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Interpreting Parts of an Expression (Grade 9)

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Interpreting Parts of an Expression

What do you call the number in front of the variable? For example, the -9 in -9y.
  1. term
  2. like term
  3. coefficient
  4. exponent
Which of the following are the coefficient(s) in the expression [math]15x^2 +3xy - 12y +8 ?[/math]
  1. [math]x, y[/math]
  2. [math]3xy[/math]
  3. [math]8[/math]
  4. [math]15, 3, -12[/math]
How many terms are in the expression below?
  1. 3
  2. 2
  3. 1
  4. 4
Which of the following are factors of [math]4x^3(y+2)^2 ?[/math] Choose all that apply.
  1. [math]4[/math]
  2. [math]y[/math]
  3. [math]x^3[/math]
  4. [math]y+2[/math]
Mike owns a chocolate shop, and is trying to create a new box of chocolate to sell. He is thinking about what to put in it, and how much he will need to charge for it. The candies he is thinking about including are: truffles, T, which cost $1.50 each; pecan chocolates, P, which cost $1.00 each; and solid milk chocolate pieces, M, which cost $0.75 each. He creates an expression to model this, as follows.

[math] 1.5T + P + 0.75M [/math]

What do the coefficients represent in this expression?
  1. The cost per chocolate.
  2. The total amount of money the box will cost.
  3. The average price of the chocolates.
  4. The number of chocolates he will include in the new box of chocolates.
Smart Financial is offering a new savings account, with an annual interest rate of 4%. The amount a person will earn by investing [math]P[/math] dollars is represented by the expression [math]P + 0.04tP[/math], where [math]t[/math] is the amount of time (in years) someone's money stays in the account. What does the second term in this expression represent?
  1. The rate of growth of their investment.
  2. The total amount of money they have in their account.
  3. The interest they will over the given time period.
  4. The original amount of money they invested.
Anna has been recording the distance she ran each day this week. So far, she has run 14.3 miles in total, and today is the last day she will be able to run this week. Although she does not know the exact distance of the route she will run today, she knows her pace very well and it stays constant throughout the run. If she will run for t hours, her total distance for the week is given by the expression [math]14.3 + 8t[/math]. What does the coefficient 8 represent?
  1. The average time it takes to run each mile, in hours.
  2. Her pace, in miles per hour.
  3. The amount of time she will run for, in hours.
  4. The distance she will run, in miles.
Carol manages admissions for a small county fair. She has created two expressions, one for the total number of people who have entered (children and adults), and one for the total amount of money collected (adults pay a higher entrance fee than children do). The expression [math]c + a[/math] represents the total number of people admitted, where [math]c[/math] is number of children, and [math]a[/math] is the number of adults admitted. The expression [math]0.75c + 1.5a[/math] represents the total amount of money collected, in dollars. What does the term [math]1.5a[/math] represent?
  1. The amount charged per adult for entry into the fair.
  2. The total number of adults who entered the fair.
  3. The amount charged per child for entry into the fair.
  4. The total amount of money from adults who have entered the fair.
Beth wants to go on a road trip this summer. She will be taking her car, which gets an average of 19 miles per gallon in fuel economy. Beth creates an expression to calculate the total cost of gas for her trip, [math]1/19 x y[/math], where x is the typical price of gas (in dollars per gallon) where she will be driving. What does the factor [math]y[/math] represent?
  1. The number of miles she expects to drive.
  2. The total cost of gas, for one fill up.
  3. The number of times she expects she will have to stop to fill up her car with gas.
  4. The total amount of gas, in gallons, needed to fill her car's gas tank.
Jake and Will work at a bakery. If J represents the number of cakes Jake can bake per day, W represents the number of cakes Will can bake per day, x represents the number of days Jake works in a week, and y represents the number of days Will works in a week, what does the expression [math]xJ + yW[/math] represent?
  1. The number of hours Jake and Will work in a week.
  2. The number of cakes made by Jake and Will in a week.
  3. The total number of cakes both Jake and Will could bake per day.
  4. The combined number of days Jake and Will work in a week.

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