MEGA Elementary Education Multi-Conent Subtest I - Practice Test
The numbers of an analog clock face are labeled outside of a circle that is 8 inches in diameter. When the time reads exactly 9:00, which of the following expressions represents the area of the smallest sector formed by the minute and hour hand? A. (1/4)𝝅4^2 B. (1/4)𝝅8^2 C. (1/2)𝝅4^2 D. (1/2)𝝅8^2
A. (1/4)𝝅4^2
Use the word problem below to answer the question that follows. A group is planning to rent some tents for a three-day long school fair and has a budget of $1,000 for this purpose. A tent rental company charges $50 per day for each tent. There is also a one-time $100 delivery fee, regardless of how many tents are rented. How many tents will the group be able to rent for the school fair? If T represents the number of tents, which of the following equations accurately models this situation? A. (3 x 50T) + 100 = 1,000 B. 50T + 100 = 1,000 C. (3 x 50T) - 100 = 1,000 D. 50T - 100 = 1,000
A. (3 x 50T) + 100 = 1,000
A student earns $5.99 for every job completed around the neighborhood. Once six jobs are completed, the student plans to purchase a new pair of headphones for $25.99. Which of the following mathematical models should students use to determine how much money will be left over after the purchase? A. (5.99 x 6) - 25.99 B. 25.99 - (5.99 x 6) C. (25.99 ÷ 6) - 5.99 D. 5.99 - (25.99 ÷ 6)
A. (5.99 x 6) - 25.99
Which of the following numbers is closest in value to 2.5 x 10^(-2)? A. 0.021 B. 2.3 C. 2/10 D. 22/100
A. 0.021
Two parents are both carriers of the recessive allele for sickle-cell anemia but do not express the disorder because they are heterozygous for the trait. The offspring of these parents have what probability of being homozygous for the sickle-cell trait? A. 25% B. 50% C. 75% D. 100%
A. 25%
Use the diagram below to answer the question that follows. The diagram consists of 3 thousands blocks, 1 hundreds flats, 5 tens sticks, and 2 ones units. Which of the following numbers is modeled using the base-ten blocks if a "flat" represents one unit? A. 31.52 B. 31.502 C. 301.52 D. 3,152
A. 31.52
In which of the following examples does a lever reduce the force required to complete a task by increasing the distance over which the force is applied? A. A bottle opener is used to pry off the cap of a bottle B. A rake is used to rake up leaves under a tree C. A single-wheel pulley is used to lift a box up to a roof D. A shovel is used to move a pile of loose dirt
A. A bottle opener is used to pry off the cap of a bottle Explanation: A bottle opener allows a person to increase the output force needed to remove the bottle cap by applying a smaller input force over a greater distance.
Climate change researchers have learned that when fossil fuels extracted from the geosphere are burned, the greenhouse gas carbon dioxide is released into the atmosphere, warming it. Over time, the ocean has absorbed increasing amounts of carbon dioxide, and several consequences to the hydrosphere have been identified, including sea level rise and changes in salinity. Which of the following effects of this process has been observed in the biosphere? A. increased marine temperatures have resulted in the bleaching of corals B. increased amounts of nutrients have led to algal blooms C. increased alkalinity has impaired the ability of oysters to form strong shells D. increased net productivity of phytoplankton has been measured
A. increased marine temperatures have resulted in the bleaching of corals
A fifth-grade teacher is demonstrating that the amount of water needed to fill a rectangular prism may be predicted before any water is poured into it. The dimensions of the prism are 5cm x 10cm x 10cm. Which of the following units should be used to measure the volume of water so that students can most easily connect the dimensions of the prism with the volume of water? A. milliliters B. liters C. cubic inches D. gallons
A. milliliters Explanation: a cubic centimeter is equivalent to the volume of 1 milliliter
A teacher provides students with printed outlines of various polygons. The teacher asks students to determine ways to divide the shapes into identical parts. Which of the following practices would be most effective in supporting the teacher's goal? A. providing students with a piece of string to test for symmetry B. measuring lengths along the perimeter of shapes with rulers C. preparing an illustration of different types of polygons and their names D. determining the number of unit squares needed to fill a shape
A. providing students with a piece of string to test for symmetry
use the table below to answer the question that follows. Number of Items in Lunch Box: 4 5 6 7 Number of Students with That Many Items: 4 6 5 2 A second-grade teacher creates an activity for students to develop an accurate visual representation of the data shown in the table. Which of the following instructional resources would best facilitate the students' creation of an accurate visual representation of these data? A. stacking plastic cubes on the floor B. drawing with erasable markers on a whiteboard C. grouping pipe cleaners on a paper plate D. nesting collections of plastic cups on a desk
A. stacking plastic cubes on the floor
Which of the following activities would be the most appropriate introduction to a unit on the five senses for first-grade students? A. students try to recognize objects hidden inside a paper bag using only their fingers B. students read out a series of letters and numbers on an age-appropriate eye chart C. students use modeling clay to make different animals of which they've seen pictures D. Students compare two pictures and circle any differences they note between the two
A. students try to recognize objects hidden inside a paper bag using only their fingers
A student uses a device to count 1,760 steps taken during a walk. The student knows that her average step is 1.5 ft long and that there are 5,280 ft in a mile. Which of the following expressions should the student use to calculate the distance walked in miles? A. (1/1,760) x 1.5 x 5,280 B. 1,760 x 1.5 x (1/5,280) C. (1/1,760) x 1.5 x (1/5,280) D. 1,760 x (1/1.5) x 5,280
B. 1,760 x 1.5 x (1/5,280)
Which of the following expressions can be used to determine the number of centimeters in 20 kilometers? A. 20(100)(10) B. 20(1,000)(100) C. 20/(100)(10) D. 20/(1,000)(10)
B. 20(1,000)(100)
The average distance from Earth to Saturn is approximately 1.44 x 10^9 km. About how long would it take a rocket traveling at 4.8 x 10V3 km per hour to reach Saturn from Earth? A. 3 x 10^3 hours B. 3 x 10^5 hours C. 6.9 x 10^12 hours D. 6.9 x 10^27 hours
B. 3 x 10^5 hours
A household appliance regularly priced at $150 was put on sale at a 15% discount. After several weeks, the appliance was discounted 20% off the sale price. When these discounts are combined, what percent of the original price would a shopper save? A. 30% B. 32% C. 35% D. 38%
B. 32%
Which of the following processes can form metamorphic rock? A. weathering sedimentary rock B. applying heat and pressure to igneous rock C. melting sedimentary rock D. cooling magma below Earth's surface
B. applying heat and pressure to igneous rock
Use the Diagram below to answer the question that follows. * * * * * * * * * * * * * * * A second-grade teacher shows students the rectangular array and asks, "What equations can you write to represent the total number of stars as a sum of equal addends?" This instructional practice is most appropriate for supporting which of the following aspects of the student's mathematics comprehension? A. extending visual mathematical stimuli B. composing equivalent expressions C. analyzing shapes to create additional sentences D. identifying numerical sequences by counting on
B. composing equivalent expressions
A teacher is introducing new vocabulary for a geometry lesson on the properties of lines and angles of two-dimensional shapes. Which of the following vocabulary strategies would be most effective in supporting the students' accurate application of the terminology? A. participating in a word race where students are given a definition and asked to rapidly identify the word B. developing a graphic organizer for students to record the definition, properties, and examples of each new word C. pre-teaching by explicitly defining new terms before sending students to work independently D. providing art supplies to create a visual representation of an assigned term based on its definition
B. developing a graphic organizer for students to record the definition, properties, and examples of each new word
Which of the following strategies would be most appropriate to promote fifth-grade students' understanding of the correct terms for scientific equipment, such as graduated cylinder, microscope, beaker, and meter stick? A. holding up each item while stating its name B. developing laboratory stations in which students use each labeled tool and record the results of each investigation C. showing a short film on the use of each device D. forming classroom groups then assigning each to research and report back to the class about one of the instruments
B. developing laboratory stations in which students use each labeled tool and record the results of each investigation
Instruction in which of the following areas would be most effective for promoting student understanding of prime numbers? A. repeated addition B. factor trees C. equal grouping D. fact families
B. factor trees Explanation: while factor families do also decompose numbers using all 4 math operations, factor trees specifically break down numbers with the goal of finding the prime numbers that make up a specific number.
A third-grade teacher wants to informally assess students' knowledge of two-dimensional shape categories and subcategories while in a whole-group setting. Which of the following assessment strategies would be most effective for the teacher to use in this setting? A. pop quiz B. hand signals C. think-pair-share D. ticket out the door
B. hand signals
On the first day of a unit on simple food chains, a fourth-grade teacher distributes photographs of a variety of plants and animals. The teacher then asks student groups to cluster photos of similar organisms together. Once students have differentiated the plants from the animals, the teacher introduces the terms producer and consumer. The photographs are then shuffled, and students are given printed labels to identify each organism as either a producer or a consumer. The primary benefit of introducing the unit in this way is that students are: A. engaging in an activity instead of simply listening to a lecture B. having the opportunity to apply relevant terms prior to the lesson C. gaining experience by working collaboratively with other students D. practicing the scientific skill of classification throughout the activity
B. having the opportunity to apply relevant terms prior to the lesson
While analyzing data from a pie chart, a teacher asks students to identify the section with the highest frequency. One student says, "The van has the highest frequency because of the location of the solid black section on the chart. It is at the top." The student's error reveals that additional instruction is needed in which of the following areas related to data representation? A. describing the features of a pie chart using its key B. interpreting the angles of the sectors of a pie chart C. describing the features of a pie chart using mathematical vocabulary D. interpreting the order in which sectors of a pie chart are arranged
B. interpreting the angles of the sectors of a pie chart
Third-grade students have been learning about circuits. In this lesson, they investigate which materials make good conductors. Using three wires with insulation stripped from the ends, pairs of students set up an open circuit.. The students touch the exposed ends of the two wires to several objects in turn, observing whether the light bulb lights up as a connection is made. Students record their observations. Which follow-up activity would best prompt students' scientific thinking once they have completed the day's activity? A. students set up light bulbs into a series arrangement B. students insert a circuit breaker into their electrical setup C. Students predict which other materials would serve as good conductors D. students run the investigation again using a ringing bell in place of a light bulb.
C. Students predict which other materials would serve as good conductors
A car's gas mileage averages 25 miles per g allon in the city and 30 miles per gallon on the highway. The car can travel 325 miles on a tank of gas in the city. Which of the following proportions can be used to determine how many miles the car can travel on the highway using the same amount of gas? A. (25/235) = (x/30) B. (25/55) = (x/325) C. (25/325) = (30/x) D. (25/55) = (325/x)
C. (25/325) = (30/x)
The diameter of a typical human cell is approximately 0.00003 meter. How would this be expressed in scientific notation? A. 3 x 10^(-4) meter B. (3/10,000) meter C. 3 x 10^(-5) meter D. (3/100,000) meter
C. 3 x 10^(-5) meter
Regina and Sam are runners. Each week, Regina runs on Monday, Wednesday, and Friday. Sam runs on Tuesday and Thursday. In addition, each weekend Regina runs 8 miles, and Sam runs 6 miles. Regina runs the same number of total miles each week as Sam runs, If r and s represent the number of miles that Regina and Sam run each weekday respectively, which of the following equations represents the relationship between r and s? A. r = 3s +8 - 6 B. s = 2r + 8 + 6 C. 3r + 8 = 2s + 6 D. 2r + 8 = 3s + 6
C. 3r + 8 = 2s + 6
Which of the following equations is justified by the associative property of multiplication? A. 5(x + 2) = 5x + 10 B. 4(6x) = (6x) • 4 C. 7(3x) = (7 • 3)x D. (8x)((1/(8x)) = 1
C. 7(3x) = (7 • 3)x Explanation: the associative property of multiplication allows the grouping of factors to be changed. The commutative property allows the order of factors to be changed The distributive property allows you to decompose the factors and distribute those across the equation
Use the table below to answer the question that follows. Car Type: SUV sedan coupe station wagon other Number of Owners: 48 96 72 12 12 What is the measurement of the central angle to be used for the SUV section in a circle graph displaying these data? A. 20 B. 48 C. 72 D. 144
C. 72
Which of the following activities would be most effective for assessing whether students accurately understand the meaning of the equals sign? A. Students are presented with a series of problems, such as 16 x 2 = and 16 x 20 = B. Students are asked to create number sentences showing a number as an addition problem with equal addends, such as 7 +7 + 7 = 21 C. Students are presented with a series of comparison problems, such as 76 + 9 = n + 13 D. Students are asked to describe how they would approach solving an equation involving an unknown, such as 62 - x = 43
C. Students are presented with a series of comparison problems, such as 76 + 9 = n + 13 Explanation: students who don't sign any value to the = symbol may solve 76 + 9 = n + 13 as n = 85 because they do not understand the full expression as n + 13 being equivalent to 76 + 9
Which of the following explains why an uncovered pot of water being heated on a stovetop burner does not change temperature once it has reached its boiling point? A. Any additional heat added to the system at the boiling point does work breaking the bonds between oxygen and hydrogen atoms. B. The heat lost to convection at that temperature balances the capacity of water to absorb and hold thermal energy C. The kinetic energy lost by the escape of fast-moving water vapor molecules at the boiling point matches the input of heat energy. D. Any thermal energy coming into the system at that temperature only increases the rate of loss by conduction.
C. The kinetic energy lost by the escape of fast-moving water vapor molecules at the boiling point matches the input of heat energy.
The increase in greenhouse gases in the atmosphere leads to further warming of the planet primarily through which of the following mechanisms? A. absorbing solar radiation and transferring it to Earth's surface B. increasing the rate of evaporation of the surface waters on Earth C. absorbing and trapping thermal radiation emitted from Earth's surface D. increasing the intensity of ultraviolet radiation hitting Earth's surface
C. absorbing and trapping thermal radiation emitted from Earth's surface
which of the following characteristics is a chemical property of a substance? A. density B. solubility C. malleability D. flammability
D. flammability Explanation: flammability is a chemical property because burning is a chemical reaction
What does a mitochondria look like on a diagram and what is it function.
It looks like a canoe with a squiggly line inside of it It produces energy in the form of ATP
A line graph would be most appropriate for which of the following types of data? A. a biologist wants to see the pattern of change in the oxygen levels of a lake that were recorded each month for a year B. A sales manager wants to compare the sales figures of four regional offices for one month. C. A meteorologist wants to determine the percent increase in rainfall from one year compared to the previous year. D. A bookstore owner wants to display the number of each category of books sold during a special sale.
A. a biologist wants to see the pattern of change in the oxygen levels of a lake that were recorded each month for a year Explanation: line graphs are typically used to provide a clear visual representation of changes over time and identify trends in data
According to research on vocabulary comprehension, which of the following teacher-led instructional sequences is most effective for teaching multiplication terminology to elementary students? A. activating background knowledge, summarizing important ideas, applying to understand using real-life examples B. conducting a mathematics talk, asking self-reflective questions, discussing similarities between peer conclusions C. displaying related work, inferring mathematical reasoning, synthesizing central components into repeated addition problems D. analyzing a multiples table, conducting mathematical inquiries, developing automaticity through repeated practice
A. activating background knowledge, summarizing important ideas, applying to understand using real-life examples
At the beginning of a unit on plants, a teacher asks elementary students to compare and contrast plants and humans. One student states, "humans carry out respiration, but plants perform photosynthesis." Further instruction on which of the following concepts would be most helpful in addressing the student's misunderstanding? A. basic life functions B. the role of the sun as an energy source C. ecosystem processes D. the biological importance of chlorophyll
A. basic life functions
From which of the following types of graphical representations is the median of a set of data most efficiently determined? A. box plot B. frequency diagram C. stem-and-leaf plot D. histogram
A. box plot
Which of the following engineering design projects would best strengthen student understanding of the general concepts of potential and kinetic energy? A. building a rubber band-powered car B. constructing a bridge to support a given weight C. modifying socks to increase friction and reduce slipping D. developing a model rowboat that will float while holding coins
A. building a rubber band-powered car
What is the primary role of nitrogen-fixing bacteria in the cycling of nitrogen through the environment? A. converting atmospheric nitrogen into a form usable by plants B. degrading nitrogen compounds present in animal feces C. releasing nitrogen from proteins in dead plant material D. returning nitrogen gas to the atmosphere
A. converting atmospheric nitrogen into a form usable by plants
A teacher sets up two glass beakers on a sunny windowsill to prepare a class demonstration on solar energy. As shown in the diagram, one of the jars has black paper lining both the bottom of the beaker and half of the interior of the beaker. The other beaker is unlined. Both beakers are placed in a position that allows equal amounts of sunlight to enter the beakers. A small thermometer is suspended from the tip edge of each jar, descending to two inches above the bottom of the beaker. After half an hour, the teacher records the temperature of the air inside the two beakers and asks the students why the air is warmer inside the beaker that is partially lined with black paper. The demonstration would help young students understand which of the following fundamental meteorological concepts? A. the role of Earth's surface in transforming sunlight into infrared energy that warms the atmosphere B. the amount of energy in
A. the role of Earth's surface in transforming sunlight into infrared energy that warms the atmosphere
For a unit on fossils, an elementary teacher prepares dough from flour, salt, and water. Students roll out the dough and press the feet of rubber dinosaurs into it. They remove the dinosaurs, then dry and examine their flour paste specimens. The learning objective most likely to be achieved by this activity is that students will: A. understand how trace fossils for various organisms are formed B. comprehend why the remains of organisms disintegrate over time C. make inferences about the similarities between extinct and modern-day organisms D. recognize which information can be learned about environmental conditions from fossil study
A. understand how trace fossils for various organisms are formed
When the numerator and denominator of a fraction are each multiplied by the same number, the resulting fraction is equivalent to the original fraction. For example, (3/4) = (9/12) because (9/12) = (3/4) x (3/3) = (3/4) x 1 = (3/4). Which of the following computation steps is justified by this property? A. lining up decimal points in order to subtract decimal numbers B. moving decimal points the same number of spaces in both the dividend and the divisor in order to divide decimal numbers C. rewriting mixed numbers as improper fractions in order to multiply the mixed numbers D. finding the lowest common denominator in order to add fractions
B. moving decimal points the same number of spaces in both the dividend and the divisor in order to divide decimal numbers Explanation: just like multiplying two fractions by their common denominators, moving decimal points of both numbers in a division problem does not change their value, but simple makes them easier to solve. With the fractions, you multiply by the common denominator. With the decimals, you multiply by ten.
Two bird species regularly visit feeders for sunflower seeds during the winter. For a month, several students take turns watching the feeding stations from 6:30 to 7:30 every morning and recording their observations. They find that whenever individuals of one species arrive at the feeder, individuals of the other species leave. The students conclude that competition for food between the species is an important factor in their ecological relationship. The students' conclusion would be most strengthened by adding which of the following elements to their study? A. including more than one type of food resource at the feeding station B. observing the feeding behaviors of both species under natural conditions C. recording feeding behaviors at different times during the day D. having the students work in pairs while making the observations
B. observing the feeding behaviors of both species under natural conditions Explanation: the artificial setting is the most invasive part of the experiment. If the experiment was done in a natural setting, a multitude of new variables would be in place.
Oil deposits are believed to form primarily from which of the following? A. the decay of vegetation that grew in ancient swamps B. plankton and other organisms that accumulated on the ocean floor C. the chemical breakdown of carbon-rich rock buried deep underground D. limestone and the organisms associated with coral reefs
B. plankton and other organisms that accumulated on the ocean floor
Which of the following activities would be most effective for developing first-grade students' knowledge of variables in subtraction equations? A. asking students to solve single-digit problems with x,y, and z in place of the numerals B. showing students how to write expressions using simple shapes in place of a missing quantity C. providing students with sums and prompting them to write numerical sentences that represent the answer D. using manipulatives to practice the act of taking away when presented with large double-digit amounts
B. showing students how to write expressions using simple shapes in place of a missing quantity Explanation: A. is too advanced C. is off topic and D. is below grade-level
Which of the following environmental problems has been the main cause of the reduction of Earth's biological diversity in recent decades? A. acid rain B. tropical deforestation C. desertification D. soil salinization
B. tropical deforestation
A fourth-grade teacher presents the following problem to students. Hardwood flooring is going to be installed in two different rooms. The first room measures 24 ft by 40 ft and the second room measures 30 ft by 60 ft. The new flooring costs $3.88 per square ft. What is the total cost for the hardwood flooring? The teacher then asks students to solve the problem,. Which of the following expressions would be most appropriate for the students to use first for this assignment? A. w ÷ h B. w x h C. w x h ÷ a D. w - h x a
B. w x h
Use the word problem below to answer the question that follows. A girl is distributing grapes into several bowls. She puts 5 grapes in the first bowl, 10 grapes in the second bowl, 20 grapes in the third bowl, 40 grapes in the fourth bowl, and 80 grapes in the fifth bowl. If the pattern continues, how many grapes will she put in the ninth bowl? A fourth-grade teacher says, "Read this word problem closely. Answer the question and then use words or symbols to express a rule for the given pattern." The teacher's actions are most effective for developing which of the following mathematical skills? A. practicing and extending rules of multiplication B. identifying and summarizing counting by 5s C. analyzing and applying doubles facts D. explaining and predicting addition sequences
C. analyzing and applying doubles facts
After a class reads a chapter about measurement conversion, the teacher observes students using improper terminology to discuss their mathematical processes. Which of the following teacher strategies would be most effective in scaffolding the students' understanding of mathematics vocabulary in future text-based discussions? A. conducting an attribute word hunt prior to beginning new units B. relating multiple-meaning words to other subject material C. completing an open word sort with students assigning categories D. building a word wall to be used as a reference throughout lessons
C. completing an open word sort with students assigning categories Explanation: open word sorts where the STUDENTS assign the categories requires critical thinking and can help build comprehension of vocabulary.
An elementary teacher is beginning a geometry unit on spatial sense. Which of the following student activities would be most effective for prompting the application of transformations? A. exploring which three-dimensional shapes are easier to slide and which are easier to roll B. creating two-dimensional shapes using rubber bands and geoboards C. filling outlines of various two-dimensional shapes with smaller polygon pieces D. composing three-dimensional shapes using sticks and foam balls
C. filling outlines of various two-dimensional shapes with smaller polygon pieces
which of the following demonstrations provides the best analogy for improving a young student's understanding of the mechanism underlying the propagation of sound? A. lining up students and having them pass a ball down the line until it reaches the last person, who then sends the ball back down the line B. driving a water wheel with the flow of tap water and then reducing the flow to slow the rotation of the water wheel C. setting up a row of dominoes half an inch apart facing each other so that when the first one is knocked over the others fall in response D. placing several plastic boats at one end of a water table and then using a fan to blow them across the water
C. setting up a row of dominoes half an inch apart facing each other so that when the first one is knocked over the others fall in response
Sixth-grade students have been learning about erosion. Students are given an engineering task: to work in groups to generate ideas and design possible mechanical solutions for reducing erosion in a hillside community. Each group constructs a model of a ill as well as a model of their group's proposed solution using everyday materials such as soil, clay, rocks, craft sticks, and netting. Which of the following would be the best step to take next in their design process? A. making modifications to their original designs B. researching the real-world costs of their solutions C. using water to test their models to observe the effectiveness D. comparing the efficiency of the various prototypes in reducing erosion
C. using water to test their models to observe the effectiveness
For an introduction to animal behavior, a teacher orders pill bugs from a reputable biological supply company. Students carry out simple investigations about the animals' preferences for types of food and habitat conditions. At the conclusion of the unit, the students want to release the pill bugs into the school's community garden. Which of the following is the best response for the teacher to make? A. "Classroom animals should only be released during the summer months." B. "It is important that students share responsibility for classroom animals and take turns caring for them at home." C. "It could harm the animals to be set free unless outside conditions are warm and dry." D. "Classroom animals should not be released into the local environment as they might compete with native species."
D. "Classroom animals should not be released into the local environment as they might compete with native species."
Use the student work sample below to answer the question that follows. *** + *** + *** + *** + *** = 1 x 2 x 5 Which of the following teacher prompts to this student would be most effective for understanding the student's reasoning for their error? A. "Tell me about how you multiplied" B. "What operation did you relate to multiplication" C. "I notice you multiplied by one first" D. "Why did you create a multiplication equation with three numbers?"
D. "Why did you create a multiplication equation with three numbers?"
Use the table below to answer the question that follows Items socks pants T-shirt Regular Price $2.99 $23.79 $8.29 Discount 25% 30% 25% A store is having a sale on the items shown in the table. A shopper wants to estimate the cost of purchasing two pairs of socks, one pair of pants, and one T-shirt. Which of the following expressions gives the best estimate of the total cost of the purchase in dollars? A. (1/4)(3 + 24 + 9) B. (1/4)(3) + (1/4)(24) + (1/4)8 C. (3/4)(6 + 24 + 9) D. (3/4)6 + (2/3)24 + (3/4)8
D. (3/4)6 + (2/3)24 + (3/4)8
Use the table below to answer the question that follows. Years since purchase: 1 2 3 4 Value in Dollars: 20,000 17,000 14,450 12,283 10,441 A car is purchased for $20,000. Each year, the car loses value as shown in the table. If the pattern continues, which of the following expressions calculates the value of the car 12 years after it is purchased? A. 20,000 - 12 x 3,000 B. 20,000 - 12 x ((3,000 + 2,550 + 2,167 + 1,842)/4) C. 20,000 - 20,000(0.15)^12 D. 20,000(1 - 0.15)^12
D. 20,000(0.15)^12 Explanation: The car is losing 15% of it's value every year, which can be represented by the above statement.
In which of the following situations would the mode be the most appropriate statistical measure? A. A homeowner measures the length and width of a section of their yard to create an outline for a garden plot B. A manager creates a biweekly work schedule for employees based on availability and store hours. C. A botanist records the average number of seedlings growing in 10 containers in a greenhouse. D. A lifeguard determines which section of a lake has the greatest number of swimmers and places a guard station there
D. A lifeguard determines which section of a lake has the greatest number of swimmers and places a guard station there
A bottle is filled with air, tightly sealed, and placed in an ice bath. Which of the following will occur as the bottle is cooled? A. pressure will increase and mass will decrease B. Pressure will increase and mass will remain constant C. Pressure will decrease and mass will decrease D. Pressure will decrease and mass will remain constant
D. Pressure will decrease and mass will remain constant Explanation: pressure of gas is directly related to temperature. As the temperature decreases, the pressure will also decrease.
At the beginning of the year, a first-grade teacher plans a math unit about place value. Which of the following activities would most effectively support students' understanding of this concept? A. playing a card game where students call out the number on their card in order after the immediately preceding number is called out by a classmate B. building double-digit numbers with foam tens rods and ones units by rolling a die to add on C. solving addition sentences that present two single-digit numbers to be added and then decomposed as a group of ten and more ones D. Using magnetic tens frames and dots to compose numbers 11 through 20 as groups of ten and additional ones
D. Using magnetic tens frames and dots to compose numbers 11 through 20 as groups of ten and additional ones. Explanation: unlike the other options, this one is exclusively concrete, without any abstract elements to it. The concrete visual representation and the kinesthetic action of moving the dots on the tens frames aligns the academic content with students' developmental needs.
Third-grade students are learning about patterns and how to explain them using the properties of operations, Which of the following approaches would most effectively support students' recognition of patterns? A. covering up multiples of ten on a hundreds chart for students to identify and write on a number slip B. providing a beginning number and prompting students with directional arrows to arrive at a mystery number C. preparing a multiplication table for students to fill in while asking them to highlight every other number D. arranging a familiar numerical sequence on the whiteboard for students to analyze and extend
D. arranging a familiar numerical sequence on the whiteboard for students to analyze and extend Explanation: D. is the only activity that practices the afore mentioned skill
An elementary school teacher performs the following demonstration: 1. The teacher fills the bottom fourth of a large glass beaker with hot water 2. The teacher holds a lit match over the open jar and then drops the match into the jar 3. The teacher quickly places an aluminum pie plate filled with ice cubes on top of the beaker At the end of the demonstration, a cloud forms within the beaker. In this demonstration, which component of the hydrologic cycle is being modeled? A. evaporation B. transpiration C .precipitation D. condensation
D. condensation
Elementary students have been learning about heat energy and transfer. In one class, groups of students perform the following investigation. 1. students place a plastic spoon, a metal spoon, and a wooden tongue depressor, all of the same height, into a glass. 2. students cut 3 pats of butter of the same size and place one pat on top of each utensil 3. Students heat water and put it into the glass to a height of 3 inches 4. Students then observe the objects in the glass to identify which pat of butter melts first. Which process is being observed in this investigation? A. radiation B. convection C. induction D. conduction
D. conduction Explanation: radiation is for subatomic particles, convection is for fluids, induction is for electricity and magnetism, and conduction is for solids.
Use the information below to answer the question that follows. A second-grade teacher has students measure the lengths of several objects using two methods. For one set of measurements, students report the number of 1-inch unit cubes needed to measure the length of the object. For the other set, students record their measurements taken with a centimeter ruler. One student's measurements are shown in the following table. Object pencil lunch box eraser 1-inch unit cubes 8 13 3 Ruler (cm) 20.3 33.0 7.6 This student concludes that the unit cube measurements are more accurate than the ruler measurements because they are reported with smaller numbers. Which of the following misconceptions best describes the student's error? A. incorrect application of measurement tools B. misunderstanding of measurement conversions C. approximate measurements due to rounding D. improper comparison of measurement units
D. improper comparison of measurement units
Use the algorithm below to answer the question that follows. Step 1. Choose a number, n. Step 2. Multiply n by 4. Step 3. Move the products's decimal point 2 places to the left. Which of the following expressions represents the output of the algorithm? A. 400n B. 25n C. n ÷ 400 D. n ÷ 25
D. n ÷ 25 Explanation: moving the decimal two places to the left is equivalent to dividing by 100, and 4n ÷ 100 = n ÷ 25
An elementary school teacher carries out a demonstration to introduce the concept of cellular respiration. The teacher places a small scoop of baker's yeast and some grape juice into a beaker and then secures a deflated balloon over the top of the beaker. The beaker is set aside. Two hours later, the students observe that the balloon has inflated over the beaker. The students hypothesized that the yeast produced a gas that inflated the balloon. Which of the following changes would make this activity closer to a scientific investigation than to a demonstration? A. running the demonstration again with a different type of juice in the beaker B. helping the students construct a simple graph of the change in the balloon's size C. having students record the exact amounts of baker's yeast and grape juice used D. providing an additional beaker setup using just grape juice and a deflated balloon
D. providing an additional beaker setup using just grape juice and a deflated balloon
A class is using common classroom manipulatives to compare the likelihood of different probability events. The students randomly select tiles labeled with numbers or letters from a bag, roll dice, or toss coins. Which of the following probability events has the highest likelihood of occurring? A. rolling a 6-sided die and observing a number less than 5 B. randomly selecting an odd number from the first 15 whole numbers C. flipping a coin twice and observing heads both times D. randomly selecting a consonant from the first 10 letters of the alphabet
D. randomly selecting a consonant from the first 10 letters of the alphabet
In an elementary class studying introductory space science, the teacher gives students a relevant hand gesture or movement to use when discussing certain key terms. For example, students move a pointed finger in a wide circle for orbit, pull their outstretched arms down toward the ground for gravity, and run in place for velocity. The primary benefit of this type of strategy is that it is: A. able to expel some of the students' energy during class B. effective with both outgoing students and those who are more reserved C. engaging students and helps focus student attention on the lesson D. reinforcing learning by having a kinesthetic association as well as a linguistic one
D. reinforcing learning by having a kinesthetic association as well as a linguistic one
A teacher introduces students to the features of a box plot at the beginning of a lesson. For the next step of the lesson, students practice creating their first box plot from a set of data. Which of the following actions can the teacher take to minimize the work necessary for constructing a box plot? A. selecting a data set that contains whole-number values B. displaying the range of a data set in addition to its values C. displaying the mean of a data set in addition to its values D. selecting a data set that contains sorted values
D. selecting a data set that contains sorted values
An inventor has designed a car that has an electric generator attached to the front wheels. the car is initially powered by a gasoline engine, but as the car moves forward, the generator charges a battery pack that can also power the car. The inventor claims that this design makes the car 100% efficient-that all of the gasoline used by the car is converted directly into the kinetic energy of the car. Which of the following laws of physics could be used to disprove the inventor's claim? A. Newton's first law of motion (inertia) B. Newton's second law of motion (acceleration) C. the first law of thermodynamics (conservation of energy) D. the second law of thermodynamics (increase in entropy)
D. the second law of thermodynamics (increase in entropy) Explanation: the second law of thermodynamics states that it is impossible to convert one form of energy to another without some loss of energy due to heat.
