Content test- MATH
The digit 8 in 21.46837 represents which of the following values? a. 8x10^-3 b. 8x10^-2 c. 8x10^2 d. 8x10^3
A
Students in a 6th grade class are manipulating triangles on geoboards. Students arrange their triangles such that the bottom row contains two vertices. Students then observe how the action of moving the third vertex, which is located in a higher row, horizontally along to different pegs affects properties of the triangles. Which of the following triangle properties varies as students move the vertex in this manner? a. the area within the triangle b. the perimeter of the triangle c. the sum of the interior angles d. the vertical midpoint of a moved leg
B
The variable a, b, c and d represent positive integers such that a/d > c/d and a<c. Which of the following inequalities must be true? a. b>d b. d>b c. a>b d. b>c
B
Use the diagram below to answer the question that follows The isosceles triangle ABC has base BC. Ray CE extended from the triangle in a direction parallel to BA. If mABC is 68, what is cACE? a. 32 b. 44 c. 56 d. 68
B
A standard die is a cube, with each of its six faces showing a different number of dots from 1 to 6. What is the probability of getting a sum of 8 from 2 rolls of a standard die? a. 1/7 b. 1/6 c. 5/36 d/ 5/12
C
Which of the following tables represents an inversely proportional relationship between x and y? a.x y 2 1 4 2 6 3 8 4 b. x y 1 2 2 3 3 4 4 5 c. x y 1 2 2 6 3 4 4 5
C
Parallelogram ABCD has three of its verticals at A=(0,-4), B=(-4,2), and C=(1,6). What is the slope of side AD of the parallelogram? a. 2/3 b. -3/2 c. 4/5 d. -5/4
Correct Response C Objective 0012. Opposite sides of the parallelogram are parallel and parallel lines have equal slopes. The slope of side AD will be the same as the slope of side BC. To find the slope of side BC, use the coordinates of the two points B and C to find the value of y2-y1/x2-x1=6-2/1-(-4). The slope of AD is 4/5.
*Use the graph below to answer the question that follows. (look at paper) The double bar graph shows the weights of the participants of a weight training class. Which of the following is the closest to the percent of the women in the class who weight less than 180 pounds? a. 22% b. 28% c. 38% D. 67%
Correct Response D Objective 0011. The shaded bars represent women in the class, and there are 2+4+4+4+1 = 15 women altogether. There are 4+4+2 women under 180 pounds. The percent of women under 180 pounds is found as follows 4+4+2/15=10=15=66.7%. The percent closest to 66.7% is 67%.
The amount of god in a piece of jewelry is measured in karats (K), where 24K represents pure gold. For a ring labeled 22K, the ratio of the mass of gold to the mass of the ring is 22:24. If a gold ring weighing 0.3 ounces is marked 18K and the value of pure gold is $1,200 per ounce, what is the value of the gold in this ring? a. $270 b. $300 c. $360 d. $480
A
Use the system of equations below to answer the question that follows. -3x+5y=7 6x+2y=-8 Which of the following is a step in solving the system of equations using the method of adding/subtracting equations? a. 8y=22 b. 8y=-15 c. 12y=6 d. 12y=-1
C
Which of the following activities best aligns with the developmental sequence of a fourth grade student learning to compare and order quantities? a. comparing the cardinality of two collections of real-life objects b. locating rational approximations of irrational numbers on a number line c. sorting different sets of nickels, dimes, and quarters in order by value d. expressing the order of two multidigit whole numbers using inequality symbols
D
Use the diagram below to answer the question that follows. The diagram shows the expression 8+6 may be evaluated with a counting strategy. Which of the following strategies is illustrated in the diagram? a. counting all b. counting on c. skip counting d. composing ten
B
Given that the fraction a/b is expressed in lowest terms and a/b=0.64, what is a/b-1? a. 2/5 b. 64/99 c. 33/50 d. 2/3
Correct Response D Objective 0009. It is given that a/b=0.64 and is expressed in lowest terms. Therefore, a/b=64/100=16/25. Hence, a=16 and b=25. It follows that a/b-1=16/25-1=16/24=2/3.
For what value of k will f(3)=g(3) given that f(x)=x^2-kx+22 and g(x)=5x-k? a. 4 b. 6.5 c. 8 d. 11.5
c
Given that f(x)=2x + 2 and g(x)=x+1/2, what is f(g(x))? a. x+1 b. x+2 c. x+3 d. x+4
C
Use the graph below to answer the question that follows. Which of the following equations could represent the graph shown above? a. y=-(x-1)^2+2 b. y=-(x-2)^2+1 c. y=-(x+1)^2+2 d. y=-(x+2)^2+1
A
Which of the following activities would best provide students with a real-world model of base-ten enumeration? a. measuring a length using a variety of metric units b. learning to read an analog clock c. converting temperatures from Fahrenheit to Celsius d. comparing weights of solids in ounces and pounds
A
Which of the following inequalities describes a restricted value for the domain of the function? g(x)=x+1/x+3 a. x does not = -3 b. x does not= -1 c. x does not = 1 d. x does not = 3
A
Use the graph below to answer the question that follows. given y=f(x), what is f^-1(2) where f^-1(x) is the inverse function of f(x)? a. 0 b. 2 c. 4 d. 6
A
A candle manufacturing company uses the graph shown to analyze the relationship between the selling price of each candle, x, and the total profit made P(x). Which of the following properties of the graph determines the candle price needed to break even? a. the minimum value of the graph b. the maximum value of the graph c. the horizontal intercept of the graph along the x-axis d. the vertical intercept of the graph along the x-axis
C
If the letter n can be any whole number, then the expression 2n + 1 must be which of the following kinds of numbers? a. prime b. composite c. odd d. even
C
Second grade students are investigating the relationships between the standard-form and expanded-form representations of the number 365. Which of the following tools would best support students understanding of this relationship? a. calculators to determine factors of numbers b. whiteboards to facilitate alignment of addends c. layered place-value cards to illustrate values of digits
C
Use the diagram below to answer the following question The diagram is composed of squares of equal sizes. The shaded and unshaded squares together represent 1 3/4 of one unit. What fraction of a unit is represented by just the shaded squares? a. 3/14 b 3/11 c. 3/8 d. 3/12
C
Use the information below to answer the question that follows. At the start of the school year, students report the number of books they each read over the summer. -the number of students who read 6 books was 1 1/2 times the number of students who read 8 books -the number of students who read 5 books was twice the number of students who read 8 books -the number of students who read 4 books was triple the number of students who read 6 books If this information is to be displayed in a circle graph, what is the measure of the central angle for the sector representing the number of students who read 5 books? a. 40 b. 60 c. 80 d. 90
C
Use the problem below to answer the question that follows. There are six teams in a tournament. Each team must play each of the other teams exactly once. How many games will be played? Which of the following problem-solving would be most effective for solving the problem shown? a. working backward b. guessing checked c. drawing a diagram d. writing an equation
C
Use the student work below to answer the question that follows. 4 3/8- 2 1/2= 4 3/8- 2 4/8= 3 13/8- 2 4/8= 1 9/8= 2 1/8 A student was asked to find the difference between 4 3/8 and 2 1/2. Which of the following activities would best help the student understand the error made in the work shown above? a. Rewriting the fractions and decimals before subtracting b. Reviewing subtraction of fractions with like denominators c. Using number lines to convert improper fractions to mixed numbers d. Drawing area models to rename wholes as sums of unit fractions
Correct Response D Objective 0009. The students error was made in renaming one of the 4 wholes into eighths. Rather than renaming the whole as 8/8, the student renamed it as 10/8, and thus changed 4 3/8 to 3 13/8. The student could benefit from working with area models to convert a whole into a given number of unit fractions.
Use the histogram below to answer the question that follows A class counted the number of first cousins for each student and displayed and displayed the results in a histogram shown below. Which of the following relationships is true for these data? a. the mean is greater than the median b. the median equals the range c. the mode is greater than the mean d. the range is twice the mode
A
Which of the following number lines shows the solution to the inequality -x+5<-1/3x+17? a. <------(-18)------> b. <------(-16)------> c. <------(-9)-------> d. <------(-8)------->
A
The expression (5-2)+(12/10-7/10) is an efficient way to perform subtraction for which of the following expressions? a. 3 7/10-1 2/10 b. 4 3/10-2 12/10 c. 5 7/10-8/10 d. 6 2/10- 2 7/10
D
A student has 6 different colors of shirts, 4 different styles of pants, and 2 different colors of sneakers. If the student is equally likely to select any clothing combination consisting of a single shirt, a pair of pants, and a pair of sneakers, then what is the probability that the student will choose a blue shirt, a pair of cargo pants, and gray sneakers? a. 1/48 b. 1/32 c. 1/12 d/ 1/13
A
A student uses snap cubes to measure the length of a piece of rope and then uses paper clips to measure the same piece of rope again. The teacher asks the student to determine whether it takes more snap cubes or more paper clips to measure the rope. Which measurement skill is the teacher most likely trying to address? a. comparing measurements using nonstandard units of length b. selecting appropriate nonstandard measurement units c. determining the attributes of an object that are measurable d. converting from one system of units to another
A
For which of the following processes will the standard deviation of any set of data remain unchanged? a. adding a constant amount to each data point b. multiplying each data point by the same constant c. removing the highest and lowest data points d. including an additional data point equal to the mean
A
For which of the following situations would collected data best be presented using a box plot? a. the distribution of salaries of electricians in a particular state b. the frequency with which people of various age classes go to the movies c. the change in annual sales per square foot for a sports equipment store over time d. the average distribution of time college faculty spend in activities such as research, teaching, and advising
A
Point P(a,b) on a coordinate place is reflected over the x-axis and its image is then reflected over the y-axis. Which of the following transformations applied to point P will have the same results for all possible values of a and b? a. a 180 rotation about the origin b. a reflection over the line y=x c. a vertical translation of a units and a horizontal translation of b units d. a dilation by a factor of b-a centered at the origin
A
The circumference of each tire on a vehicle is about 94 inches. Which of the following expressions can be used to calculate the number of miles this vehicle travels when the tires make 15,000 revolutions? a. 15,00 rev x 94 in/1 rev x 1 ft/ 12 in x 1 mile/ 5,280 ft b. 15,000 rev x 94 in/ 1 rev x 12 in/ 1 ft x 1 mile/ 5, 280 ft c. 15,000 rev x 1 rev/ 94 in x 1 ft/ 12in x 1 mile/ 5,280 ft d. 15,000 rev x 1 rev/ 94 in x 1 ft/ 12 in x 5,280/ 1 mile
A
The graph of which of the following functions will cross the x-axis in exactly two places? a. y=-2(x-5)^2+3 b. y=4(x+2)^2+0 c. y=-3(x+4)^2-2 d. y=5(x-3)^2+1
A
Use the diagram below to answer the question that follows. Trapezoid FGHJ has bases FJ and GH. What is the length of KJ? a. 18 b. 20 c. 28 d. 32
A
Use the tape diagram below to answer the question that follows. Which of the following problems can be modeled using this tape diagram? a. a 30-ounce container of juice is poured into three smaller containers in the ratio of 2:3:5. How much juice is in each of the smaller containers? b. a rectangular prisms height is 1 in greater than the width and 2 in greater than its length. What are the dimensions of the rectangle if the volume is 30 cubic inches? c. there are 30 students in a class. Half of them have a dog, one-third of them have a cat, and one fifth of them have a fish. What fraction on the class has all three types of pets? d. the ratio of hours it takes three different people to fabricate a part is 2:3:5/ If all three people fabricate a total of 30 of these parts, how many hours will it take?
A
When students learn to divide decimals they are taught to move the decimal point so that a problem like 24.37 + 2.1 becomes 243.7 + 21. which of the following properties of real numbers justifies this technique? a. the multiplicative identity property b. the closure property of multiplication c. the multiplicative property of reciprocals d. the associative property of multiplication
A
A forest ranger is monitoring the population of an invasive insect that has recently arrived from another continent. The ranger estimates that the population, P, will double every five years. If the current population in a forest is 2,000 insects, which of the following equations can be used to estimate the population in the forest n years from the present? a. P=10n+200 B. P=(2000)2^0.2n c. P=5n^2+2000 d. P=(2000)2^5n
B
Use the problem below to answer the question that follows Use base-ten blocks to model this problem 60-20=? To solve the problem shown above, a student places 6 ten-rods on a table and removes 2 of them. Then the student writes 60-20=4. Which of the following activities would best help the student understand the error in this solution? a. rewritting the problem vertically b. exchanging the ten-rods for single cubes c. reviewing one-digit number facts d. using a calculator to check the answer
B
Use the students work below to answer the question that follows. Problem: what number goes in the blank? 4 [3-(-2)]=__-8 Students response: 4[3-(-2)]=20-8=12 The response indicates that the students has a misconception regarding which of the following concepts? a. distributive property b. meaning of the equality symbol c. operating on signed numbers d. order of operations
B
Which of the following statements regarding the classification of polygons is true? a. all right triangles are also scalene triangles b. a square is both a rectangle and a rhombus c. each of the angles in an isosceles triangle is acute d. parallelograms are special kinds of trapezoids
B
*A car and a truck traveled towards the same bus station during the same time. Both vehicles traveled at a constant rate of speed. The car traveled at a faster speed than the truck, but started from a point further away from the bus station. Which of the following graphs best models the situation? (look at paper)
Correct Response A Objective 0010. The graph shows the relationship between time and the distance from the station. The car should start at a further distance away from the bus station so it's graph should have a higher y-intercept. The car should travel at a faster speed, so the slope of its line should be steeper. Both vehicles are traveling towards the bus station so both lines should decrease over time. The graph that correctly shows all this information is the graph in response A.
To find the height of the tree, a student placed a 3 foot stick 6 inches vertically into the ground and measured the shadow to be 1 foot long. The shadow of the tree measures 66 inches long. Which of the following is closest to the height of the tree? a. 14 feet b. 17 feet c. 19 feet d. 26 feet
Correct Response A Objective 0012. Drawing a quick diagram of the situation shows that two similar triangles are formed since they each share at least two angles of equal measure. Because the triangles are similar, corresponding sides are proportional and a proportion can be set up relating the length of the shadows and heights of the stick and the tree. The stick is 6 inches, or 0.5 foot, deep into the ground, so the exposed height of the stick is (3-0.5)feet=2.5 feet. The shadow length of the tree is 66 inches. Converting 66 inches to feet by dividing 12 inches/foot, the length of the tree shadow is 5.5 feet. The resulting proportion is written below. height of stick/shadow length of stick=height of tree/shadow length of tree Letting x= the height fo the tree and substituting the given numerical values into the proportion gives the following: 2.5feet/1foot=x feet/5.5feet x feet=2.5feetx5.5feet=13.75feet, which is the height of the tree. This answer is the closest to 14 feet.
*Which of the following number representations would be most appropriate for introducing concepts and principles associated with positive and negative integers? a. area model b. number line c. pattern blocks d. tape diagram
Correct Response B Objective 0008. A number line is an effective tool for teaching students about positive and negative numbers, since numbers greater than zero are located to the right of zero, and numbers less than zero are located to the left of zero. The number line also provides an excellent representation of the absolute value of a positive or negative integer along with operations involving adding and subtracting positive and negative integers.
*Students in a fifth grade class are beginning to learn about decimals. The teacher wants students to develop a conceptual understanding of the fractional equivalent of common decimal numbers involving the tenths place, an example of which is show below. 0.2=2/10=1/5 0.4=4/10=2/5 0.5=5/10=1/2 Which of the following strategies is likely to be most effective in helping students develop this understanding? a. using long division to convert the fractions to decimals b. representing the decimals using an area model based on a 1-by-10 grid c. making connections between the concept of a decimal and a percent d. setting up a proportion involving each fraction and its decimal equivalent
Correct Response B Objective 0008. Of the responses given, the most effective way for the students to develop a conceptual understanding of the equivalence between the decimals and the fractions would be to use a 1-by-10 grid to represent each decimal.
Use the diagram below to answer the question that follows. <-|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|-> 200 250 268 300 A teacher is working with students on using a number line to represent numbers. As part of the activity, the teacher emphasizes how the numbers relate to benchmarks, as shown in the diagram above. This activity will most likely support the student's development of which of the following number concepts? a. skip counting b. rounding numbers c. extending patterns d. solving proportions
Correct Response B Objective 0008. Placement of the number on a number line as shown clearly indicates how "close" a given number is to a benchmark. This representation makes it clear that 268 is closer to 300 than it is to 200, and closer to 250 than to 300 and will support the student's development of the concept of rounding.
A student was confused as to where to place the decimal point in the result of the product 24.5x0.02. Which of the following activities would best help the student understand decimal point placement when finding the product of two decimal numbers? a. Practicing counting decimal places in decimal numerals b. Converting decimals to fractions equivalents and finding the fraction products c. Finding decimal products on a calculator and recording the result d. Adding zeros to the decimal numerals so that they have the same number of decimal places
Correct Response B Objective 0009. By converting the decimals to their fraction equivalents, the decimal problem 24.5×0.02 becomes 245/10x 2/100. After multiplying fractions, the student will understand that the result must be a decimal that has the digits to the thousands place: 245/10x2/100=490/1000= 0.490.
A student consistently simplifies algebraic expressions as shown below. 2x+3x+5=20 10x=20 x=2 This work provides the most direct evidence that this student does not understand which of the following mathematical concepts? a. Commutative property of multiplication b. Distributive property of multiplication over addition c. Division as the inverse of multiplication d. Associative property of multiplication and addition
Correct Response B Objective 0010. In mathematics all operations must be justified using fundamental properties. There is no mathematical justification for adding 2x+ 3X +5 to get 10x, because the operation does not follow from the principles of arithmetic. To simplify 2x+ 3X apply the distributive property to factor the expression x(2+3)=x(5)=5x. Since the student simply added all of the terms on the left of the equation, one can conclude from the evidence that the student does not understand the distributive property.
Use the table below to answer the question that follows. Number of lbs. of potatoes | Number of lbs. of carrots x y 0 37 10 32 20 27 30 22 40 17 The table above shows the relationship between x, the number of pounds of potatoes and y, the number of pounds of carrots, a chef can purchase for $18.50 at a local vegetable market. Which of the following equation's best models the data in the table a. y=37-5x b. x+2y=74 c. x+10=y-5 d. 10x-5y=37
Correct Response B Objective 0010. The data shown in the table follow a linear pattern. The slope can be found using change in y/change in x. The slope for the table is 22-27/30-20=-5/10=-0.5. The Y intercept for the table is 37, as indicated by the data point (0,37). The equation that models the data table is y=-0.5x+37. Transforming this equation to standard form, first add 0.5X to both sides and next multiply the equation by 2: y=-0.5x+37->0.5x+y=37->2(0.5x+y=37->x+2y=74.
*A rectangular garden is to be enclosed with 48 feet of fencing. The ratio of length to width of the garden needs to be 5:3. What is the area of the garden if all the fencing must be used? a. 90 Square feet b. 135 Square feet c. 215 Square feet d. 540 Square feet
Correct Response B Objective 0011. The length and width of the garden can be represented by 5x and 3x respectively. The perimeter of the garden is 2(5x+3x)=2(8x)=16x. Solving the equation 16x=48 results in x=3. The length of the garden is 5(3)=15 and the width is 3(3)=9. To find the area, multiply length by width: 15x9=135 square feet.
*Teacher asks students to use pattern blocks to cover geometric designThis activity plays the foundation for a. Classifying two-dimensionalFigures based on properties b. decomposing polygons into similar shapes c. Identifying lines of symmetry and polygons d. Understanding connections between arithmetic and geometric properties
Correct Response B. Pattern blocks typically consist of an equilateral triangle, a rhombus, a hexagon, and other shapes. These blocks can be used to compose more complicated shapes and also to decompose polygons into similar shapes. Students' natural inclination is to make pictures and designs with pattern blocks helps to build an understanding of how more complex polygons can be decomposed into similar shapes with properties that are easier to analyze and quantify.
*As part of learning the standard multiplication algorithm for multidigit numbers, a student performs computations as shown below. 23=20+3 x16=10+6 ---------- 18 120 30 + 200 ---------- 368 One significant characteristic of this approach is that it directly illustrates properties of place value and: a. the associative law b. inverse operation c. the distributive law d. prime factorization
Correct Response C Objective 0008. The distributive law combines the operations of addition and multiplication and states that a(b+c)=ab+ac. This can also be written as (b+c)a=ac+ab by using the commutative property of addition and multiplication. In the example given, the problem uses the distributive law two times: (20+3)6=6x3+6x20=18+120 and (20+3)10=10x3+10x20. In addition to a solid understanding of place value, understanding the distributive law is key for understanding the standard multiplication algorithm.
*Use the diagram below to answer the question that follows. <---|-------A--|--B----|--C---> 0 1/2 1 A teacher poses the question "Which point on the number best represents 15/28?" A student responds, "I know that 1/2 of 28 is 14, so 15/28 is more than 1/2, and 28/28 would equal 1 whole, so it is less than 1 whole. It must be point B. "This student is most likely using which of the following strategies to solve the problem? a. converting the fraction to its decimal equivalent b. understanding that a larger denominator indicates smaller-sized pieces c. relating the fraction to a benchmark fraction d. rewriting a fraction in terms of a new denominator
Correct Response C Objective 0009. A benchmark fraction is a common fraction that can be used to gain an understanding of the magnitude (i.e., size) of other fractions. The numbers 0, 1/2, and 1 are often used as benchmark fractions to help students gain an understanding of the magnitude of other fractions. In this example, the student is comparing the given fraction to 1/2 and to 1, which are common benchmark fractions.
Use the values shown below to answer the question that follows. A=K/0.5 B=1 1/2 x K C=7/8 of K D=20% of K Given that K is a positive integer, which of the following lists orders the values above from least to greatest? a. A<B<D<C b. A<C<D<B c. D<C<B<A d. D<A<C<B
Correct Response C Objective 0009. The value of A is K/0.5=K/1/2=Kx2=2K. The values of B is 1 1/2xK=1.5xK=1.5K. The value of C is 7/8 of K=7/8xK=0.875xK=0.875K. The value of D is 20% of K=0.2xK=0.2K. Putting these in order from least to greatest, o.2K<0.875K<2K, so D<C<B<A.
Use the problem and student work shown below to answer the question that follows. Simplify: 2x+5=3(x-1) Student work: Step 1: 2x+5-3(x-1)=2x+5-3x+3 Step 2: 2x+5-3x=2x-3x+5+3 Step 3: 2x-3x+5+3=(2-3)x+5+3 Step 4: (2-3)x+5+3=-x+8 Which of the following properties justifies step 2 in the students work? a. associative property b. closure property c. commutative property d. distributive property
Correct Response C Objective 0010. In step 2, the student changed the order of the addends, applying the commutative property: 2x+5-3x+3=2x+5+(-3)+3=2x+(-3x)+5+3=2x-3x+5+3.
A circle graphs is created to represent a bag of colored gumballs that contains four-color groups as follows 24 of the gumballs are red 20% of the gumballs are blue 9/10 of the gumballs are green 1/4 of the gumballs are yellow What is the degree measure of the central angle for this sector of the circle that represents the red gumballs? a. 10° b. 24° c. 36° d. 160°
Correct Response C Objective 0011. The percent of the gumballs that are blue is 20%, the percent green is 9/20=45/100=45%, and the percent yellow is 1/4=25/100=25%. This leaves 10% for the percent that are red: 100-20-45-25 = 10. The sum of the central angles in the circle graph is 360°: 10% of 360 is 10/100×360 = 36.
Use the diagram below to answer the question that follows. (look at paper) The right circular cylinder above, which is closed at both ends, is 3/4 full and contains 144pie cubic centimeters of liquid. What is the surface area of the cylinder? a. 90pie b. 112pie c. 128pie d. 280pie
Correct Response C Objective 0011. The volume of a cylinder can be found by multiplying the area of the base by the height. Since the cylinder is 3/4 full, the equation 3/4(pier^2 x h)=144pie can be used to fund the radius of the base of the cylinder. Solve for r^2 as follows: 3/4(pier^2 x 12)=9pier^r=144pie results in r^2=16, so r=4. To find the surface area, find the circumference of the circular base and multiple that by the height then add on the area of the two circular bases. Cxh=pie(2r)x12=pie(2x4)x12=96pie and pier^2-pie(4)^2=16pie.
*A 12 foot ladder and an 8 foot ladder are leaning against the side of a house such that each of the ladders forms the same angle with the ground. The 12 foot ladder reaches 9 feet up the side of the house. Which of the following expressions can be used to find how high up the side of the house the 8 foot ladder reaches? a. 12÷(9x8) b. 9÷(12x8) c. (8x9)÷12 d. (9x12)÷8
Correct Response C. The triangles formed by the ladders, the side of the house, and the ground are similar triangles. The sides will be proportionate and can be related with the equation 9/12=X/8, where x represents how high up the side of the house the 8 foot ladder reaches. Solve the equation for X by multiplying both sides by 8.
Use the number line below to answer the question that follows. c a a a |--|-----|-----|-----| <-|-------------------|-> 0 b The diagram above models which of the following equations? a. cx3a=b b. b-a=3+c c. 3(a+c)=b d. b/a=3+c/a
Correct Response D 0010. The line diagram shows the segment b units long divided into 3 segments each a units along with a segment c units long left as the remainder. The result of b/a, or b divided into groups of a, can be modeled by this diagram. The result is 3 remainder c. Since each full group is made up of a segment of the length a units, the remainder c represents c/a or c divided by a of a group. The diagram shows the equation b/a=3+c/a.
Given the problem 3005/21 and the expression 3005=Ax100x21+Bx10x21+C+Dx1, where A, B, C, and D are all whole numbers less than 10, what is the value of B? a. 1 b. 2 c. 3 d. 4
Correct Response D Objective 0008. Performing the operations 3005/21 using long division results in 143 r 2. This means that 3002=21x(143)+2=21x(100+40+3)+2. The only whole-number value less than 10 that can be used for A is 1, because Ax100 must equal 100. Since Bx10+C has to sum to 43 and both B and C must also be whole number values less than 10, B has to be 4. Note that the standard long division algorithm is a method used to find these values: 3005=2100+840+63+2=1x100x21+4x10x21+3x21+2=1.
Use the information below to answer the question that follows There are six blocks on a table. A child counts each block while saying the numbers 1, 2, 3, 4, 5, 6. Which of the following provides the best evidence that the child has developed the concept of cardinality?
Correct Response D Objective 0008. The cardinality of a set corresponds to the number of elements in a set or collections. When counting the number of objects in a collection, the last number the child says indicates the number of elements in the set. A child who can state the number of elements in the set without having to recount them has developed the concept of cardinality.
Due to previous knowledge of fractions and the use of area models for representing their values, the students are likely to understand how the decimal notation relates to the concept of a fraction. While learning how to solve subtraction problems by regrouping, a third grade student does the problems as shown below. 23-16=13 34-28=14 In working with the student on solving the problem 26-19=?, it would be most important for the teacher to emphasize that the: a. student should borrow a 1 and change the 2 to a 1 b. numbers should be aligned in columns c. operation of subtraction is the inverse of addition d. value of 26 is equal to 1 ten and 16 ones
Correct Response D Objective 0008. The student is solving the problems by simply taking the absolute value of the difference of the digits in each place value. The student is having difficulty understanding place value. In order to learn to solve these problems by regrouping, it would be most appropriate for the student to use principles of place value to decompose 26 into 10+16-10-9=0+16-9=7.
Given that a and b are positive integers such that a>b, which of the following fraction comparisons must be true? a. a/b < b/a b. a/a+1 < b/b+1 c. b/a+b > a/a+b d. a-1/1 > b-1/b
Correct Response D Objective 0009. The fraction a-1/a is 1/a away from 1 whole. Likewise, the fraction b-1/b is 1/b away from 1 whole. Since a>b, the fraction 1/a<1/b, and the fraction that needs a smaller amount to make 1 whole is the larger fraction. a-1/a is the larger fraction.
*Use the diagram below to answer the question that follows/ Given that the shape formed by the pattern block above is one unit, what fraction of a unit is the shaded figure? a. 1/6 b. 3/6 c. 1/5 d/ 3/8
Correct Response D Objective 0009. The whole is represented by the trapezoid and 5 triangles. Three triangles can fill the trapezoid, so there are 3+5 equal triangular parts to make up the whole shape. The trapezoid represents 3 of the 8 parts, so it is 3/8 of a unit.
A teacher has students modeling the integers from 2 through 20 by creating rectangular arrays using square tiles. The students notice that some numbers can be modeled using different arrays; for example, 8 can be modeled with a 2 by 4 array and a 1 by 8 array. If only one array is possible for a given integer n, where n>1, then it must be true that n is: a. Odd b. Even c. Composite d. Prime
Correct Response D Objective 0010. If only one array is possible for a given integer, the number must have only two factors. Prime numbers have exactly 2 factors: the prime number itself and one.
*Use the diagram below to answer the question that follows. (look at paper) A television stations logo is made up of a circle inscribed in a square, as shown in the diagram above. What is the area of the shaded region of the logo if the circle circumferences 16 pie? a. 64-8pie b. 64-16pie c. 256-16pie d. 256-64pie
Correct Response D Objective 0011. The circumference of the circle, 16pie, is equal to pie times the diameter of the circle. The diameter of the circle is 16, as is the side fo the square. The radius of the circle is half the diameter, or 8. The area of the shaded region can be found by subtracting the area of the circle from the area of the square: 16^2-pie(8^2)=256-64pie.
A hotel charges $3325 per week for a room during peak season. Which of the following expressions can be used to determine this cost in dollars per minute? a. 7days/3325 dollars x 24hrs/1 day x 60min/1hr b. 3325dollars/7days x 24hrs/1day x 1hr/60min c. 7days/3325dollars x 1day/24hrs. x 60min./1hr. d. 3325 dollars/7days x 1 day/24hrs. x 1hr/60min.
Correct Response D Objective 0011. To find the number of dollars per minute, start with the information given for dollars per days. Then use conversion fractions until arriving at the desired unit, dollars per minute. The conversion fraction units should cancel out, until left with dollars for the numerator and minutes for the denominator. (see paper)
A kindergarten teacher asks a student to represent the number 11 with base ten blocks. The student first builds a ten-rod and then positions a single cube nearby. Afterward, the student holds up the single cube and says, "eleven". This response indicates that the student may have a misconception about which of the following pairs of counting concepts? a. numeral positions and place value b. one-to-one correspondence and base-ten numbers c. conservation of number and counting all d. ordinal numbers and cardinal numbers
D
A researcher analyzes Data from the survey of 500 randomly selected dentist and determines that 48% of all dentist are employed in group practices. This measurement is reported with a plus or minus 5% margin of error and a 95% confidence interval. Based on this information which of the following statements is accurate? a. At least 90% of the 500 dentists contacted responded to the survey b. The probability that 48% of dentists are in group practices is between 90% and 100% c. The sample 500 dentists surveyed constitutes between 43% and 53% of the population of dentist eligible to be surveyed d. There's a 95% probability that the actual percentage of dentists working in group practices is between 43% and 53%
D
Use the diagram below to answer the question that follows A student uses the lattice algorithm as shown in the diagram above to find the product of 361 and 75. What is the value represented by the circle 4 in the lattice? a. 4 b. 40 c. 400 d. 4,000
D
Use the diagram below to answer the question that follows The shaded region on the face of the square prism shown is the pattern for a curved pillar to be carved from the prism. Each of the congruent arcs is centered at a corner of the square. The square face has edged of 12 in and the prisms height is 24 in. Which of the following expressions represents the volume of the resulting pillar in cubic inches? a. 3,456 - 216pie b. 3,456-288pie c. 3,456-576pie d. 3,456-864pie
D
Which of th efollowing expressions is equivalent to 3 1/4 x 2 3/5? a. (3x2) + (1/4 x 3/5) b. (3x 3/5) + (1/4 x 2) c. (3x 1/4) + (3+2) + (2x 3/5) + (1/4 x 3/5) d/ (3x 3/5) + (3x2) + (2x 1/4) + (1/4 x 3/5)
D
A particular triathlon includes swimming, running, and biking. The distance participants run is 11 times the distance they swim. The distance they bike is 43 miles longer than the distance they run. The total of all three distances is 70 miles. If x represents the length of the swim, which of the following equations models this situation? a. 11x + 43=70 b. 12x+43=70 c. 22x+43=70 d. 23x+43=70
D
Use the box plot below to answer the question that follows. The box plot represents values, in thousands of dollars, of scholarships awarded to members of the incoming class at a particular college. Which of the following statements is true regarding the data displayed in the box plot? a. only one $18,000 scholarship was awarded b. the mean value of the scholarships is $13,000 c. more than half of the scholarships were less that $13,000 d. at most, 25% of the incoming students were awarded more than $15,000
D
