Integrated Math One – Quarter 1 Benchmark Review

Jesse bought a new Ford F-150 for $38,000 Jesse bought a new Ford F-150 for $38,000. After owning for a few years he began thinking of selling it. He knows that the value of the car after x years can be found using this formula: 𝑓 𝑥 =38000 .9 𝑥 𝐽𝑒𝑠𝑠𝑒 𝑘𝑛𝑜𝑤𝑠 𝑡ℎ𝑎𝑡 𝑎𝑓𝑡𝑒𝑟 5 𝑦𝑒𝑎𝑟𝑠 𝑡ℎ𝑒 𝑡𝑟𝑢𝑐𝑘 𝑖𝑠 𝑤𝑜𝑟𝑡ℎ $22438.62. 𝐻𝑒 𝑤𝑎𝑛𝑡𝑠 𝑡𝑜 𝑘𝑛𝑜𝑤 ℎ𝑜𝑤 𝑚𝑢𝑐ℎ It is worth after 6 years but he doesn’t have a calculator. Explain how he can find the answer   Find the answer

Jose has a collection of 100 Pokémon cards Jose has a collection of 100 Pokémon cards. His little sister was drinking juice and spilled some on x of his cards. Each of the undamaged cards is worth $10 but the damaged cards are only worth $7 each. The expression below represents the total value, dollars , of Jose’s collection. 10 100−𝑥 +7𝑥 What does the first term represent?   What does the second term represent? What does the third term represent?

Assume that the pattern in the table continues, At the time Pokémon go was released there was 1 person playing. The number of people playing is shown in the following table. Assume that the pattern in the table continues, Write the equation to find when the number of people playing Pokémon will hit 5,000,000. Solve your equation. Time (Hours) Number of people playing 1 5 2 25 3 125

Solve the following equation: −6+2 3−𝑥 =8   3𝑥+ 1 3 𝑥+ 1 4 𝑥=4

Solve the following equation: 21−5𝑥=8−2𝑥   𝑊ℎ𝑒𝑛 𝑥=0, 𝑦=10 𝑊ℎ𝑒𝑛𝑒𝑣𝑒𝑟 𝑥 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑠 𝑏𝑦 1, 𝑦 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑠 𝑏𝑦 6% Write the explicit formula for this situation.

Kyle does yard work to make some extra money Kyle does yard work to make some extra money. He worked 9 hours one Saturday and made $108. He worked 4 hours the next Saturday and made $48. What is the slope of the line for this situation?   Write the equation of the line in point-slope form. Write the equation of the line in slope-intercept form.

Here is an equation: 𝑦+3= 1 2 (𝑥−1) How is this equation different from point-slope form that you learned? What is the point? What is the slope? Graph the equation

Graph the following equation: 𝑦=−2𝑥+5

The value of y is negative three times two raised to the power of x The value of y is negative three times two raised to the power of x. Write the explicit formula for this situation.   Graph the following equation: 𝑦= 3 4 𝑥+ 1 2

The sequence 2, 4, 8, 16, 32, …𝑐𝑎𝑛 𝑏𝑒 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑓 𝑛 = 2 𝑥 What is the domain of the function?   Here is a function: 𝑓 𝑛 =500+150𝑛 Write the first five terms.

The following sequence represents the amount that Brianna charges for babysitting: 4.00, 7.50, 11.00, 14.50, … Write the explicit formula for the sequence.   Here is a sequence: 𝑓 𝑛 =.4+.15 𝑛−1 . What is the 10th term of the sequence?

At one minute, there is one dot. At two minutes, there is 5 dots At one minute, there is one dot. At two minutes, there is 5 dots. At three minutes, there is 9 dots. At four minutes, there is 13 dots. Write the explicit formula for this situation.   There were 8000 people living in Waterford in 2013. The population is growing at a rate of 2%. Write the explicit equation if f(n) represents the population of Waterford n years after 2013.

𝑦=2𝑥−3 What is the y-intercept? What is the slope?   What is the slope? What is the meaning of the slope?

𝑦=𝑚𝑥+𝑏 What is the y-intercept? What is the slope?   What is the slope? What is the meaning of the slope?

What is the common ratio in the following graph?

Give an example of a linear situation.   Give an example of an exponential situation.

The value of a car decreases by 5% each year The value of a car decreases by 5% each year. Linear, exponential, or neither? How do you know?   The value of a car decreases by $1000 each year. Linear, exponential, or neither? How do you know?

The value of a car decreases by $500 the first year, $750 the second year, $1000 the third year and so on. Linear, exponential, or neither? How do you know?  

Which phone is decreasing by a constant difference? Mom and son each have a different kind of phone. The following table shows the value of each phone x months after purchase. Which phone is decreasing by a constant difference?    Which phone is decreasing by a constant percentage?   Time (months after purchase) Value of Mom’s phone Value of son’s phone $500 $200 1 $450 $170 2 $405 $140 3 $364.5 $110

Write the explicit function for the following sequence: Y 2 1 10 50 3 250

The table below shows two points on the graph of an exponential function of the form 𝑦=𝑎 𝑏 𝑥 What is the value of b? X Y 1 3 36

Look at the following graph of two functions, 𝑓 𝑥 =2𝑥+3 𝑎𝑛𝑑 𝑔 𝑥 =1 (2) 𝑥 . Where does g(x) exceed f(x)? Where does f(x) exceed g(x)?

Graph the following functions: 𝑓 𝑥 =3𝑥 +2 𝑎𝑛𝑑 𝑔 𝑥 =1 (3) 𝑥 𝑎𝑛𝑑 ℎ 𝑥 =𝑥+9 Graph them Will either of the two lines eventually exceed the curve? Explain   Will the curve eventually exceed the two lines? Explain

A Cell phone plan costs a certain amount for the first 100 texts and then an additional amount for every text after the first 100. The equation below can be used to determine the total cost, in dollars, of the phone bill. 𝑦=2.50+.10(𝑥−100) What does the 2.50 represent in this situation?   What does the .10 represent in this situation?

Megan got her mom a plant for her birthday Megan got her mom a plant for her birthday. In the equation y represents the height of the plant and x represents the months since Megan gave it to her mom. The equation is: 𝑦= 1 2 𝑥+6 What does the ½ represent in this situation?   What does the 6 represent in this situation?