MTTC Mathematics Test Questions

A fifth-grade teacher is writing an article about mathematics activities in the classroom. The article describes how students used manipulatives to solve measurement problems. The teacher included trademark symbols with the name of the manipulatives. The teacher also included photographs of students working with the manipulatives. None of the students in the photographs were identified by name. To ensure compliance with ethical guidelines, the teacher should take which of the following actions prior to posting the article on the Internet? A. providing links to the manufacturers of the manipulatives that have trademarked names B. providing a disclaimer stating that the school district does not endorse the pedagogical methods used C. explicitly identifying the manipulatives being used in a caption below each photograph D. obtaining permission from parents/guardians before posting pictures of the students

D

According to the order of operations, what could be the first step in simplifying the expression below? 4/3 [6^2 - 3^2) + 9 - 6] A. (8^2 - 4^2) + 12 -8 B. 4/3 [(3^2) + 9 -6] C. 4/3 [6^2 - 3^2) - 3] D. 4/3 [(36-9) + 9 - 6]

D

What is the measure of angle x in the diagram below? "The diagram shows a triangle with two equal sides and a shorter base. The angle between the long sides is dimensioned as 40 degrees. The baseline is extended beyond the long sides of the triangle, and the exterior angle from one long side to the baseline extension is labeled x." A. 65°degrees B. 70°degrees C. 110°degrees D. 115°

C

Which of the following problem-solving strategies would be most effective and appropriate to use in solving the problem below? A company puts a free toy in each box of cereal and states that there is a one in four chance of getting the astronaut toy with each purchase. On average, how many boxes will need to be purchased to get an astronaut? A.expressing numbers in base four B. working backwards to find an equation C. simulating the situation using a random process D. graphing points on a coordinate system to find a pattern

C

If the pattern below continues, what will be the sixth term in the sequence? 1/3, 5/3, 13/3, 29/3, ___, ? A. 58 over 3 B. 61 over 3 C. 122 over 3 D. 125 over 3

D

In which of the following situations would a box-and-whiskers graph be the most appropriate visual representation to use to display data? A. An homeowner wants to compare the amount of money spent on individual household expenses in a particular month to the total monthly expenses. B. A business owner wants to see trends in sales data over a 24-month period. C. A bookstore employee wants to compare the numbers of each type of book sold in the previous two months. D. An environmentalist wants display several statistics to summarize a large number of pH readings from a stream.

D

The center of the circle in the diagram below is at (-negative1, 1). "The circle is plotted on a Cartesian graph with the axes labeled at negative 5 and 5. The edges of the circle extend horizontally from negative 4 to 2 and vertically from negative 2 to 4." What is the circumference of the circle? A.B3πpi B. 4πpi C. 5πpi D. 6π

D

Which of the following activities is most effective for creating a foundation for understanding the concept of multiplication? A. practicing basic addition facts with numbers 1 through 10 B. using base-ten blocks to model two-digit numbers C. modeling equality of numbers with a balance scale D. skip counting by different intervals on a number line

D

An individual wants to purchase an air conditioner and can choose between two different options. Both options have an original price of $200. The first option offers 30% off the original price and charges $20 for shipping. The second option offers 15% off the original price and shipping is free. What is the difference in savings between the two options? A. $5 B. $10 C. $15 D. $20

B

A fourth-grade teacher is planning a unit in which students will use a computer application to create their own tessellations. The teacher would like to develop a series of related activities and assessments to help develop students' mathematical reasoning skills related to the use of the application. Which of the following topics would be most appropriate for the additional materials to address? A. reflections, rotations, and translations B. area of composite figures C. similarity and proportional reasoning D. graphs of simple equations

A

In solving the division problem 2.4 square rooted by 47, a student transforms the problem to 24 square rooted by 470. This operation is equivalent to which of the following? A. 47/2.4 x 10/10 B. (47 / 10) / 2.4 C. 2.4/47 X 10/10 D. (47 / 2.4) / 10

A

Students in a fifth-grade class draw a 1 unit by 1 unit square on a piece of paper, cut the square out, and use a scale to find its mass. The students then draw various irregular shapes on the same type of paper, cut them out, and find their masses, and compare them with the mass of the square. This activity is an example of using: A. indirect measurement to determine area. B. direct measurement to determine area. C. indirect measurement to determine perimeter. D. direct measurement to determine perimeter.

A

The use of the balance and shapes shown in the diagram below would be most appropriate in promoting students' skills in which of the following areas? "Balance one with 5 cubes (different shapes) one with 7 cubes (same shape)" A. equations in two variables B. volumes of irregular solids C. decimals and percentages D. negative and positive integers

A

Two narrow strips of paper, one on top of the other, are aligned parallel to the edge of a ruler that is marked in inches. The top strip of paper extends from 0 to 4 and 3 eighths. The bottom strip of paper extends from 1 and 7 eighths to three and 3 fourths. In the diagram, a ruler is used to measure two strips of paper in inches. How much longer is the larger strip of paper than the smaller one? A.2 and 1 half inches B. 2 and 5 eigths inches C. 2 and 3 fourths inches D. 2 and 7 eigths inches

A

Which of the following functions is represented by the graph below? "A single data line is plotted on a Cartesian graph with the axes labeled from negative 6 to 6 in intervals of 1. The data line is a smooth, narrow U shape pointing upward and centered on the y axis. It passes through the following points: (negative 3, negative 6), (negative 2, negative 1), (negative 1, 2), (0, 3), (1, 2), (2, negative 1), and (3, negative 6)." A. y = −negativex2squared + 3 B. y = x2squared −minus 3 C. y = −negative(x + 3)2squared D. y = (x + 3)2

A

Which of the following problems can be modeled using the fraction strips shown below? *PICTURE IS IN FRACTION STRIPS 2/3 1/4 1/12 A. A farmer plants 2 thirds of a field in the morning and 1 fourth of the same field in the evening. How much of the field did the farmer plant that day? B. Dario had some cookies and gave 1 cookie away. Now Dario has twice as many cookies as Shawn. If Shawn has 3 cookies, how many cookies did Dario start with? C. A painter uses gallon of paint to paint one wall in a large room. How much paint will be needed to paint 4 walls? D. A teacher has 2 gallons of juice. If each cup holds 4 ounces, how many cups of juice can the teacher pour?

A

Given the two equations below, what is the value of b in terms of c? 2a = 2b + 6 a = 3c A. b = 2c −minus 6 B. b = 3c −minus 3 C. b = 6c + 6 D. b = 3c + 6

B

If the least common denominator is used to perform the operation , what will be the value of the numerator for the equivalent representation of ? A. 2a B. 5a C. 6a D. 15a

B

A teacher would like to have an activity in which students can compare a theoretical probability with an experimental probability. Answering which of the following questions would be most appropriate for this activity? A. What is the probability that a student in the school selected at random will be wearing a red shirt? B. What is the probability that a six-sided number cube will come up 5 when rolled? C. What is the probability of correctly guessing a number between 1 and 1000? D. What is the probability that the third-grade class will have 100% attendance on Mondays?

B

A table has a rectangular center portion and two semicircular ends that can be folded out to increase its size, as shown in the diagram below. "The diagram shows a rectangle with a semicircle at each end to form a capsule shape. Each end of the rectangle is shown as a dashed line that corresponds to the diameter of the corresponding semicircle. The long side of the rectangle is dimensioned as 5 feet." When the ends are folded down, the rectangular portion has a length of 5 feet and an area of 30 square feet. Which of the following expressions represents the area of the table when the semicircular ends are folded out? A. 30 + 6πpi square feet B. 30 + 9πpi square feet C. 36πpi square feet D. 39πpi square feet

B

"There is a diagram of four double cones. Each double cone is composed of two cones on a common vertical axis, with their tips touching. Each double cone is intersected by a shaded plane. The hidden edges of the cones, the planes, and their intersections are shown as dashed lines. The first double cone is intersected by the plane horizontally through the upper cone. The second double cone is intersected by the plane through the upper cone at a shallower angle than the side of the cone, such that the resulting intersection forms a closed shape. The third double cone is intersected by the plane through the lower cone at a steeper angle than the side of the cone, such that the resulting intersection forms an open shape. The fourth double cone is intersected vertically by the plane through both cones at a distance from the vertical axis of the cones." The diagram shows four double cones, each intersected by a plane. In which figure is the resulting cross section an ellipse? A. Figure A B. Figure B C. Figure C D. Figure D

B

A person buys an item that costs $3.60 and pays for it with a $5.00 bill. The amount of change, in dollars, represents a number from which of the following sets? A. natural numbers B. rational numbers C. whole numbers D. nonnegative integers

B

Mia and Liam live in the same apartment building and are planning a trip to the lake in separate cars. The map below shows two different routes to the lake. "The map shows the lake, Mia and Liam's apartment building, and Jason's house. The distance from Mia and Liam's apartment building to the lake is marked as 15 miles. The distance from Mia and Liam's apartment building to Jason's house is marked as 12 miles. The distance from Jason's house to the lake is marked as 10 miles." Liam travels at 30 miles per hour to Jason's house, stops for 1 minute to pick up Jason, and drives to the lake at the same speed. Mia travels the more direct route at an average speed of 45 miles per hour. How much longer will it take Liam to get to the lake than Mia? A.15 minutes B. 25 minutes C. 30 minutes D. 45 minutes

B

The diagram below shows two triangles with congruent corresponding parts. "The diagram shows two triangles rotated with respect to each other such that the first one points down and the other points up. The vertices of the first triangle are labeled A, B, and C. The vertices of the second triangle are labeled D, E, and F. Lines A C and D F are marked with a single slash, and lines B C and E F are marked with a double slash." What additional information could be used to show that the two triangles are congruent? <=angle A. m<A = m<D B. AB=DE C. CB/FE=AC/DF D. AC/DF=AB/DF

B

Twenty-seven cubic centimeters is equivalent to how many liters? A.0.03 liters B. 0.027 liters C. 0.003 liters D. 0.0027 liters

B

Use the problem and solution below to answer the question that follows. Problem: Show that x + x = 2x. Solution: Use the distributive property to factor an x from the expression shown below. x + x = xtimes(1 + 1) We know that 1 + 1 = 2. Therefore, x + x = xtimes(1 + 1) = xtimes(2), which is the same as 2x by the commutative property. The solution provided can best be described as: A. an axiom. B. a proof. C. a postulate. D. a definition.

B

A box of cookies contains 8 chocolate chip cookies, 12 peanut butter cookies, and 4 oatmeal cookies. A child randomly selects 2 cookies, one at a time. Which of the following expressions represents the probability that both cookies will be peanut butter? A. 12 over 24 plus 12 over 23 B. 1 over 12 plus 1 over 11 C. 12 over 24 times 11 over 23 D. 1 over 12 times 1 over 11

C

A small company wants to produce toy robots. The company determines that they will have an initial investment of $10,000 for equipment and tools and that each robot will cost an additional $15 to make. If n equals the number of toy robots made, which of the following functions gives the total cost, C(n), of producing n robots? A. C(n) = 10,000n + 15n B. C(n) = 10,000n + 15 C. C(n) = 10,000 + 15n D. C(n) = 10,000 + 15 + n

C

A student's work sample is shown below. 2/3 + 2 3/4 = 2/3 + 3/4 +2 = 2/3 * 4/4 + 3/4 * 3/3 = 8/12 + 9/12 = 17/12 + 2 = 1 17/12 +2 = 1 5/12 + 2 = 3 5/12 Which of the following statements best evaluates the student's work? A. The student found the common denominator incorrectly. B. The student converted the mixed numeral incorrectly. C. The student used the equal sign incorrectly. D. The student used the order of operations incorrectly.

C

A teacher shows students how they can improve their computational fluency by providing them with frequent opportunities to use mental math to solve problems such as the ones shown below. 2 + 8 + 7 + 3 = ? 9 + 4 + 3 + 3 = ? 3 + 7 + 2 + 3 = ? Which of the following best describes the teacher's approach? A. finding sums by working from left to right B. using a combination of addition and subtraction together C. finding number pairs that sum to easily recognizable numbers D. converting addition problems into multiplication problems

C

In which of the following pairs are the numbers equivalent? A. 106.0 ×times 104to the power of 4 and 1,060.0 B. 8.63 ×times 10-5to the power of negative 5 and 0.00863 C. 5.72 ×times 105to the power of 5 and 572,000.0 D. 0.3374 ×times 10-4to the power of negative 4 and 0.0003374

C

Integers are a subset of which of the following sets of numbers? A. negative numbers B. natural numbers C. rational numbers D. irrational numbers

C

The chart shows the funds raised by two charities during the first three months of the year. "The title of the chart is Funds Raised by Two Charities over a Three-Month Period. The vertical axis is labeled Funds Raised, in thousands of dollars, and has values marked from 0 to 35 in increments of 5. The horizontal axis is labeled Month, and has labels for January, February, and March. Both data lines are straight. The data line for Charity A has points at 5 for January, 15 for February, and 25 for March. The data line for Charity B has points at 20 for January, 25 for February, and 30 for March." If the trend continues at the same rate for both charities, what will be the mean value of the funds raised by the two charities for the month of May? A. $32,500 B. $40,000 C. $42,500 D. $50,000

C