This document provides examples to help with a mastery assignment on writing expressions. It includes 9 examples of writing expressions to represent various mathematical scenarios involving variables. For each example, it provides the steps to write the expression, such as adding or subtracting terms, distributing polynomials, or finding half of an expression.

1. CMODULE 8 LESSON 1
Examples to Help With Your Mastery Assignment

2. 1. The perimeter of a stop sign has a
perimeter of 16x2 - 80x. What is the
length of one side?
A stop sign has 8 sides, so do 8(the
polynomial) and distribute.

3. 2. There are nickels and dimes in a
candy jar. If there are 22 more nickels
than dimes write an expression that
represents of the total number of coins
if the number of dimes is d.
If d is the number of dimes, then the
nickels would be d + 22. To find the
total, add those two expressions.

4. 3. The distance from Charlotte to
Abletown is given by 4x4 + 10x + 8. If
John leaves Charlotte and travels to
Abletown and stops at a gas station
halfway to his destination, how far is it
from the gas station to Abletown?
Since we are looking for halfway, do
1/2(the polynomial) and distribute.

5. 4. A boat is travelling at a velocity represented by
2x3 - 10x2 + 7. At the same time, current is
pushing the boat in the same direction with a
velocity given by 5x3 + 19x2 + 4x. What is the
total travelling velocity of the boat?
To find the total velocity, we have to account for
the current which slows us down. Do the boat’s
velocity minus the current’s velocity.

6. 5. In a triangle, the longest side is 6x2 + 8 and
the base is 12x -3. If the shortest side is half of
the length of the longest side, what is the
perimeter of the triangle?
A triangle has three sides, and its perimeter is the
sum of all 3. For this one, we will use the two
sides we are given as well as 3x2 + 4 which is
half the longest side. Add those up for the
perimeter.

7. 6. Suzie is five years older than her
brother, Michael. Write an expression
to represent the sum of their ages of
Michael's age is represented by x.
If x represents Michael’s age, then
Suzie is x + 5. Add the two
expressions together for the total.

8. 7. Johan's age is given by the
polynomial x2 - 3x + 7. Bret is younger
and his age is given by the polynomial
x2 - x + 1. What is difference in their
ages?
Difference means to subtract, so do
Johan – Bret.

9. 8. The number of boys in a pre-school
class is given by x + 6. The number of
girls is given by
x - 1. What expressions represents the
total number of students?
Total means to add, so do boys + girls.

10. 9. Find the perimeter of a square that
has a side length of x + 3.
A square has four sides of equal
length, so add x + 3 four times.