Question 1

A rectangular garden has a length of 12 meters and a width of 7 meters. A triangular flower bed with a base of 6 meters and a height of 4 meters is placed inside the garden. What is the total area of the garden not covered by the flower bed?

$$	ext{Area of rectangle} = l 	imes w$$

$$	ext{Area of triangle} = \frac{1}{2} b h$$

Accepted Answer

$$72\ 	ext{m}^2$$

Question 2

A recipe calls for a ratio of $$2:5 of $$lemon juice to water. If you want to make $$21$$ cups of the drink, how many cups of lemon juice should you use?

$$	ext{Let } 2x + 5x = 21$$

Accepted Answer

$$6$$

Question 3

A car travels $$180$$ miles in $$3$$ hours. What is its unit rate in miles per hour?

$$	ext{Unit rate} = \frac{	ext{total miles}}{	ext{total hours}}$$

Accepted Answer

$$60$$ miles per hour

Question 4

A map uses a scale of $$1:50,000. If $$two cities are $$3$$ centimeters apart on the map, what is the actual distance between them in kilometers?

$$	ext{Actual distance} = 3 	imes 50,000 = 150,000\ 	ext{cm}$$

$$1\ 	ext{km} = 100,000\ 	ext{cm}$$

Accepted Answer

$$15 km$$

Question 5

A baker has $$\frac{3}{4} of a $$cup of sugar. Each cookie recipe requires $$\frac{1}{8} of a $$cup. How many full recipes can the baker make?

$$\frac{3}{4} \div \frac{1}{8}$$

Accepted Answer

$$8$$

Question 6

Calculate $$5.6 \div 0.8.$$

Accepted Answer

$$7$$

Question 7

Which of the following expressions is equivalent to $$3(x + 4)$$?

$$	ext{Use the distributive property.}$$

Accepted Answer

$$3x + 12$$

Question 8

A store increases the price of a $$\40$ jacket by 15$$\%$$. What is the new price?

$$	ext{Increase} = 0.15 	imes 40$

Accepted Answer

$$\46$

Question 9

Which number has the greatest absolute value?

$$-12,\ 7,\ -9,\ 5$$

Accepted Answer

$$-12 ($$absolute value = 12)$

Question 10

Evaluate: $$-7 + 12 - (-3)$$

Accepted Answer

Question 11

A student scored $$80, 85, 90, 95, 100 on $$five quizzes. What is the mean (average) score?

$$	ext{Mean} = \frac{80 + 85 + 90 + 95 + 100}{5}$$

Accepted Answer

$$90$$

Question 12

A rectangular prism has a length of $$5 cm$$, width of $$3 cm$$, and height of $$4 cm. $$What is its surface area?

$$	ext{Surface area} = 2(lw + lh + wh)$$

Accepted Answer

$$94\ 	ext{cm}^2$$

Question 13

If $$y = 3x + 2$$, what is the value of $$y$$ when $$x = -2$$?

Accepted Answer

$$-4$$

Question 14

A store offers a $$20\%$$ discount on a $$\75$ item. What is the sale price?

$$	ext{Discount} = 0.20 	imes 75$

Accepted Answer

$$\60$

Question 15

Which of the following is a solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 16

A company’s profit increased from $$\2$$,000$$ to $$\$$2,500. $$What is the percent increase?

$$	ext{Percent increase} = \frac{	ext{new} - 	ext{original}}{	ext{original}} 	imes 100\%$$

Accepted Answer

$$25\%$$

Question 17

Which point is located at $$( -3, 4 ) on $$the coordinate plane?

Accepted Answer

3 units left and 4 units up from the origin

Question 18

What is the result of $$-5 	imes (-3) + 2$$?

Accepted Answer

$$17$$

Question 19

A survey of 50 students found that 18 prefer soccer, 12 prefer basketball, and the rest prefer baseball. What percent prefer baseball?

$$	ext{Percent} = \frac{	ext{number}}{50} 	imes 100\%$$

Accepted Answer

$$40\%$$

Question 20

A rectangular field is $$60$$ meters long and $$40$$ meters wide. A path $$2$$ meters wide runs all the way around the inside edge of the field. What is the area of the path?

$$	ext{Area of field} = 60 	imes 40$$

$$	ext{Area of inner rectangle} = (60-4) 	imes (40-4)$$

Accepted Answer

$$416\ 	ext{m}^2$$

Prealgebra Study Syllabus: Key Topics and Concepts

Study Guide - Practice Questions

Study Guide - Flashcards