^2+𝟏𝟓𝒙−𝟏𝟖=𝟎$$ ?

• x=-6

• x=-3

• x=-2

• x=1

• x=3

Multiple Choice

A runner trains for a marathon and finds the average mileage of a short, medium, and long run. The expression $$\frac{(𝒙−𝟓)+𝒙+(𝒙+𝟒)}{3}$$ miles represents the scenario.

Which statement is true?

• The short run is 5 miles less than the medium run, and the medium run is 4 miles less than the long run.

• The short run is 5 miles less than the long run, and the long run is 4 miles more than the medium run.

• The short run is 4 miles less than the medium run, and the medium run is 5 miles less than the long run.

• The short run is 4 miles less than the long run, and the long run is 5 miles more than the medium run.

Multiple Choice

A teenager goes to the fair with a group of friends and has $𝟐𝟓 to spend. A ticket to get into the fair costs $𝟕, and each ride costs an additional $𝟎.𝟕𝟓 per ride.

Which inequality represents the number of rides, 𝒓, that the teenager can afford to ride while at the fair?

• 0.75𝑟+7≤25

• 0.75𝑟+7<25

• 7𝑟+0.75≤25

• 7𝑟+0.75<25

Multiple Select

Which are the solutions to the equation $$(𝒙−𝟑)^2=𝟒𝟗$$ ? Select ALL that apply.

• x=-10

• x=-4

• x=-3

• x=4

• x=10

Multiple Choice

Which expression is equivalent to $$𝟔−(𝟐𝒙^2+𝟒)−(𝟐𝒙^2+𝒙−𝟓)+(𝒙^2+𝟕)$$ ?

• $$−3𝑥^2−𝑥$$

• $$−3𝑥^2−x+12$$

• $$−3𝑥^2−x+14$$

• $$−3𝑥^2+x+14$$

Multiple Choice

The equation $$𝟏𝟓𝟎(𝟎.𝟕𝟔)^x=𝟏$$ can be used to find the amount of time it takes a certain population of pests to drop to 𝟏, where 𝒙 is in days. In order to solve the equation $$𝟏𝟓𝟎(𝟎.𝟕𝟔)^x=𝟏$$ , a student graphs the equations $$𝟏𝟓𝟎(𝟎.𝟕𝟔)^x=𝟏$$ and 𝒚=𝟏.

What is the approximate solution to the equation $$𝟏𝟓𝟎(𝟎.𝟕𝟔)^x=𝟏$$ ?

• x=0.009

• x=6.593

• x=18.258

• x=114.000

Multiple Choice

A dog is 𝟑 times as old as a cat. In 𝟖 years, the dog will be twice as old as the cat will be then.

If 𝒙 represents the age of the cat, in years, which statement is true?

• The equation 3𝑥+8=2(𝑥+8) can be used to find the age of the cat, and the age of the cat is 8 years.

• The equation 3𝑥+8=2(𝑥+8) can be used to find the age of the dog, and the age of the dog is 8 years.

• The equation 3𝑥=2(𝑥+8) can be used to find the age of the cat, and the age of the cat is 16 years.

• The equation 3𝑥=2(𝑥+8) can be used to find the age of the dog, and the age of the dog is 16 years.A