Quiz & test questions Grade 8 Math

Kingfisher Mills Water System: A Grade 8 Volume and Functions Test

A grade 8 unit test on a fictional town's water system covering scientific notation, tank volume, systems of equations, and linear functions.

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

Standards

8.EE.A.3 Common Core Math

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

How this material aligns: Items 1 and 2 write the reservoir volume and daily use in scientific notation and find how many times as much one is than the other.

All materials for 8.EE.A.3 →

8.G.C.9 Common Core Math

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

How this material aligns: Items 3 and 4 apply the cylinder volume formula to a tank and convert the result from cubic feet to gallons.

All materials for 8.G.C.9 →

8.EE.C.8 Common Core Math

Analyze and solve pairs of simultaneous linear equations, understanding that solutions correspond to points of intersection, and solving systems by graphing and algebraically in the context of real-world problems.

How this material aligns: Items 5 and 6 write and solve a system of two linear repair-cost equations and compare the two plans at a stated number of segments.

All materials for 8.EE.C.8 →

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 7 and 8 read the rate of change and initial value of a tank-filling linear function and evaluate it at a given time.

All materials for 8.F.B.4 →

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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 apply scientific notation, volume, systems, and linear functions to one water system.
Students will interpret the rate of change and initial value of a linear model.

Vocabulary

Key words: scientific notation, volume, system of equations, linear function

Teacher overview

This 40-minute unit test is worth 27 points and covers four grade 8 skills through one water system: scientific notation, the volume of a cylinder, a system of two linear equations, and a linear function. It mixes multiple-choice, short-answer, and computation items so students both recall and apply. Every scenario value belongs to a fictional town, so no outside data is needed.

Kingfisher Mills Water System: A Grade 8 Volume and Functions Test — Grade 8 Math

Name: ____________________________ Date: ______________

Assessment

Kingfisher Mills is a fictional town upgrading its aging water system. Use 3.14 for pi and the fact that one cubic foot holds 7.48 gallons.

(2 points) Kingfisher Mills stores about 5,000,000 gallons of water in its reservoir. Which shows 5,000,000 in scientific notation?
- A) 5 x 10^5
- B) 5 x 10^6
- C) 5 x 10^7
- D) 0.5 x 10^6
(3 points) The reservoir holds 5,000,000 gallons, and the town uses 250,000 gallons each day. Write both numbers in scientific notation, then find how many days the reservoir would last at that rate.
(4 points) A cylindrical storage tank is 20 feet across (its diameter) and 20 feet tall. Find its volume in cubic feet using Volume = 3.14 x radius squared x height. Show your work.
(2 points) Convert the tank volume from item 3 to gallons by multiplying by 7.48.
(4 points) Two repair plans are offered. Plan X costs 40x + 1,200 dollars for x pipe segments, and Plan Y costs 55x + 600 dollars. Write the system and solve for the number of segments where the two plans cost the same.
(3 points) Using the plans in item 5, which plan is cheaper for 20 segments, and by how much?
(3 points) A pump fills a second, taller tank so its water level is L = 3t + 5 feet after t hours. State the rate of change and the initial value, and explain what each one means for the tank.
(2 points) Using L = 3t + 5, what is the water level after 6 hours?
(2 points) Explain why L = 3t + 5 is a function.
(2 points) Which situation is a proportional relationship, shown by a graph through the origin (0, 0)?
- A) A plan that charges $5 for every 1,000 gallons and nothing else.
- B) A plan with a $600 fixed fee plus $55 per segment.
- C) A tank that starts at 5 feet and rises 3 feet each hour.
- D) A daily cost of $900 plus $0.60 per 1,000 gallons.

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) 5 x 10^6.
5,000,000 is 5 followed by 6 zeros, so it is 5 x 10^6.
Answer: 20 days.
5,000,000 = 5 x 10^6 and 250,000 = 2.5 x 10^5. Dividing, 5 x 10^6 divided by 2.5 x 10^5 = 20, so the reservoir lasts 20 days.
Answer: 6,280 cubic feet.
Radius = 10 ft (half of 20 ft). Volume = 3.14 x 10 squared x 20 = 3.14 x 100 x 20 = 6,280 cubic feet.
Answer: 46,974 gallons.
6,280 cubic feet x 7.48 = 46,974.4, which rounds to 46,974 gallons.
Answer: 40 segments.
Set 40x + 1,200 = 55x + 600. Subtract 40x: 1,200 = 15x + 600. Subtract 600: 600 = 15x, so x = 40 segments. At 40 segments each plan costs $2,800.
Answer: Plan Y is cheaper by $300.
Plan X: 40(20) + 1,200 = 2,000. Plan Y: 55(20) + 600 = 1,700. Plan Y costs $2,000 - $1,700 = $300 less for 20 segments.
Answer: Rate of change 3, initial value 5.
The rate of change is 3 feet per hour, the fill rate. The initial value is 5 feet, the level already in the tank when t = 0.
Answer: 23 feet.
L = 3(6) + 5 = 18 + 5 = 23 feet.
Answer: Each time gives exactly one level.
For every value of t there is exactly one value of L from the rule 3t + 5, so the relationship is a function.
Answer: A) A plan that charges $5 for every 1,000 gallons and nothing else.
Only option A has no fixed amount, so its graph passes through the origin and it is proportional. The others have a nonzero starting value.

Differentiation

Support

Provide a formula card with the cylinder volume formula and the cubic-foot-to-gallon conversion, and pre-solve the radius (10 feet) for item 3. Allow a calculator for every computation item, and give students the setup 40x + 1,200 = 55x + 600 already written for item 5.

Extension

Ask students to find, for the plans in item 5, the full range of pipe-segment counts over which Plan X is the cheaper choice, and to justify the range using the break-even point they found.

ELL supports

Provide a labeled diagram of the cylindrical tank for item 3 and a small glossary of "scientific notation," "volume," "system," and "rate of change." Allow item 9 to be answered with a completed sentence frame: "It is a function because each ___ gives one ___."