Free Printable PHS/TMS Final Review!

1.

The parent function $f\left(x\right)=x^2$ is reflected across the x-axis, vertically stretched by a factor of 5, and translated left 8 units to create g(x). Use the dexcription to write the quadratic function in vertex form.

a)

$g\left(x\right)=-5\left(x+8\right)^2$

b)

$g\left(x\right)=-5\left(x-8\right)^2$

c)

$g\left(x\right)=-5\left(x+5\right)^2$

d)

$g\left(x\right)=8\left(x+5\right)^2$

2.

Which of the following most accurately describes the translation of the graph $y=\left(x+3\right)^2-2$ to the graph $y=\left(x-2\right)^2+2$ ?

a)

Up 4 and 5 to the right

b)

Down 2 and 2 to the right

c)

Down 2 and 3 to the left

d)

Up 4 and 2 to the left

3.

Convert the function $f\left(x\right)=x^2+8x+9$ into vertex form.

a)

$f\left(x\right)=\left(x+4\right)^2+7$

b)

$f\left(x\right)=\left(x-4\right)^2-7$

c)

$f\left(x\right)=\left(x-4\right)^2+7$

d)

$f\left(x\right)=\left(x+4\right)^2-7$

4.

A ball is thrown into the air. Its height, h, after t seconds is given by the function $h\left(t\right)=-16t^2+128t+100$ . What is the maximum height the ball reaches?

a)

100 feet

b)

212 feet

c)

356 feet

d)

548 feet

5.

Which equation could be represented by the accompanying graph?

a)

$y=\left(\frac{1}{2}\right)^x$

b)

$y=-2^x$

c)

$y=2^{-x}$

d)

$y=-\left(\frac{1}{2}\right)^x$

6.

What is the range of the function $f\left(x\right)=3^x+5$ when the domain is {-3, 0, 4}?

a)

{-4, 5, 17}

b)

(5.037, 5, 86}

c)

{5.037, 6, 86}

d)

All real numbers

7.

Theresa is comparing the graphs of $y=3\cdot2^x$ and $y=6^x$ . Which statement is true?

a)

$y=6^x$ has a greater y-intercept, but $y=3\cdot2^x$ is steeper

b)

$y=3\cdot2^x$ has a greater y-intercept, but $y=6^x$ is steeper

c)

$y=3\cdot2^x$ has a greater y-intercept, and $y=3\cdot2^x$ is steeper

d)

$y=6^x$ has a greater y-intercept, and $y=6^x$ is steeper

8.

Two populations of bacteria increased at exponential rates. The table shows the bacteria for sample A, A(x), after x weeks.

The graph shows the bacteria population size for the sample B, $B\left(x\right)=500\left(2\right)^x$ , after x weeks.

Which bacteria sample (A or B) had a smaller initial population? What was that value?

a)

Sample A, initial population = 600

b)

Sample A, initial population = 0

c)

Sample B, initial population = 2

d)

Sample B, initial population = 500

9.

You open your first interest-bearing savings account with an initial deposit of $4,500. Interest is compounded quarterly at a rate of 3.9%. Assuming you do not deposit any more money into the account, how much money will you have in the account after 8 years?

a)

$15,307.70

b)

$4,863.21

c)

$6,138.41

d)

$6,111.35

10.

A scientist began a study with a smaple of bacteria. He noticed that the number of bacteria in the sample after t days can be modeled by the equation $P=2,000\cdot3^t$ . In this equation, what do the 2,000 and the $3^t$ represent?

a)

The 2,000 represent the initial population, and the $3^t$ represents that the number of bacteria increases by 3 bacteria each day.

b)

The 2,000 represents the initial population, and the $3^t$ represents that the number of bacteria increases by t bacteria after 3 days.

c)

The 2,000 represents the initial population, and the $3^t$ represents that the number of bacteria increases by a factor of 3 each day.

d)

The 2,000 represents the initial population, and the $3^t$ represents that the number of bacteria increases by a factor of t each 3 days.

11.

The growth of a population of ladybugs can be modeled by an exponential function. The graph models the population of the ladybug colony P(t) as a function of the time t, in days, that has passed. What does the domain represent in this context? The initial population of the ladybug colony was 2

a)

The domain is all nonnegative real numbers. The domain represents the time, in days, that have passed

b)

The domain is the real numbers greater than 2. The domain represents the time, in days, that have passed

c)

The domain is all real numbers greater than 2. The domain represents the population of ladybugs after a given number of days

d)

The domain is all nonnegative real numbers. The domain represents the population of ladybugs after a given number of days

12.

There are only about 20,000 blue whales left in the world today. They are classified as endangered by the International Union for Conservation of Nature, and the population continues to decrease by 8% per year. What will the population of blue whales be in fifty years?

a)

309

b)

466,134

c)

69

d)

734

13.

A laboratory has purchased 3,000mg of an isotope which has a half-life of 48 hours. How much of the isotope will remain after two weeks?

a)

15.625 mg

b)

2121.3203 mg

c)

0.9143 mg

d)

23.4375 mg

14.

Two insect colonies start out with the same populations but have different growth rates. Compare the colonies by finding and interpreting the average rates of change from week 0 to week 25

a)

Colony A increased faster by about 55 more insects per week

b)

Colony B increased faster by about 55 more insects per week

c)

Colony A increased faster by about 65 more insects per week

d)

Colony B increased faster by about 65 more insects per week

15.

Which function describes the sequence 2, 8, 32, 128, … ?

a)

$f\left(n\right)=2\cdot n^4$

b)

$f\left(n\right)=4^n+2$

c)

$f\left(n\right)=4\cdot2^{\left(n-1\right)}$

d)

$f\left(n\right)=2\cdot4^{\left(n-1\right)}$

16.

The functions $f\left(x\right)=2\left(x+1\right)^2+4$ and $g\left(x\right)=2^{\left(x+2\right)}+4$ are graphed on the coordinate plane.

a)

$1<x<3$

b)

$x>3$

c)

$-\infty<x<1$

d)

$-\infty<x<1\ and\ x>3$

17.

Ben has $250 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $55 a year. Under plan B, he will increase his account balance by 12% each year. How much more will he save with plan B after 15 years?

a)

$42

b)

$293

c)

$645

d)

$2,436.61

18.

Mathias asked ten friends how many text messages they sent today and how many they received today. The line plots below show his data.

Which statement correctly describes Mathias' data?

a)

The range in the number of texts received is less than the range in the number of texts sent.

b)

The median number of texts sent is less than the median number of texts received

c)

The mean absolute deviation of the number of texts sent is less than the mean absolute deviation of the number of texts received

d)

There is less variability in the number of texts received than in the number of texts sent

19.

Men and women were asked if they would support the new restaurant on the corner. See the results in the table below. Which is NOT a true statement about the data?

a)

44.5% of the people polled were men

b)

12.5% of the people polled did not support the new restaurant

c)

About 76% of women who were polled said they would support the restaurant

d)

About 40% of the people who did not support the restaurant were men

20.

Carly conducted research on the amount of time people spent at the mall and the amount of money they spent. Carly calculated the line of best fit as f(x) = 1.75x – 8.63 and correlation coefficient of r = 0.58 for her data set. Which statement best describes the relationship between the amount of money spent and the amount of time people were in the mall?

a)

The events have a strong negative linear correlation

b)

The events have a strong positive linear correlation

c)

The events have a moderate positive linear correlation

d)

There is little or no linear correlation

PHS/TMS Final Review!

Total questions: 20

Worksheet time: 2hrs 40mins

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