Algebra 1

End-of-Unit Assessment

End-of-Unit Assessment with Regents Questions

The population of a city increases by 5% every year. If its population today is 300,000, what will its population be in 2 years?

$300{,}000 \cdot (0.05)$

$300{,}000 \cdot (1.05)$

$300{,}000 \cdot (1.05) \cdot (2)$

$300{,}000 \cdot (1.05)^2$

The tables below show the input and output values of four different functions.

x	f(x)
$-2$	$6$
$-1$	$1$
$0$	$-2$
$1$	$-3$
$2$	$-2$
$3$	$1$

x	g(x)
$-4$	$3$
$-3$	$2$
$-2$	$1$
$-1$	$0$
$0$	$1$
$1$	$2$

x	h(x)
$-2$	$-1$
$-1$	$-2$
$0$	$-4$
$1$	$-8$
$2$	$-16$
$3$	$-32$

x	j(x)
$-3$	$-11$
$-2$	$-7$
$-1$	$-3$
$0$	$1$
$1$	$5$
$2$	$9$

Which table represents a linear function?

$f(x)$

$g(x)$

$h(x)$

$j(x)$

For which function does $f$ decrease by 15% every time $x$ increases by 1?

$f(x) = 0.15^x$

$f(x) = 0.85^x$

$f(x) = 15^x$

$f(x) = 85^x$

The function $c(x) = 72 \cdot (1.04)^x$ models the cost in dollars, $c$ , of 1 ounce of a certain chemical used in a laboratory. $x$ represents the number of years since 2010.

Does the cost of the chemical increase or decrease over time, and by what percentage per year does it do so?
How much does an ounce of the chemical cost in 2018? Show your reasoning.

Here is a graph that represents $f(x) = 5.4321 \cdot 2^x$ .

Graph of an exponential growth curve passing through the origin region, with point A marked near x=1 and point B marked near x=4.

The coordinates of $A$ are $(1, c)$ and the coordinates of $B$ are $(4, d)$ . What is the value of $\dfrac{d}{c}$ ? Explain your reasoning.

When a child is born, her grandfather decides to put $100 in an account that earns interest. He plans to make no other deposits or withdrawals for 18 years. When the child turns 18 years old, the money in the account will be a birthday gift. The grandfather is choosing between two options:

Option 1: An account that grows by 10.5% each year.
Option 2: An account that grows by $20 each year.

Which option will result in a better 18th birthday gift? Explain your reasoning.

The equation that represents the sequence $-2, -5, -8, -11, -14, \ldots$ is

$a_n = -3 + (-2)(n - 1)$

$a_n = -2 + (-3)(n - 1)$

$a_n = 3 + (-2)(n - 1)$

$a_n = -2 + (3)(n - 1)$

Determine the 8th term of a geometric sequence whose first term is 5 and whose common ratio is 3.

Answer Key

The cost increases by 4% per year.
About $98.54. Sample reasoning: $72 \cdot (1.04)^8 \approx 98.54$ .

8. $f(x)$ doubles each time $x$ increases by 1. From $A$ to $B$ , $x$ increases by 3, so $f(x)$ doubles 3 times: $\dfrac{d}{c} = 2^3 = 8$ .

Option 1 (10.5% per year) results in a better gift. With Option 2, the balance after 18 years is $100 + 18 \cdot 20 = $460$ . With Option 1, the balance is $100 \cdot (1.105)^{18} \approx $603.28$ , which is more than Option 2.

10,935. Using $a_n = a_1 \cdot r^{n-1}$ : $a_8 = 5 \cdot 3^7 = 5 \cdot 2187 = 10{,}935$ .