Quiz & test questions Grade 8 Math
Redhawk Water System Benchmark: Systems, Volume, and Data
A grade 8 unit test covering scientific notation, cylinder volume, systems of equations, and scatter plots, with multiple-choice and computation items.
Objectives
- Students will apply scientific notation, cylinder volume, and systems of equations to water-system data.
- Students will interpret a scatter plot's association and outlier.
Vocabulary
Key words: scientific notation, volume, system of equations, association
Teacher overview
This 45-minute unit test is worth 24 points and covers four grade 8 skills through one fictional utility, the Redhawk Water System: scientific notation, the volume of a cylinder, systems of two linear equations, and reading a scatter plot. It mixes two multiple-choice items, one short-answer item, and seven computation or data items. Use 3.14 for pi and 7.48 gallons per cubic foot where needed.
Assessment
All figures below belong to the fictional Redhawk Water System.
(2 points) Write 6,200,000 gallons in scientific notation.
- A) 6.2 × 10^5
- B) 6.2 × 10^6
- C) 62 × 10^5
- D) 6.2 × 10^7
(2 points) A storage tank is a cylinder 40 feet across and 30 feet deep. Find its volume in cubic feet using V = pi × r^2 × depth.
(2 points) Convert your answer from item 2 to gallons, using 7.48 gallons per cubic foot.
(3 points) Tank A drains and Tank B fills, with depths in feet after t minutes given by A = 24 - 0.5t and B = 6 + 0.7t. Solve the system to find the time t when the two depths are equal.
(2 points) What is the equal depth, in feet, at the time you found in item 4?
(2 points) Short answer: On a graph of the two equations in item 4, what does the solution of the system represent?
(3 points) The table shows the reservoir level each spring. Describe the association between year and level, and name the outlier year.
Year Level (ft) 2019 88 2020 84 2021 80 2022 92 2023 72 2024 68 (3 points) Ignoring the outlier, about how many feet does the reservoir level fall per year on average from 2019 to 2024?
(2 points) The reservoir holds about 3 × 10^8 gallons and the storage tank holds about 3 × 10^5 gallons. About how many times as much does the reservoir hold?
- A) 10
- B) 100
- C) 1,000
- D) 10,000
(3 points) A pump fills the empty storage tank at 400 gallons each minute. Using your gallons from item 3, about how many minutes does it take to fill? Round to the nearest minute.
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) 6.2 × 10^6. The decimal point moves 6 places, since 6,200,000 = 6.2 × 1,000,000.
- Answer: 37,680 cubic feet. The radius is 20 feet. V = 3.14 × 20^2 × 30 = 3.14 × 400 × 30 = 3.14 × 12,000 = 37,680 cubic feet.
- Answer: 281,846 gallons. 37,680 × 7.48 = 281,846.4, which rounds to 281,846 gallons.
- Answer: 15 minutes. 24 - 0.5t = 6 + 0.7t. Subtract 6 and add 0.5t: 18 = 1.2t, so t = 15.
- Answer: 16.5 feet. Use t = 15: A = 24 - 0.5(15) = 24 - 7.5 = 16.5 feet, and B = 6 + 0.7(15) = 6 + 10.5 = 16.5 feet.
- Answer: The point where the two lines cross. The solution is the time and depth at which the two equations give the same value, which on a graph is their intersection.
- Answer: Negative association, outlier 2022. The level generally falls as the years go on, so the association is negative; 2022's reading of 92 feet is far above the falling pattern, making it the outlier.
- Answer: 4 feet per year. From 88 feet in 2019 to 68 feet in 2024 is a drop of 20 feet over 5 years, and 20 ÷ 5 = 4 feet per year.
- Answer: C) 1,000. (3 × 10^8) ÷ (3 × 10^5) = 10^(8-5) = 10^3 = 1,000.
- Answer: 705 minutes. 281,846 ÷ 400 = 704.6, which rounds to 705 minutes.
Differentiation
Support
Provide a formula strip with the cylinder volume formula, the 7.48 conversion, and a worked scientific-notation example. Give the radius (20 feet) already found for item 2, and allow a calculator on every computation item.
Extension
Ask students to write, using the reservoir's average yearly fall from item 8, a linear function for the level in terms of years since 2019, then use it to predict the level in 2026 and note why the outlier makes that prediction less certain.
ELL supports
Provide a labeled diagram of the cylindrical tank marking the diameter, radius, and depth, and a small word bank with "association," "outlier," and "intersection." Allow the short-answer item 6 to be answered with a labeled sketch of two crossing lines.