Quiz & test questions Grade 8 Math

Verdant Springs Water Utility: A Grade 8 Functions and Data Test

A grade 8 unit test on a fictional water utility covering linear functions, slope, solving equations, and fitting a line to scatter plot data.

Grade: Grade 8
Subject: Math
Material: Quiz & test questions
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

8.F.B.4 Common Core Math

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description, a table, or a graph, and interpret them in terms of the situation modeled.

How this material aligns: Items 1 through 3 read the rate of change and initial value of the tank filling function L = 4t + 6 and evaluate it at a stated time, the linear function work this standard names.

All materials for 8.F.B.4 →

8.EE.C.7 Common Core Math

Solve linear equations in one variable, including equations with variables on both sides, and recognizing equations with one solution, infinitely many solutions, or no solutions.

How this material aligns: Item 4 solves a one-variable linear equation for the fill time, and item 9 sets two cost expressions equal and solves for the usage level where they match, both core to this standard.

All materials for 8.EE.C.7 →

8.EE.B.5 Common Core Math

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

How this material aligns: Items 5, 6, and 10 compare two pump rates as slopes and identify which relationship is proportional through the origin, the slope-as-unit-rate reasoning this standard requires.

All materials for 8.EE.B.5 →

8.SP.A.2 Common Core Math

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and assess the model fit by judging the closeness of the data points to the line.

How this material aligns: Items 7 and 8 judge whether a straight line fits the temperature and demand data well and use the trend to estimate demand at a new temperature, exactly the informal line-fitting this standard describes.

All materials for 8.SP.A.2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will interpret and evaluate a linear function and solve a linear equation.
Students will compare rates as slopes and assess how well a line fits scatter data.

Vocabulary

Key words: linear function, rate of change, slope, line of best fit

Teacher overview

This 40-minute unit test is worth 25 points and covers four grade 8 skills through one fictional water utility: reading a linear function, solving a linear equation, comparing rates as slopes, and fitting a line to scatter data. It mixes multiple-choice, short-answer, and computation items so students both recall and apply. Every value belongs to the fictional town of Verdant Springs, so no outside data is needed.

Verdant Springs Water Utility: A Grade 8 Functions and Data Test — Grade 8 Math

Name: ____________________________ Date: ______________

Assessment

Verdant Springs is a fictional town. Answer every item, and show your work on the computation items.

(2 points) A pump fills a tank so the water level is L = 4t + 6 feet after t hours. What is the rate of change?
- A) 6 feet per hour
- B) 4 feet per hour
- C) 10 feet per hour
- D) 4 feet
(2 points) Using L = 4t + 6, state the initial value and explain what it means for the tank.
(2 points) Using L = 4t + 6, what is the water level after 5 hours?
(3 points) Using L = 4t + 6, solve for t: after how many hours is the water level 34 feet?
(3 points) The utility compares two pumps. Pump 1 moves 50 gallons per minute. Pump 2 is shown by g = 40t, where g is gallons after t minutes. Which pump is faster, and by how many gallons per minute?
(2 points) On a graph of gallons pumped across minutes, which pump from item 5 has the steeper line?
- A) Pump 1
- B) Pump 2
- C) They are equally steep
- D) Neither line passes through the origin
(3 points) The table shows the summer high temperature and the daily water demand for the town. Does a straight line fit this data well? Explain.

High temp (degrees F) Daily demand (thousand gallons)

80 300

85 340

90 360

95 400

100 440
(3 points) Using the trend in item 7, estimate the daily demand when the high temperature is 88 degrees F.
(3 points) Two storage plans have costs, in dollars, of C = 20g + 300 and C = 35g + 150, where g is thousand gallons. Solve for g, the usage where the two plans cost the same.
(2 points) Which situation is a proportional relationship, with a graph through the origin (0, 0)?
- A) A pump modeled by g = 40t with no starting amount.
- B) A tank level given by L = 4t + 6.
- C) A cost given by C = 20g + 300.
- D) The demand data in item 7.

High temp (degrees F)	Daily demand (thousand gallons)
80	300
85	340
90	360
95	400
100	440

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: B) 4 feet per hour.
In L = 4t + 6, the number multiplied by t is the rate of change, so the level rises 4 feet each hour.
Answer: 6 feet.
The initial value is 6 feet, the water level when t = 0, meaning the tank already holds 6 feet of water before the pump starts.
Answer: 26 feet.
L = 4(5) + 6 = 20 + 6 = 26 feet.
Answer: 7 hours.
34 = 4t + 6. Subtract 6: 28 = 4t. Divide by 4: t = 7 hours.
Answer: Pump 1 by 10 gallons per minute.
Pump 1 moves 50 gallons per minute. Pump 2's rate in g = 40t is 40 gallons per minute. Pump 1 is faster by 50 - 40 = 10 gallons per minute.
Answer: A) Pump 1.
Slope is the rate. Pump 1's rate of 50 is larger than Pump 2's rate of 40, so Pump 1's line is steeper.
Answer: yes, a straight line fits well.
As the temperature rises, the demand rises by a fairly steady amount each step, so the points lie close to a straight line and a linear model fits well.
Answer: about 350 thousand gallons.
At 85 degrees demand is 340 and at 90 degrees it is 360, so at 88 degrees the demand should be between them, about 350 thousand gallons.
Answer: 10 thousand gallons.
Set 20g + 300 = 35g + 150. Subtract 20g: 300 = 15g + 150. Subtract 150: 150 = 15g, so g = 10 thousand gallons.
Answer: A) A pump modeled by g = 40t with no starting amount.
Only option A has no starting value, so its graph passes through the origin and it is proportional. Options B and C start at a value other than zero, and the item 7 data have no constant ratio (300 ÷ 80 = 3.75 but 440 ÷ 100 = 4.4).

Differentiation

Support

Provide a formula reminder that the rate of change is the number multiplied by t and the initial value is the number added on, and pre-set the equation 34 = 4t + 6 for item 4. Allow a calculator on every computation item.

Extension

Ask students to write the linear function that fits the temperature and demand data in item 7, using the roughly constant increase they see, then use it to predict the demand at 105 degrees and judge how much to trust that prediction.

ELL supports

Provide a small glossary card for "rate of change," "initial value," "slope," and "proportional," each with a tiny sketch. Allow item 2 and item 7 answers to use the sentence frames "The initial value is ___, which means ___" and "A line fits ___ because ___."