Lesson 4: Practice Problems

Problem 1

Evaluate:

$10^{0}$
$\frac{10^{3}}{10^{3}}$
$10^{2} + 10^{1} + 10^{0}$

Problem 2

Write each expression as a single power of 10.

$\frac{10^{3} \cdot 10^{4}}{10^{5}}$
$(10^{4}) \cdot \frac{10^{12}}{10^{7}}$
${(\frac{10^{5}}{10^{3}})}^{4}$
$\frac{10^{4} \cdot 10^{5} \cdot 10^{6}}{10^{3} \cdot 10^{7}}$
$\frac{{(10^{5})}^{2}}{{(10^{2})}^{3}}$

Problem 3

The Sun is roughly $10^{2}$ times as wide as the Earth. The star KW Sagittarii is roughly $10^{5}$ times as wide as the Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.

Problem 4

Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)

1 in to 1 mi
1 cm to 1 km
1 in to 10 mi
1 ft to 100 mi
1 cm to 200 km
1 in to 100 mi
1 cm to 1000 km

Problem 5 From Unit 4 Lesson 8

Select all the expressions that are equivalent to $- 36 x + 54 y - 90$ .

$- 9 (4 x - 6 y - 10)$
$- 18 (2 x - 3 y + 5)$
$- 6 (6 x + 9 y - 15)$
$18 (- 2 x + 3 y - 5)$
$- 2 (18 x - 27 y + 45)$
$2 (- 18 x + 54 y - 90)$

Problem 6 From Unit 6 Lesson 3

Bananas cost $1.50 per pound, and guavas cost $3.00 per pound. Kiran spends $12 on fruit for a breakfast his family is hosting. Let $b$ be the number of pounds of bananas Kiran buys and $g$ be the number of pounds of guavas he buys.

Write an equation relating the two variables.
Rearrange the equation so $b$ is the independent variable.
Rearrange the equation so $g$ is the independent variable.

Problem 7 From Unit 5 Lesson 1

Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed $\frac{1}{3}$ of the speed her mom bikes. Sketch a graph of both of these relationships.

A graph of time (hours) on the x from 0 to 1.2 in 0.1 increments and distance on the y from 0 to 8 in increments of 1.