NCM1 Unit 1 Review

A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches.

Which equation models this?

Answer explanation

Start with the formula for the perimeter of a rectangle.

Use the known information given in the scenario for the length and perimeter of the rectangle and substitute those values into the formula.

Use the commutative and symmetric properties to rewrite the equation.

Tags

NC.M1.A-CED.1

Mathematical Equivalence

ON

Answer explanation

While there are many ways to approach this problem, here are the two most common/straightforward

On the left: We can distribute to eliminate the parentheses, then use inverse operations to isolate the variable. Making sure we convert our fractional answer to a decimal (since the question specifically asks for a decimal answer)

On the right: We can use inverse operations to eliminate the coefficient first, then use other inverse operations to isolate the variable.

Tags

NC.M1.A-REI.3

Answer explanation

Two ways to solve:

On the left: Substitute the value in for C, then solve for F using inverse operations.

On the right: Solve for F first, then substitute the value in for C.

Tags

NC.M1.A-REI.3

The graph of a function is shown.

Which whole-number inputs of this function result in an output of 5?

• 1

• 3

• 6

• 8

• 9

Answer explanation

Identify where the output is equal to 5.

Since our y-values represent outputs, any point with a y-value of 5 represents an output of 5.

I drew a horizontal line through all points with a y-value equal to 5 to see where that line intersects the function.

From the graph we can see that y (our output) is equal to 5 when x is equal to 1, 3, and 8.5. 8.5 was not an answer choice, so only 1 and 3 are selected.

Tags

NC.M1.F-IF.1

A plumber opens a tap to drain water from a tank.

The graph shows the amount of water, in gallons, left in the tank t minutes after opening the tap.

Which statement is true?

• The tap drains approximately half the water from the tank in 15 minutes.

• The tap drains exactly one gallon from the tank every minute.

• The tank initially has 30 gallons of water.

• The tank takes 50 minutes to drain completely.

Answer explanation

A) Correct. We can see that the tank started with 50 gallons of water and was empty after 30 minutes. At 15 minutes, there were 25 gallons left in the tank. 25 is one-half of 50.

B) Incorrect. Since the tank takes 30 minutes to drain and it started with 50 gallons of water, finding the unit rate, 50 gallons per 30 minutes would not equal 1 gallon per minute.

C) Incorrect. The orange point represents the starting amount, when time equals 0 and nothing has been drained. There were 50 gallons of water in the tank at the start.

D) Incorrect. The green point represents when the tank has been drained completely, when the amount of water is equal to 0. The tank is empty after 30 minutes.

Tags

NC.M1.F-IF.4

Which statement is true about the function f ?

Answer explanation

Remember: positive is above the x-axis and negative is below the x-axis. When reading the graph from left to right, increasing is "uphill" and decreasing is "downhill".

Orange: Intervals 2 ≤ x ≤ 3 and 6 ≤ x ≤ 7 which are not decreasing.

Yellow: Intervals -2 ≤ x ≤ 0 and 7 ≤ x ≤ 9 which are not both increasing (only 7 ≤ x ≤ 9 is increasing)

Blue: Interval 1 ≤ x ≤ 7 which is not negative and decreasing over the entire interval. It is only negative and decreasing over 1 ≤ x ≤ 2.

Green: Interval 0 ≤ x ≤ 1 which is positive and decreasing.

Tags

NC.M1.F-IF.4

The table represents the depth of a diver, in meters, y, after x minutes of being in the ocean.

What is the average rate of change of the diver over the interval from x =2 to x =20?

• -1.8 meters per second

• -1.5 meters per second

• -0.9 meters per second

• -0.1 meters per second

Answer explanation

Over the interval of 2 seconds to 20 seconds, the change in values is 20 seconds.

Using the corresponding depths at those times, -0.6 meters and -2.4 meters, we can calculate the total change in depth over that time interval is -1.8 meters.

Since we want to find the average rate of change (in meters per second), we create a ratio and simplify.

Tags

NC.M1.F-IF.6

The chart shows the U.S. inflation rate from 1980 to 2000.

What was the approximate average rate of change of the inflation rate from 1982 to 1986?

• -6% per year

• -4% per year

• -2% per year

• -1% per year

Answer explanation

Finding the average rate of change (in percent per year) requires that we find the change in years and the change in percents.

Once we know how each individual measure changed, we can write a ratio and simplify to find the average rate of change.

Tags

NC.M1.F-IF.6

Mathematical Equivalence

ON

Answer explanation

First, we need to evaluate the function for the given x-values.

Then we can determine the rate of change over that interval.

Since we're asked to find the average rate of change of f(x), that will be represented in the numerator.

Find the difference/change in our function values, the difference/change in our x-/input values (keep the order consistent!), then simplify.

Tags

NC.M1.F-IF.6

• The original price of the sweater before discount and tax

• the percent discount of the sweater.

• the percent sales tax on the sweater

• the price of the sweater after discount and tax

Answer explanation

0.2 represents the percent discount on the sweater.

Multiplying the original cost x by 0.2 represents a 20% of the original cost. When we subtract that 20% from the original cost, we would have the discounted price.

Multiplying the discounted price by 1.065 represents the total cost plus the amount of tax being collected.

Tags

NC.M1.A-SSE.1.a