TEXES Math/Science 4th through 8th
Use the figure below to answer the question that follows. The spinner shown is in the shape of a circle divided into equal sections numbered 1, 2, 3, 4, 5, 6, 7, and 8. When the arrow on the spinner is spun, it is equally likely that the arrow will land in any of the 8 sections. If the arrow is spun three times, what is the probability that the arrow will land on 8 all three times? (1/8 )(1/8)(1/8) (1/8 )(1/7)(1/6) (7/8)(7/8)(7/8) (7/8)(6/7)(5/6)
(1/8 )(1/8)(1/8)
Five cards are randomly chosen without replacement from an ordinary deck of 26 black and 26 red cards. What expression shows the probability that all five cards are red? (1/26)(1/25)(1/24)(1/23)(1/22) (26/52)(26/52)(26/52)(26/52)(26/52) (1/52)(1/51)(1/50)(1/49)(1/48) (26/52)(25/51)(24/50)(23/49)(22/48)
(26/52)(25/51)(24/50)(23/49)(22/48) A full deck has 52 cards, 26 of which are red. The chance of drawing a red is (26/52)=(1/2). Without replacement, the next choice has a possibility of 25 red out of 51 cards or (25/51). As cards continue to be drawn, the probabilities become (24/50),(23/49), and (22/48). The probability of selecting 5 red cards in a row from a full deck is the product of these individual probabilities.
Which of the following is the prime factorization of 900? (4)(9)(25) (16)(5)(11) (2^3)(3^3)(5^3) (2^2)(3^2)(5^2)
(2^2)(3^2)(5^2)
A teacher engages students in a discussion of prime and composite integers. The students are asked to discuss whether 1 is a prime number, whether negative integers can be called primes, and whether fractions can be called prime or composite numbers. The teacher most likely designed this activity to address which of the following objectives? Demonstrating the use of multiple representations of mathematical concepts Demonstrating the use of formative and summative assessments Demonstrating how abstract mathematical concepts relate to a variety of careers and professions Demonstrating the use of mathematical terminology as a precise means of expressing mathematical ideas
Demonstrating the use of mathematical terminology as a precise means of expressing mathematical ideas Option D is correct because the precise definition of prime numbers is critical to applications and uses of prime numbers. Option A is incorrect because multiple representations of mathematical concepts are not discussed. Option B is incorrect because no assessments were discussed or given with this activity. Option C is incorrect because careers and professions are not discussed.
Which of the following is the next step after students develop a hypothesis? Design an experiment Develop a theory Analyze experimental data Draw conclusions
Design an experiment Option A is correct because after a hypothesis is developed, an experiment should be designed to test the hypothesis. Option B is incorrect because a theory is not developed until various experiments have been done that result in data that support a hypothesis. Options C and D are incorrect because analyzing data and drawing conclusions are done after the experiment is conducted.
In the United States, automobiles are one of several primary producers of carbon dioxide that is emitted into the atmosphere. Imagine cars could run on each of the following fuels. Of the following, which fuel has the greatest potential to minimize the amount of carbon dioxide produced and emitted by automobiles? Electricity from power plants Diesel fuel Coal Kerosene
Electricity from power plants Since power plants can also operate with non-carbon based fuels, such as nuclear power and wind, electric cars have the greatest potential for minimizing carbon dioxide emissions.
Which of the following is true of evolution? Offspring are genetically identical to their parents. Individual organisms change over time. Mitosis is responsible for the genetic variation in most animal populations. Evolution can result in new species.
Evolution can result in new species. Populations, not individuals, change over time.
Students are using a curve-fitting computer simulation program. Which of the following is the best activity for the teacher to ask students to do using the software? Find the zeros of a quadratic function. Find the intersection points of three circles in a plane. Find the least common denominator of a set of fractions. Find the area of a figure from a drawing and its dimensions.
Find the zeros of a quadratic function. The zeros of a quadratic function can be determined from a curve-fitting computer simulation program.
Students are using computer software that allows them to create compass and straightedge constructions on the computer. Which of the following is the best activity for the teacher to ask students to do using the software? Finding the zeros of a polynomial Finding the maximum and minimum values of differentiable functions Finding the circle in the plane that passes through three noncollinear points Finding the list of prime numbers greater than 1000 but less than 2000
Finding the circle in the plane that passes through three noncollinear points Option C is correct because the circle in the plane that passes through three noncollinear points can be found with compass and straightedge constructions. Options A and B are incorrect because these applications can be done with graphing calculators or graphing software. Option D is incorrect because the determination of prime numbers cannot be done with compass and straightedge constructions.
Some power plants burn natural gas to produce electricity. Which THREE of the following are alternative sources of power that can be used to reduce the amount of carbon dioxide produced and emitted into the atmosphere during electrical power production? Coal power plant Hydropower plant Wind turbines Nuclear power plant
Hydropower plant Options B, C and D are correct because hydropower plants, wind turbines, and nuclear power plants do not directly produce and emit carbon dioxide during their operation and if they are used as an alternative to combustion-powered plants, will result in a reduction in the production and emission of carbon dioxide. Option A is incorrect because coal power plants produce carbon dioxide as a by-product of combustion.
Which of the following is an ionic compound? LiF CH4 SO2 H2O
LiF Lithium fluoride forms with an ionic bond from the lithium ion, Li^+1 and the Fluorine ion, F^-1.
Which of the following organisms are cold-blooded, lay eggs, and have backbones and dry, scaly skin? Spiders Chickens Salamanders Lizards
Lizards Lizards are reptiles, which have all of the listed characteristics.
A laboratory sample initially contains 1.2 g of radioactive material. After 8 days, the sample contains 0.6 g of the material and after 16 days, the sample contains 0.3 g. Which of the following functions best models the mass M of the sample as a function of time t, in days? M(t)=1.2(2)^(t/16) M(t)=1.2(21)^(t/8)
M(t)=1.2(21)^(t/8) The mass of the radioactive material as a function of time can be modeled by the exponential decay function M(t)=M0(21)^(t/h) where M0 is the initial mass of the sample, h is the half-life of the material, t is the elapsed time in the same units as the half-life, and M(t) is the remaining mass after time t. This general function leads to M(t)=1.2(21)^(t/8) for this specific case.
Of the following, which is the best example of homeostasis? In humans, the enzyme salivary amylase catalyzes the digestion of some starches in the mouth. Marine birds use salt glands to remove excess salt from the seawater they drink to maintain a balance between salt and water. Spores are produced internally in mushrooms and then are dispersed externally. When a blood vessel is damaged, blood that leaks out undergoes processes that result in a blood clot that stops blood loss.
Marine birds use salt glands to remove excess salt from the seawater they drink to maintain a balance between salt and water. Option B is correct because homeostasis is a process that maintains the stability of internal conditions such as the maintenance of a balance between salt and water in a marine bird. Option A is incorrect because the chemical process involving salivary amylase is an example of a digestive process. Option C is incorrect because the production and dispersal of mushroom spores is an aspect of asexual reproduction. Option D is incorrect because the processes that result in blood clotting and a cessation of bleeding from a blood vessel is called hemostasis.
Which of the following units can be used to represent pressure? g·cm/s N·m N/m2 g/cm^3
N/m2 Pressure is force per unit area. Force units are newtons (N) and area units are square meters (m^2) so pressure can be measured in N/m^2.
If the relative humidity is 95% on a day when the air temperature is 85.0°F, which of the following is most likely closest to the dew point? 95.0°F 85.0°F 84.0°F 45.0°F
84.0°F Option C is correct because the dew point of this particular air sample must be slightly below 85.0°degreesF, so the correct answer is 84.0°degreesF. Relative humidity is the amount of water vapor in the air compared to the amount required for saturation, expressed as a percentage. The maximum amount of water vapor that can be in the air decreases with decreasing temperature. The dew point is the temperature to which an air sample would have to be cooled for saturation to occur (dew is likely to form at this temperature). Therefore, when the relative humidity is very high (such as 95%) the air is almost saturated and the temperature would only have to decrease a small amount to reach saturation (100% relative humidity). Option A is incorrect because if the air temperature were 95.0°degreesF, the relative humidity would be lower than 95% and well above the dew point. Option B is incorrect because the relative humidity is only 95% at 85.0°degreesF, and relative humidity is 100% at the dew point. Option D is incorrect because the air would become saturated (100% relative humidity) and therefore dew would start to form long before the temperature dropped to 45.0°degreesF.
Which of the following is the best example of homeostasis? Flowering plants produce seeds, which are scattered and become new plants. A person's blood pressure is too high and their brain sends signals to slow their heart rate. Flowering plants produce seeds, which are scattered and become new plants. A snake basks in the sun and its temperature rises. A person consumes a high number of calories each day and gains weight.
A person's blood pressure is too high and their brain sends signals to slow their heart rate. Homeostasis is the tendency to maintain a stable equilibrium. The heart rate decreases in response to high blood pressure, resulting in a lowering of the blood pressure.
Which of the following describes the process of sublimation? A pure liquid changes directly into a gas. The atoms in a material combine with pure oxygen. Pure water breaks into charged ions of hydrogen and hydroxide. A pure solid changes directly into a gas.
A pure solid changes directly into a gas. In sublimation a pure solid experiences a phase transition directly to a gas.
Of the following, which describes an atoll? A sandy landform that extends out from a mainland coast A sandy landform that is parallel to a mainland coast A long narrow inlet with steep sides created by glacial erosion A ring-shaped coral reef that partially or completely encircles a lagoon
A ring-shaped coral reef that partially or completely encircles a lagoon Option D is correct because an atoll is a ring-shaped coral reef that partially or completely encircles a lagoon. Option A is incorrect because a spit is a sandy landform that extends out from a mainland. Option B is incorrect because a barrier island is a sandy landform that is parallel to a coastline. Option C is incorrect because a fjord is a long narrow inlet with steep sides that was created by glacial activity.
Which of the following illustrates the concept of equilibrium? Leaves burning A ball rolling down a hill Heat entering into an open refrigerator A saturated sugar solution with some solid sugar present
A saturated sugar solution with some solid sugar present Option D is correct because in the saturated sugar solution the rate of sugar crystallizing is equal to the rate of sugar dissolving, thus achieving a balance. Option A is incorrect because as leaves burn, carbon combines with oxygen to form carbon dioxide that escapes into the atmosphere along with smoke particles. Option B is incorrect because a ball rolling down hill is not at equilibrium. Option C is incorrect because heat entering an open refrigerator is not an example of equilibrium.
Of the following, which is a statement of Newton's first law of motion? Kinetic energy is conserved during the elastic collision of two objects. An object at rest will remain at rest unless acted on by an external net force. An object's linear momentum is proportional to its mass and speed. The acceleration of an object depends on the mass of the object and the net force acting on the object.
An object at rest will remain at rest unless acted on by an external net force. Option B is correct because a statement of Newton's first law of motion is that an object at rest will remain at rest unless acted on by an external net force. Option A is incorrect because although there is conservation of kinetic energy in an elastic collision, it is not a statement of Newton's first law of motion. Option C is incorrect because while linear momentum is the product of the mass and velocity of an object, it is not a statement of Newton's first law of motion. Option D is incorrect because it is a statement of Newton's second law.
Of the following, which is a statement of Newton's second law of motion? An object's acceleration depends on its mass and the net force acting on the object. The force of gravity between two objects depends on their masses and the distance between them. For every force on one object by a second, there is an equal and oppositely direct force on the second object by the first. An object's kinetic energy depends on its mass and speed.
An object's acceleration depends on its mass and the net force acting on the object. Newton's second law can be expressed by F = ma, where F is the net force on the object, m is the object's mass, and a is the object's acceleration.
A photogate is used to measure the velocity of an object moving along a straight line. If a graph of velocity versus time is produced, what does the slope of a tangent line to the graph represent? Average acceleration Instantaneous acceleration
Average acceleration slope = velocity steeper is faster acceleration not steep is slower acceleration
Use the formula below to answer the question that follows. C = (5/9)(F − 32) The formula above shows the relationship between C degrees Celsius and F degrees Fahrenheit. In an experiment, a certain chemical is to be kept in a temperature interval between 10°C and 45°C. What is this temperature interval in degrees Fahrenheit? Between 8.4°F and 15.4°F Between 10°F and 45°F Between 50°F and 113°F Between 75.6°F and 138.6°F
Between 50°degreesF and 113°degreesF
The half-life of carbon-14 is 5,730 years. How much of the original quantity of carbon-14 in a sample remains after 22,920 years? One-half One-quarter One-eighth One-sixteenth
One-sixteenth Option D is correct because 22,920 years is four half-lives (four times 5,730 years), and after four half-lives elapse, one-sixteenth of the original quantity of carbon-14 remains. During each half-life, half of the remaining carbon-14 radioactively decays. So after four half-lives, the amount of carbon-14 in the sample is equal to (1/2)(1/2)(1/2)(1/2) times the original quantity of carbon-14 (one-sixteenth of the original quantity). Options A, B, and C are incorrect because they do not represent the correct quantity of carbon-14 remaining.
The initial population of a bacteria culture is 300. After 2 hours, the population doubles to 600, and after 4 hours, the population doubles again to 1200. Which of the following functions best models the population, P, of the bacteria as a function of time, t, in hours? P(t)P of t = 300(2t) P(t)P of t = 300(2 + t) P(t)P of t = 300t^2 P(t)P of t = 300(2)^(1/2)
P(t)P of t = 300(2)^(1/2)
Which of the following is a metamorphic rock? Slate Granite Basalt Sandstone
Slate Option A is correct because slate is a metamorphic rock. Options B and C are incorrect because granite and basalt are igneous rocks. Option D is incorrect because sandstone is a sedimentary rock.
Which of the following organisms have an exoskeleton and jointed appendages? Frogs Spiders Alligators Earthworms
Spiders Option B is correct because spiders are arthropods and have an exoskeleton and jointed appendages. Options A, C and D are incorrect because frogs and alligators are vertebrates that have an endoskeleton, and earthworms do not have a skeleton.
Which of the following processes involves a pure solid changing directly into a gas? Oxidation Vaporization Condensation Sublimation
Sublimation Option D is correct because in the process of sublimation, a pure solid undergoes a phase transition to a gas. Option A is incorrect because oxidation is not a phase transition but is a chemical process. Option B is incorrect because vaporization is the phase transition in which a liquid becomes a gas. Option C is incorrect because condensation is the phase transition in which gas becomes a liquid.
Which statement correctly describes information about the following set of data? {8, 10, 12, 14, 14, 26} The mean is less than the mode. The mean is greater than the median. The mean and the median are equal. The median is greater than the mode.
The mean is greater than the median. The mean is the average of the six values (8 + 10 + 12 + 14 + 14 + 26) ÷ 6 = 14 The median is the average of the two center values (12 + 14) ÷ 2 = 13
Use the list below to answer the question that follows. List L: 64, 81, 96, 77, 93, 81, 71, 69 13. Which of the following statements is true about the numbers in list L? The mean of the numbers in list L is equal to the mode. The mean of the numbers in list L is greater than the mode. The mean of the numbers in list L is equal to the median. The mean of the numbers in list L is greater than the median.
The mean of the numbers in list L is equal to the median.
Which of the following statements is an example of a misconception about science? The ozone hole causes the greenhouse effect. Some natural processes affect the climate on earth. Water can experience a phase change directly from a solid to a gas. It is impossible to reach a temperature of absolute zero at which all molecules stop vibrating.
The ozone hole causes the greenhouse effect. The ozone hole is due to destruction of ozone and increases the number of harmful ultraviolet rays that reach the earth's surface. The greenhouse effect is caused by an excess of greenhouse gases, such as CO2, in the atmosphere. They are separate issues.
Use the student work below to answer the question that follows. Solve for x: x^2 − 8x = -15 Step 1. x^2 − 8x + 15 = -15 + 15 Step 2. x^2 − 8x + 15 = 0 Step 3. (x − 3)(x − 5) = 0 Step 4. x − 3 = 0 or x − 5 = 0 Step 5. x = 3 or x = 5 Which of the following is the justification for step 4 in the student work above? 0 is the identity element for addition. (a)(0) = 0 for all real numbers a. Division by 0 is undefined. The zero product property was used.
The zero product property was used.
John made a circular garden in his backyard. The garden has a diameter of 20 feet. He used ⅓ of the garden for tomatoes, his favorite vegetable. He enclosed the entire garden with a picket fence that was 12 inches high. Which of the following questions could NOT be answered with the information provided? What is the area of the tomato patch? What is the area of John's garden? What is the volume of the dirt in the garden? How many feet of fence does John need?
What is the volume of the dirt in the garden? Only this question cannot be answered with the information given because we do not know the depth of the soil to be planted.
Which of the following is a late stage in the life cycle of most low-mass stars? Black hole White dwarf Red supergiant Supernova
White dwarf Option B is correct because for most stars of low mass, white dwarf is a late stage in the life cycle of the star. Options A, C and D are incorrect because they are stages in the life cycle of a star with a very large mass.
A short written multiple-choice quiz given after the first section of a unit on chemical and physical properties of matter is an example of a formative assessment. a performance assessment. a summative assessment. a self-assessment.
a formative assessment. Option A is correct because a formative assessment is used to monitor student progress and to inform both student and teacher of areas that need additional work. Option B is incorrect because a performance assessment involves assessing a student's performance of a task, such as a lab activity, to assess how well the student understands the concepts he or she has learned. Option C is incorrect because a summative assessment occurs after completion of learning and assesses what has been learned and how well it has been learned. Option D is incorrect because a self-assessment involves the student evaluating his or her own learning.
A test given at the end of a unit on weather and climate is an example of: a performance assessment. a summative assessment. a formative assessment. a self-assessment.
a summative assessment. A summative assessment is given at the end of a unit to find out what standards students have met.
A mathematics teacher is conducting a lesson on mathematical modeling. The teacher asks the students to determine how long it would take to walk from Nome, Alaska, to Houston, Texas. By assigning this task, the teacher has asked the students to demonstrate: an understanding of proofs in mathematics. an understanding of estimation and its appropriate uses. an understanding of symbolic mathematics. the use of manipulatives.
an understanding of estimation and its appropriate uses. Option B is correct because to determine how long it would take a student to walk from Nome, Alaska, to Houston, Texas, the students should make a variety of estimates and apply the estimates to a mathematical model. Option A is incorrect because the activity is not designed to use mathematical proofs. Option C is incorrect because the use of estimation is more important in this activity than symbolic mathematics. Option D is incorrect because manipulatives are not needed for the task.
Which of the following is an igneous rock? shale basalt marble gneiss
basalt Basalt is an extrusive igneous rock. Igneous rock is volcanic.
Which of the following is the basic structure of every living organism? tissue organs cells organ systems
cells All living things have cells as their basic structure. Cells combine to make tissue, tissue combines to form organs, and organs group together to make organ systems.
In which of the following types of bonds are electrons shared between 2 atoms? covalent intermolecular ionic metallic
covalent Two or more atoms share electrons in a covalent bond. Electrons are not removed from any of the atoms.
During a lesson on using models in mathematics, a teacher asks the students to figure out how many hours they spend on homework for all their classes each year. In asking this question, the teacher has asked the class to: demonstrate the use of symbols to represent mathematical quantities. demonstrate an understanding of the estimation process. demonstrate their proficiency with the use of proofs. demonstrate their ability to use statistics with data.
demonstrate an understanding of the estimation process. Students will need to apply several estimates to determine the amount of time they spend on homework each year.
Ms. Hernandez gives her mathematics class a 15-minute multiple-choice quiz each Friday covering the material that had been discussed in class that week. The options in the multiple-choice questions include the correct answer as well as incorrect answers that are common misconceptions and common arithmetic mistakes. Ms. Hernandez counts the number of correct answers and determines the number of students making the same mistakes or making the same misconceptions. By using this testing strategy, Ms. Hernandez is demonstrating how to: use mathematics to model and solve problems in other disciplines. develop a variety of assessments and scoring procedures that assess mathematical understanding and inform instruction strategies. use manipulatives and technological tools. provide instruction along a continuum from concrete to abstract.
develop a variety of assessments and scoring procedures that assess mathematical understanding and inform instruction strategies. Option B is correct because by tracking common errors and misconceptions, the teacher can assess the level of mathematical understanding and address those errors through instruction. Option A is incorrect because the testing strategy may be used for any mathematical content, not just solving problems in other disciplines. Option C is incorrect because manipulatives may or may not be used in each weekly assessment. Option D is incorrect because the primary goal of the testing strategy is to identify errors and misconceptions.
A teacher engages her class in a discussion of the coordinate plane. The students are asked to identify the quadrants, the coordinate axes, and the mathematical notation for various points in the plane. Students are asked to develop a way to quickly identify the quadrant in which various points lie. Which of the following objectives is the teacher most likely trying to address with this lesson? encouraging student use of mathematics manipulatives and technological tools developing precise mathematical language when expressing mathematical ideas augmenting an understanding of estimation and its appropriate uses demonstrating how to model and solve real-world problems using mathematics
developing precise mathematical language when expressing mathematical ideas The precise use of mathematical language is required when using and describing information in the coordinate plane.
A student was given the following equation: 4(2x + 3) + 8x = 924(2x+3)+8x=92 In solving this problem for x the first step of a student's solution is: 4·2x + 4·3 + 8x = 924⋅2x+4⋅3+8x=92. Which of the following is the justification for this step? multiplicative inverse property distributive property additive identity property associative property of multiplication
distributive property The distributive property allows one to multiply 4 by the sum of 2x + 3 by first multiplying 4 by each term in the sum and adding the result.
Technology is best utilized in the classroom when it can accomplish which of the following? decreases the cost to the school district enhances the learning objective decreases the time the teacher must spend on instruction allows students to complete their homework more quickly
enhances the learning objective Technology is best used to enhance the learning objective of the lesson.
Ship A and ship B start sailing from the same harbor at the same time. Ship A is moving due north at a constant rate and has sailed a distance of x(t) where t is the number of hours since the ships began moving. Ship B is moving due east at a constant rate and has sailed a distance of y(t). The distance between the ships at time t is given by the function . Which of the following can be used to find the instantaneous rate of change of the distance between the two ships at time t? f ′(t) f ′′(t) (f(t) − f(0))/t ∫ f(t)dt
f ′prime(t)
The value of a car that Nakeshia purchased was $11,300. Assuming that the value of the car decreases by $900 every year, which of the following functions correctly models the value of the car, f, after x years? f(x)f of x = 11,300x + 900 f(x)f of x = 11,300x −minus 900 f(x)f of x = 11,300 + 900x f(x)f of x = 11,300 −minus 900x
f(x)f of x = 11,300 −minus 900x
In humans, the allele for freckles (F) is dominant and the allele for no freckles (f) is recessive. Which of the following is a genotype of people without freckles? Ff FF ffff ff
ff Both alleles must be recessive if a person is to exhibit a recessive trait such as lack of freckles.
Pitch is a characteristic of sound that is related to which of the following properties of a sound wave? frequency amplitude phase speed
frequency The higher the frequency of a sound wave, the higher the pitch.
Which of the following units is used to represent density? g mL g/mL cm^3
g/mL Option C is correct because density is a measure of mass per unit volume and can be represented by g/mL, which is equivalent to g/cm^3. Options A, B and D are incorrect because g is a unit of mass, and mL and cm3cm cubed are each a unit of volume.
Which of the following is typically a primary consumer in a food chain? leafy plant grasshopper mountain lion bluebird
grasshopper A grasshopper is the primary consumer because it eats primary producers like leafy plants.
An eighth-grade mathematics teacher notices that students are having difficulty understanding the difference between the mean and the median of a set of data. The teacher asks the students to find 10 different data sets from newspapers and Web sites. For each data set the students should calculate the mean and the median and write a paragraph explaining the data set and the significance of the mean and the median. With this activity the teacher demonstrates an understanding of the: procedures for developing instruction that establishes transitions between concrete, symbolic and abstract representations of mathematical knowledge. use of visual media, such as graphs, tables, diagrams and animations, to communicate mathematical information. structural properties common to the mathematical disciplines. implications of current trends and research in mathematics and mathematics education.
procedures for developing instruction that establishes transitions between concrete, symbolic and abstract representations of mathematical knowledge. Option A is correct because the activity asks the students to relate concrete data with abstract concepts. Option B is incorrect because students are not asked to use visual media. Option C is incorrect because the activity references statistics and is not about connections to other mathematical disciplines. Option D is incorrect because the activity does not reference current trends in mathematics education.
Which of the following is a stage in the life cycles of both low-mass and high-mass stars? white dwarf red giant supernova black hole
red giant Both low- and high-mass stars experience a red giant stage. A supernova occurs after the red giant stage only for high-mass stars.
Which of the following sets of numbers and number representations is in the correct order from least to greatest? (−3.1)^2, (13/7), square root of 2, π π, square root of 2, (−3.1)^2, (13/7) (13/7) ,π, (−3.1)^2, square root of 2 square root of 2, (13/7) ,π, (−3.1)^2
square root of 2, (13/7) ,π, (−3.1)^2 Make sure to convert all of the numbers to one format, such as decimals. The order from least to greatest is the square root of 2 =1.414...; (13/7)=1.857...; π =3.14...; (-3.1)^2 =9.61.
When deciding to house a live animal in the classroom, the risk of a potential health hazard to the student or animal must be weighed against the educational value added. What guidelines must first be considered to address this potential hazard, prior to making a choice of getting the animal for the classroom? standards for keeping the conditions sanitary and odor free plans for food, housing and comfort of the animal the children that might be affected by allergic symptoms procedures for caring for the animal during weekends and holidays
the children that might be affected by allergic symptoms Safety standards require that any live animal in the classroom must be fed and kept in sanitary conditions every day. Although the care and comfort of the animal is important, the safety concern with regards to the students is the teacher's first priority.
A teacher is preparing a unit on simplifying algebraic expressions and plans to use the expression shown as an example. Before introducing the example, which of the following concepts is best for the teacher to review? (6x^2y^-5z^4)^2(2x^-1y^-2z^3) the properties of addition of integers the distributive property the properties of multiplication of integers the laws of exponents
the laws of exponents The laws of exponents will be used to simplify the expression.
During a unit on solving linear equations and finding the area of geometric shapes, a geometry teacher developed a lesson using a motion detector to graph the velocity versus time of a walking student. Students found the area of the trapezoid between 0 and 5 s and compared it with the distance the student traveled in that time. Which of the following calculus topics could the teacher also demonstrate during this lesson? the concept of the derivative of a function at a point the meaning of an integral the idea of the limits of an asymptotic function the chain rule for derivatives of composite functions
the meaning of an integral Taking the integral of a function yields the area bounded by the function and the axes. The integral of a linear function of velocity versus time yields the distance traveled. The derivative yields the slope of the tangent line of a function.
Closure is when an operation (such as "adding")on members of a set (such as "real numbers")always makes a member of __________________. the same set a different set
the same set
A yellow pea plant with a Yy genotype has which of the following? no alleles one allele; yellow one allele; Yy two different alleles; Y and y
two different alleles; Y and y The big Y represents one allele and the little y represents a different allele.
In a particular variety of plant, the allele for red flowers (capital W) is dominant and the allele for white flowers (w) is recessive. Which of the following is the genotype of plants with white flowers? WW Ww ww w
ww Option C is correct because in complete dominance, only an individual with the genotype ww can have the phenotype of white flowers. Options A and B are incorrect because individuals with the genotype of WWcapital W capital W or Wwcapital Ww will each have the phenotype of red flowers since capital W is the dominant allele. Option D is incorrect because each plant has two copies of the gene for flower color, so the genotype of white plants is ww.
Which of the following represents the equation of a line in the xy-plane that is the reflection of the line y = 4x − 1 about the y-axis? y = 4x − 1 y = 1/4x − 1 y = -4x − 1 y = - 1/4x − 1
y = -4x − 1
Which of the following is the reflection in the xy plane of the line y=x^2-3x+6 across the x-axis? y=−x^2+1/3x−1/6 y=x^2+3x+6 y=x^2−1/3x+1/6 y=−x^2+3x−6
y=−x^2+3x−6 A reflection across the x-axis changes the sign of every y-value. In this case, the entire right side of the function is the sum of y-values so the sign of every term is changed.
Use the figure below to answer the question that follows. In the figure above lines l and m are parallel, and the triangle containing ∠3, ∠5, and ∠6 is not isosceles. Which of the following angles are congruent to ∠6? Select all that apply. ∠1 ∠2 ∠3 ∠4 ∠5 ∠7
∠1 ∠7
A baseball pitching machine is oriented so the baseball is launched straight up. The magnitude of the vertical velocity, v, of the baseball as a function of time, t, is described by the function v(t) = 45.3 - 7.9t + 0.68t^2. If the velocity function versus time is graphed on the coordinate axes, which of the following can be used to find the area bounded by the velocity curve and the x-axis between the instant of launch and time, t? v′′(t) v′(t) ∫ t 0 v(t)dt t⋅v(t)
∫ t 0 v(t)dt The integral gives the area under the curve formed by the function. The first derivative gives the slope of the curve.
A math teacher plans her instructional delivery method on resolving the difficulty students have distinguishing between mode and median. She plans to have students first work alone calculating the mode and median of sets of performance results from the school track team. Next, her students will work in groups of 2 or 3 to discuss and interpret their results, and record a summary of the significance of the results on whiteboards. Finally, the groups will present their summaries to the class, along with a teacher-led discussion of the findings. By planning such an activity, the teacher demonstrates that she understands: how to apply a variety of instructional delivery methods that can help students develop their mathematical thinking. how technological tools and manipulatives can be used to assist students in developing mathematical thinking. how students' prior mathematical knowledge can be used to build conceptual links to new knowledge. how to use a variety of questioning strategies that encourage mathematical discourse and help students analyze and evaluate their mathematical thinking.
how to apply a variety of instructional delivery methods that can help students develop their mathematical thinking. The teacher's plans show she understands how to use individual, small-group, and large-group instruction methods to help students develop their mathematical thinking. The teacher plans to incorporate questioning strategies, but her plans do not demonstrate an understanding of how to use a variety of these strategies.
Freshwater is a limited resource that is needed to sustain much of life on Earth. Which of the following reduces the availability of fresh drinking water for humans and animals? increased melting of glaciers and ice caps increased nitrogen pollution in oceans increased crop irrigation increased desalination of ocean water
increased crop irrigation As humans increase their use of freshwater to water crops, there is less available for other uses.
A mathematics teacher gives her class a two-question clicker quiz at the end of each class period and tabulates their answers according to their mathematical understanding, misconceptions, and error patterns. If her goal is improvement in her students' mathematical proficiency, her best use of the data would be to use it to: inform upcoming instructional strategies. develop instruction that connects mathematical concepts and procedures. create a display highlighting mathematical vocabulary for English-language learners. teach students to model and solve problems in other disciplines.
inform upcoming instructional strategies. Data on student understanding, misconceptions, and error patterns is best used to inform instructional strategies on the same or subsequent topics. The data may show that mathematical connections are lacking, in which case the upcoming instructional strategies would have this focus, however, in general, this is not the best use of the data.
Irrational numbers are _______________ under addition, subtraction, multiplication, and division. This is in contrast to rational numbers which are closed under all these operations. closed not closed
not closed
Which of the following is an ionic compound? KCl CO2 CH4 NH3
KCl Option A is correct because the compound KCl has ionic bonding between metallic K+positive ions and nonmetallic Cl-negative ions. Options B, C and D are incorrect because CO2, CH4, and NH3 are covalently bonded molecules.
A doctor prescribed a 250 mg capsule of a common antibiotic for strep throat. The pharmacist had only 1 gram of the antibiotic in stock. How many capsules of medicine can the patient get from the pharmacist? 4 25 40 0
4 The pharmacist has 1000 mg (since 1 gram = 1000 milligrams). Since each capsule needs 250 mg, proportional reasoning can be used. (1 cap/250 mg)=(x cap/1000 mg)
A trapezoid has an area of 600 mm^2. What is the area of the new trapezoid formed by dilating the original by a factor of 3? 1800 mm^2 5400 mm^2 500 mm^2 200 mm^2
5400 mm^2 An area is a square measure. If each side is dilated, or enlarged, by a factor of 3, the area dilates by a factor of 32 or 9. (600 mm^2)(9) = 5400 mm^2. Area is a square measure, not a linear measure.
Salome's mousetrap car completed a 30-meter stretch of track in 17 seconds. Which of the following is closest to the speed of the car in kilometers per hour? 5.8 kilometers per hour 6.3 kilometers per hour 1.8 kilometers per hour 7.1 kilometers per hour
6.3 kilometers per hour
The leg of a dog and the flipper of a whale are best described as examples of which of the following? Homologous structures Identifying structures Analogous structures Vestigial structures
Homologous structures Homologous structures are similar and share common traits and a common ancestor in evolutionary biology, but serve a different purpose. A leg allows a dog to walk and a flipper allows a whale to swim.
A student is investigating the growth of Elodea under different light sources. Which of the following is the best research question for this student? How does the amount of time spent in the sun affect the growth of Elodea plants? How does the distance from the light source affect Elodea plants? How does the color of an Elodea plant affect its growth under different light sources? How does the type of light source affect the rate of photosynthesis of Elodea plants?
How does the type of light source affect the rate of photosynthesis of Elodea plants? This is the best and most testable research question.
The wing of a bat and the arm of a gorilla are best described as examples of which of the following? Primary structures Vestigial structures Homologous structures Analogous structures
Homologous structures Option C is correct because in evolutionary biology a bat wing is homologous to the arm of a gorilla. Homologous structures are adapted to different purposes as a result of descent with modification from a common ancestor. Option A is incorrect because the term "primary structures" is not a term associated with the relationship between a bat wing and the arm of a gorilla. Option B is incorrect because a vestigial structure has lost much or all of the functions it had in its ancestors, such as the eyes of a mole, which are covered by a layer of skin and no longer function. Option D is incorrect because analogous structures, such as the wings of a bat and the wings of a moth, have similar functions in two different organisms, but were not present in a common ancestor and evolved separately.
Which of the following systems is NOT in equilibrium? Picnic foods have been sitting out on the picnic table for most of the day. A deep-sea diver floats at a certain depth in the water. Hot air is forced into a room after the thermostat is adjusted. A pendulum is stopped and hangs downward.
Hot air is forced into a room after the thermostat is adjusted. A room in which the temperature is changing is not in equilibrium.
Use the following conversion factors to answer the question below. 1 Pa = 0.00750062 mmHg (at 0°C) 1 atm = 1.01375 x 105 Pa During an experiment, a student measures and records a pressure of 1.20 x 105 Pa. What is this pressure in atmospheres and millimeters of mercury at 0°C? 1.22 x 10^10 atm and 900 mmHg 1.18 atm and 1.60 x 10^7 mmHg 1.18 atm and 900 mmHg 1.22 x 105 atm and 1.60 x 10^7 mmHg
1.18 atm and 900 mmHg
A high school has a total of 1100 students. A student in a statistics class takes a random sample of 100 students and finds that 9 of the students sampled are taller than 6 feet. Based on this sample, which of the following is the best estimate of the number of students at the high school who are taller than 6 feet? 1 10 100 1000
100
Which of the following is the greatest common divisor of 3300 and 1050? 2 150 100 3
150 The prime factors of 3300 are 22 · 3 · 52 · 11 and the prime factors of 1050 are 2 · 3 · 5^2 · 7. The prime factors that are common to the two numbers are 2 · 3 · 5^2 = 150.
Equilateral triangle ABC has sides of length 2. Equilateral triangle XYZ has sides of length 8. The area of triangle XYZ is how many times the area of triangle ABC? 4 8 16 64
16 because all equilateral triangles are similar. For similar triangles, there is a similar ratio of the sides and a similar ratio for the areas that is the square of the similar ratio of the sides. Since the ratio of the sides is 4:to1, the ratio of the areas is 16:to1, or 16 times greater. 4 is incorrect because the ratio of the sides is not equal to the ratio of the areas. 8 is incorrect because the similar ratio of the areas is not two times the ratio of the sides. 64 is incorrect because the ratio is 16:to1, not 64:to1.
Which of the following is an example of the commutative property of multiplication? 112+271=271+12 6(5−2)=5(6−2) 8(8+8)=8(8−8) 2×8=8×2
2 x 8 = 8 x 2 "Commute" where the terms change places The commutative property of multiplication states that it does not matter the order of the multiplication sequence, the answer will be the same. This can be represented by the equation axbxc=cxbxa
Which of the following numbers are greater than π? Select all that apply. 3 3.14 22/7 3.142
22/7 3.142 because the approximation of πpie to five decimal places is 3.14159, and therefore 22/7= 3.142857 is greater than π and 3.142 is greater than π. Options A and B are incorrect because 3 is less than π and 3.14 is less than π.
The side lengths of parallelogram X are 2 and 3. A similar parallelogram Y has side lengths 10 and 15. The area of parallelogram Y is how many times the area of parallelogram X? 5 3 25 135
25 The ratio of the sides of the two parallelograms is 5:1. The ratio of the areas is the square of the ratio of the sides, or 25:1. Parallelogram Y has an area 25 times that of X.
An equilateral triangle has a perimeter of 24 centimeters. If the triangle is dilated by a factor of 1.5, what is the perimeter of the new triangle? 12 centimeters 16 centimeters 36 centimeters 108 centimeters
36 centimeters Option C is correct because the length of each side of the new triangle is 1.5 times the length of the corresponding side of the original triangle. The perimeter of the original equilateral triangle is 24 centimeters, so the length of each side is 24 ÷divided by 3 = 8 centimeters. The length of each side of the new triangle is 8 ×times 1.5 = 12 centimeters, and the perimeter of the new triangle is 12 + 12 + 12 = 36. Option A is incorrect because the length of each side of the new triangle is 12. Option B is incorrect because 16 = 24 ÷divided by 1.5 would be the perimeter of the new triangle if the equilateral triangle were dilated by a factor of (1 ÷divided by 1.5). Option D is incorrect because 108 = 1.5(24 + 24 + 24) would be the perimeter of the new triangle if each side of the equilateral triangle were length 24.
Which of the following is typically a secondary consumer in a food chain? Tree Deer Squirrel Fox
Fox Option D is correct because a fox is a secondary consumer. Foxes eat animals such as squirrels that are primary consumers. Option A is incorrect because a tree is a primary producer. Primary producers are the organisms in an ecosystem that produce biomass from inorganic compounds. Options B and C are incorrect because deer and squirrels are primary consumers. Primary consumers eat primary producers.
Suppose Mike's actual weight is 165 lbs. His scale says his weight is 164 lbs. What can be said about his scale? It is accurate. It is precise. It is neither precise, nor accurate. It is both precise and accurate.
It is accurate. This scale is accurate because it gives a weight close to his actual weight.
Loudness is a characteristic of sound that is related to which of the following properties of a sound wave? Frequency Speed Intensity Wavelength
Intensity Option C is correct because loudness is a characteristic of sound that is related to the intensity of the sound wave. Options A, B and D are incorrect because loudness is not related to the frequency, speed, or wavelength of the sound wave.
Why is it important for scientists around the world to adhere to the same system of measurement? It allows for easier and more consistent communication of results. The results of experiments are more likely to support hypotheses. The metric system does not relate to real life, so it is easier to use for conceptual purposes. The imperial system of measurement is inaccurate.
It allows for easier and more consistent communication of results. A consistent system of measurement allows scientists to compare results more easily and remain consistent in their findings.
Which of the following student statements is an example of a student misconception about science? Positively charged ions have lost electrons and have an imbalance between positive and negative charges. The boiling point is the highest possible temperature of a substance. Even though an object is not moving, it has energy. The Moon orbits Earth in approximately 27.32 days.
The boiling point is the highest possible temperature of a substance. Option B is correct because the student statement that the boiling point is the highest temperature possible of a substance is a misconception. After a substance undergoes a phase transition from liquid to gas at its boiling point, its temperature can increase above the boiling point if additional energy is absorbed by the substance. Option A is incorrect because the student statement that positively charged ions have lost electrons and have an imbalance between positive and negative charges is not a misconception, but is true based on current models of the atom. Option C is incorrect because the student statement that an object that is not moving still has energy is not a misconception; it is true. For example, an object that is not moving has potential energy based on its position relative to the ground due to gravitational forces, and it has potential energy based on the relative positions of the atoms in the material from which it is made. Option D is incorrect because the student statement that the Moon orbits Earth in approximately 27.32 days is not a misconception but is correct based on measurements of the Moon's motion around Earth relative to distant stars.
Use the equation below to answer the question that follows. x^2 + x + 2 = 0 Which of the following statements is true about the equation above? The equation has no solutions. The equation has two real solutions. The equation has two complex solutions. The equation has one real solution and one complex solution.
The equation has two complex solutions.
