EC-6 Core Mathematics Rep Exam Questions Study Guide

Michael is standing in a park that can be represented by the point (4, 6) on a coordinate plane. He walked the distance that is equivalent to three units to the right and two units down on the coordinate plane and arrives at a pet shop. Which ordered pair represents the location of the pet shop on the coordinate plane?

(7,4)

Which TWO of the following numbers are neither prime nor composite?

0,1

Malik wants to find 25 percent of 84 by doing a mental calculation. Which of the following numbers is best for Malik to use to multiply by 84 to find 25 percent of 84?

1/4

A teacher writes the problem shown above on the white board for students to solve and tells them to combine like terms as the first step in solving the equation. Which of the following equations written by a student best demonstrates an understanding of combining like terms in the first step? 7x-5+4x-3=14

11x-8=14

In rectangle ABCD shown below, the length of BD is 10x+8 and the length of AC is 9x+20. What is the value of x?

12

Joseph lays out 8 number cards on his desk as shown below. He arranges them to create the smallest possible 8-digit number with the 2 in the thousands place. What number did he create?

13,452,678

Mr. Daniels displays the base ten blocks, shown below, and asks students to suggest an algorithm that the blocks could represent. Which of the following students' responses best answers the teacher's question?

140+40

Which of the following is a correct factor tree for finding a prime factorization of the given number?

2 <5,4 <2,2

Questions 31 and 32 refer to the task below A class is instructed to get into groups, spin a spinner 100 times, and record the number that the arrow lands on each time. The spinner is partitioned into five sectors labeled with the numbers 1 through 5 as shown. The spinner is equally likely to land in each numbered sector. If there are 10 groups of students participating in the spinner activity, which of the following is most likely the total number of times the spinner will land on the number 4 sector?

204

Which of the following shows a correct computation for the answer to the problem shown below? David always works half days when he goes into work. If he goes into work 21 days, how many full days of work does he complete?

21 x 1/2

Water starts running into an empty 25-gallon tub at the rate of 2 quarts per 30 seconds. How many minutes will it take to completely fill the tub with water? (1 gallon = 4 quarts)

25

What is the perimeter, in feet, of a rectangular room that has a length of 25 feet and a width of 16 feet?

82

A first-grade teacher asks each of the students in the class to say which one of three popular foods is his or her favorite. Which of the following visual representations of the collected data is most appropriate for the students to construct to compare the numbers of students who chose of three foods?

A pictograph

Which of the following activities will best allow a teacher to demonstrate socioeconomic diversity for students in a math class?

Discussing in groups how to plan budgets for various income amounts

A teacher of a linguistically diverse class is beginning a mathematics unit that includes some new vocabulary words. Which of the following strategies is best for the teacher to use to reach all the students in the class?

Explaining each new term and providing examples of how each new term is used.

Which of the following activities best helps students distinguish between fixed and variable expenses?

Categorizing the costs of operating a lemonade stand into expenses that depend on sales volume and those that do not

Both Task A and Task B shown below meet a teacher's goal that students explore the relationship between the perimeter and area of rectangles. For which of the following additional goals is Task A more appropriate than Task B? Task A: You have 36 meters of fence to build a rectangular pen for a pet dog. What pen could you build with the fence that gives the dog the greatest area to play? Task B: The length and width of a rectangle add up to 18 inches. What is the greatest area the rectangle can have?

Connecting math to the real world

Ms. Wingate is teaching a lesson on patterns. She provides her students with cubes of various colors and instructs them to create a pattern on their own. After the students each create a pattern, they will take turns presenting and explaining their patterns. Which of the following theories of learning best matches the activity Ms. Wingate is using with her students?

Constructivist learning theory

A teacher's goal in a math lesson is to have the students use calculators to develop conceptual understanding. Which of the following activities best addresses the goal?

Having students type 4+4+4+4+4+4 and 4x6 into their calculators, then determine why the values are equal

Which of the following cultures is credited with developing the base ten decimal systems, which is based on the concept of place value?

Hindu-Arabic

The table shown below give the number of sweaters knitted and sold by four people. If the number of sweaters sold by Jocelyn, Ruben, Kody, and Austin is directly proportional to the number of sweaters by each knitted, who is most likely to sell a sweater if he or she knits another sweater?

Kody

Based on the figure below, which of the following statements is true?

Lines CD and EF are parallel

A teacher is planning to demonstrate the concept of multiplication to students for the first time. Which of the following is best for the teacher to do when first introducing the concept?

Solving a multiplication problem using some type of concrete manipulative

During a unit on finances, a teacher begins an activity by assigning a job and a salary to each student in the class. Which of the following real-life simulations is best for the teacher to add to the activity to help students learn one way they can use their earnings to gain extra money?

Students can choose to purchase certificates of deposit

Ms. Greko observed students in her class as they completed multiplication exercises. Many students arrived at the same incorrect answer when multiplying 24 and 23, as shown in the student work below. Which of the following is most likely the error made by the students?

The 10 composed from the multiplication of 3 ones and 4 ones was counted as both a ten and a hundred.

Which of the following is an example of a clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill stated below?

The learner will understand and explain which of two fractions is greater by using concrete objects

Ms. Anderson gives students the table shown below. She then takes a piece of yarn, folds it in half, and cuts across the piece of yarn. She then makes a second cut across the piece of yarn and demonstrates how many pieces of yarn there are after each cut. She asks students to fill in the rest of the table and then write a summary of how the number of pieces, y, is related to the number of cuts, x. Which of the following best demonstrates an understanding of how x and y are related?

y= 2x+1

The table above shows a linear relationship between the variables x and y. Which of the following equations correctly defines the relationship?

y=2x+5

Which of the following linear equations is written in slope-intercept form?

y=mx+b

During the week, the teacher has students participate in similar activities. At the end of the week, students are asked to research careers in which the mathematical ideas explored during the week could be used. Which of the following scenarios best demonstrates how the math concept explored during the week is applied in a career context?

An actuary working for an insurance company calculating the chance that a customer will have a collision

A class is learning about situations that involve ratios and proportions. The teacher tells the class that the school has between 300 and 400 students, and between 18 percent and 21 percent of the students have blue eyes. Which of the following is the most reasonable estimate of the number of students in the school who have blue eyes?

70

What is the median of the median of the data shown below?

61

Molly went back-to-school shopping and purchased 6 different shirts, 4 different pairs of pants, and 2 different skirts. If an outfit consists of one shirt and either one pair of pants or one skirt, how many different outfits can Molly choose from to wear to school?

36

Joey and Jenny are playing a game in which they take turns choosing from a set of letter tiles that are face down on a table. The set includes 16 consonant tiles and 5 vowel tiles. Jenny chooses a tile first, and it is a vowel. She keeps the tile for her next turn and does not return it to the set of letters. If Joey chooses a tile second, what is the probability that he will select a vowel tile?

4/20

Jennifer sold cookies for x dollars a box and earned a total of $424. Which of the following expressions represents the number of boxes Jennifer sold?

424/x

In which of the following scenarios is the use of estimation most appropriate?

A meteorologist is talking about the high temperature predicted for tomorrow.

After completing a unit on graphic data, students are given the table shown below and asked to determine what type of graph is most appropriate for displaying the data. Which of the following graph types is most appropriate for displaying the data in the table?

Bar graph - Unsure of this answer.

Mr. Bailey provides his students with graph paper that shows an xy-plane with the axes labeled. He asks the students to draw a 4-sided shape of their choice on the xy-plane. He then instructs his students to graph the shape that is found by adding 20 to all of the x-coordinates and 15 to all the y-coordinates of each point on the original 4-sided shape. Which of the following graph transformations is Mr. Bailey most likely working on with his students?

Translation

Mr. Tesh gave a test on basic multiplication following an introductory unit. After grading the test, he noticed that a number of students struggled with the material. Which of the following strategies would be best to improve to the students' understanding of the concept of multiplication?

Using manipulatives to demonstrate that the multiplication of two numbers such as 2 and 3 is the repeated addition of 2 three times.