Certify Teacher EC-6 (391) Mathematics (902) Practice Test

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• Add 3 1/4 and 2 2/3. What is the sum in mixed number form?
• What is the slope of the line through points (0, 0) and (4, 6)?
• A line has slope 3 and passes through (2,-1). What is its equation in slope-intercept form?
• Which property defines a rectangle?
• In an early childhood lesson series on addition, after modeling with cubes of two colors, what should be the next step for the students?
• If a student earns 90% on a 100-point test, how many points did they earn?
• What does an amortization schedule illustrate?
• Two independent events have probabilities 1/3 and 1/4. What is the probability that both occur?
• An ancient papyrus problem describes dividing 100 loaves among 10 men, with three men receiving double portions. What mathematical development does this illustrate?
• The sum of interior angles of a quadrilateral is?
• Expand (x + 4)(x + 3).
• Tanya is helping a third‑grade student check for mathematical reasonableness. If the student calculated 8 + 7 = 21, which estimation technique could help?
• What is the distance between the points (0,0) and (3,4)?
• A line with slope -2 passes through (4,6). What is its equation in slope-intercept form?
• What is the formula for the area of a circle with radius r?
• A data set contains 3, 7, 7, 2, 9. Compute the mean, median, and mode.
• If 6 red and 4 green marbles are in a bag and you draw two marbles without replacement, what is the probability both are red?
• With three coins dropped on a board offering scores of 0, 1, 3, and 5, what is the maximum possible score?
• An algebra tiles activity forms a rectangle; which equation represents the area and its factorization?
• What is the hypotenuse of a right triangle with legs 5 and 12?
• The mode of the dataset {1,1,2,3,3,3,4} is what?
• If a probability is 0.25, what is the fraction form?
• Given a gross monthly income of $5150 and monthly debt payments totaling $1035, the bank will approve a loan payment up to 24% of the adjusted income. What is the maximum monthly loan payment?
• Compute 1^3 × 1 + 2^3 × 2.
• What is the median of the numbers 2, 8, 10, 14?
• If a rectangle has base B and height H and a triangle sits on the rectangle with its vertex touching the opposite side, what is the area of the triangle in terms of B and H?
• The area of a parallelogram with base 7 and height 4 is what?
• What is the area of a triangle with base 6 cm and height 4 cm?
• A net consisting of a hexagonal base and six congruent triangular faces meeting at a common apex represents which solid?
• If radius r is 1, the area of the circle is:
• Solve for x: 4x - 7 = 2x + 9.
• What term describes the portion of monthly income used to cover debt payments when evaluating loan eligibility?
• Which is larger: 4/5 or 7/9?
• Simplify the fraction 18/42.
• If a line is perpendicular to a line with slope -2, what is the slope of the perpendicular line?
• In a triangle, an exterior angle measures 145 degrees and one of the remote interior angles measures 93 degrees. What is the measure of the other remote interior angle?
• Troy mows every 3 days and Walter mows every 5 days. How many days will pass before they both mow on the same day?
• What percent is represented by 0.14 as a percent?
• If 1 block equals 1 step, 3 blocks equals 2 steps, 6 blocks equals 3 steps, what is the total number of cubic blocks needed to build 6 steps?
• Subtract 7 2/5 minus 3 3/7. What is the result in mixed number form?
• A rectangle has length 8 cm and width w. Which function expresses its area A(w)?
• How many terms are in the bottom layer expression 1+3+7+15+31+63+7?
• Evaluate the fraction 24/32 and choose its lowest terms.
• A classroom buys 3 packs of pencils with 12 pencils per pack. How many pencils?
• Convert the fraction 3/4 to a percent.
• Around a point, four angles sum to 360 degrees. If three angles measure 125°, 90°, and 80°, what is the measure of the fourth angle?
• What is the area of a rectangle that measures 8 cm by 3.5 cm?
• Expand the product (x+5)(x+3).
• If a circle's diameter is d, what is its radius?
• The slope of the line through points (2, 3) and (6, -1) is what?
• What is the probability that a couple's first or second child will be a boy?
• Calculate the total amount paid over the life of a loan if the monthly payment is $583.56 and there are 360 payments.
• From the 400-student data, what is the probability that the gift occasion is Christmas?
• The range of the data set {5, 5, 7, 9, 12} is?
• Compute the distance between (1,2) and (4,6). Which value is correct?
• What is the sum of the interior angles of any triangle?
• Find the sum of the arithmetic sequence with first term 2, common difference 3, and 6 terms.
• If a data set has frequencies 5, 7, and 3 for categories A, B, and C, what is the relative frequency of B?
• If triangle ABC is similar to triangle DEF, with AB corresponding to DE and AC corresponding to DF. Given AC = 10, DF = 5, and DE = 4, what is AB?
• If A/B = 5 and B/C = 2, what is the value of A/(B+C)?
• Which approach best assists with planning, delivering, and reevaluating instruction to ensure that every student learns sound and significant mathematics and develops a positive disposition toward mathematics?
• Compute 5/6 ÷ 1/3.
• If you have 5 apples and you eat 2, what fraction of apples is left?
• In a histogram, what type of data is being displayed?
• In a stem-and-leaf plot with a stem of 4 and leaves 2 and 7, which values are represented?
• The slope of the line through (0,0) and (4,2) is what?
• Solve for x: 2x + 5 = 17.
• A price increases from $60 to $66. What is the percent increase?
• The class placed numbers 2.03, 8√2, -3.5, 9/2, π, and 2.1 in order from smallest to largest. This exercise primarily assesses which number concept?
• What is a key property of similar triangles?
• Using the distributive property, simplify 3(4 + x).
• A worker earns hourly pay at rate r for h hours and receives a fixed weekly gas allowance of 50 dollars. Which expression represents gross weekly pay?
• The area of a trapezoid with bases 8 and 3 and height 4 is what?
• The volume of a cube with side length 3 is what?
• In a class of 24 students with the ratio of boys to girls 3:5, how many girls are there?
• Which fraction is in lowest terms?
• What is the formula for the volume of a rectangular prism in terms of length, width, and height?
• For an amortization project, what is the best approach to assigning a purchase?
• Why is it important for students to be exposed early to diversity in acquiring mathematical concepts?
• Which expression correctly computes the area of a trapezoid with bases b1 and b2 and height h?
• Convert 2 feet to inches.
• The probability of drawing a red marble from a bag with 4 red and 2 blue marbles is what?
• What is the volume of a rectangular prism with length 4 cm, width 3 cm, height 5 cm?
• What is 0.75 minus 0.25?
• Which assessment method would be least appropriate for identifying the concepts students find most difficult in a new lesson?
• Estimate 39 × 42 by rounding to the nearest ten.
• What is the sum of 4 and 16?
• If a line is horizontal, what is the slope of a line perpendicular to it?
• Which formula gives the lateral surface area of a right circular cylinder (not including the top and bottom)?
• Alex claims it is possible to obtain any score from 0 to 15 by dropping exactly three coins on a board with scores 0, 1, 3, and 5. Which conclusion follows?
• A velocity vs. time graph for a runner is measured at 2-second intervals. To estimate the total distance from 0 to 12 seconds, which approach should be used?
• If a rectangle has length 8 cm and width w, what is A(3)?
• Sam tosses four coins. What is the probability that all four land on heads?
• Solve for x: 3x = 9.
• Why did the teacher choose tasks with real-world context that require explanations and multiple steps but no manipulatives?
• Reduce the fraction 18/24 to lowest terms.
• Which strategy best demonstrates applying a math concept to another subject?
• The least common multiple of 6 and 8 is?
• Which polyhedron has all square faces?
• What is the least common multiple of 3 and 5?
• Subtract 5 1/4 minus 2 3/8. What is the result in mixed number form?
• What is the area formula for a trapezoid with bases b1 and b2 and height h?
• A ratio of apples to oranges is 3:5. If there are 40 fruits total, how many apples?
• Which linear inequality matches a graph with a boundary at x = 5 and shading to the left?
• In a rectangle, which statement about the diagonals is true?
• The sum of interior angles of a triangle is 180 degrees. If a triangle has angles 50° and 60°, what is the third angle?
• Is this graph misleading? A survey shows Christmas 45%, Birthday 10%, Anniversary 35%, Valentine’s Day 15%, Mother’s Day 15%. The sum of the percentages appears to exceed 100%.
• For a triangle with base b and height h, which expression gives the area?
• Add 2/3 and 1/4. What is the sum?
• What is the probability that both a couple's first two children will be boys?
• Placing similar shapes in columns is foundational for which data representation?
• What is the area expression for a rectangle with dimensions 2 and x+2?
• If A = 5B and B = 2C, which expression represents A in terms of C?
• Which description correctly characterizes the real-world context tasks used in the classroom as described in the material?
• What is the median of the following grades: 45, 85, 95, 83, 82, 76, 76, 92?
• Convert 3 2/5 to an improper fraction.
• If a distribution has mean 50 and standard deviation 5, approximately what values lie within one standard deviation of the mean?
• Which expression represents the sum of interior angles of a five-sided polygon?
• Find the sum of the arithmetic sequence with first term 7, common difference 4, and 5 terms.
• Convert 1.8 square kilometers to square miles using 1 square mile = 2.6 square kilometers. Which value is closest?
• Solve using a tape diagram: 3/4 + 1/8.
• What is the distance between (0,0) and (3,4)?
• A triangle has sides 5, 5, and 6. What type of triangle is it?
• In the 500-man survey, what percentage chose Christmas?
• What is the probability of getting at least two tails in tossing three coins?
• In a hexagonal pyramid, how many lateral triangular faces are there?
• The reflection of (3, 2) across the y-axis is which point?
• Complete the pattern: 3, 6, 12, 24, what is the next term?
• What is 6.75 minus 2.4?
• Which is larger: 2/3 or 3/5?
• Convert 250 centimeters to meters.
• The median of {3,5,1,9,7} is what number?
• The range of {3,7,2,10} is what?
• Compare 3/5 and 2/3; which is larger?
• If P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color and not haircut)?
• What is the product of 3/4 and 2/3?
• From the 400-student gift survey, what is the probability of not receiving a Mother’s Day gift?
• What is the value of 2(x+2) when x = 3?
• If the mean is 60 and the standard deviation is 4, between which values do about one standard deviation lie?
• What is the name of a polygon with eight sides?
• What is the mean of the numbers 2, 4, 6, 8?
• The mean of the numbers 10, 20, 30, 40 is what?
• What is the area of a triangle with base b and height h?
• What is the value of the digit 7 in the number 4,276,511?
• The difficulty with expressions like 12 + (7 × 2) - 2(5 + 3) is most likely due to misunderstanding of which concept?
• Which option represents a percent value?
• The probability of rolling an even number on a fair die is what?
• If a line has slope m = 0, what is its orientation?
• Simplify the expression 2a - 3a + 4.
• A class average increases from 78 to 84 after adding scores. What happened to the mean?
• Which number is prime between 10 and 20?
• What is the mean of the numbers 1, 3, 5, 7, 9?
• Which x-value satisfies the inequality x < 5?
• Convert 0.625 to a fraction.
• If a, b, c are whole numbers greater than zero with a < b < c, which of the following numbers is greatest?
• Solve for x in the equation 3x + 5 = 20.
• Express 7/12 as a decimal rounded to two decimal places.
• Convert 3 1/4 to an improper fraction.
• What is the result of evaluating the expression -7 minus 12?
• Around a point, four angles sum to 360 degrees. If the three angles are 120°, 60°, and 60°, what is the measure of the fourth angle?
• Which statement supports Herzig’s claim about the twenty‑first century math workforce?
• Complete the pattern: 2, 4, 8, 16, what is the next term?
• For the line with slope -2 passing through (4,6), what is the y-intercept?
• In a triangle, if two angles are 50° and 60°, what is the third angle?
• What is the perimeter of a rectangle measuring 5 cm by 7 cm?
• A triangle has base 10 cm and height 6 cm. What is its area?
• Which of the following is an integer?
• If a quantity decreases from 72 to 54, what is the percent decrease?
• Calculate 5/8 of 40.
• Convert 0.75 to a fraction in lowest terms.
• If a rectangle has length 6 and width 7, what is its area?
• If 3/4 of a rectangle is shaded, what fraction of the rectangle is shaded?
• Which activity would be appropriate for integrating multiplication into a second-grade science curriculum?
• Which expression is equivalent to 4(2 + y)?
• If the ratio of boys to girls is 3:5 and there are 24 students total, how many boys are there?
• What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?
• What is 20% of 150?
• Convert 1500 mL to liters.
• In a right triangle with legs 3 and 4, what is the length of the hypotenuse?
• Which point is the image of (2, -7) after reflecting across the y-axis?
• Using base-ten blocks to model a subtraction with regrouping, which operation is being illustrated?
• Convert 2.5 to a fraction.
• A shirt costs a compatible price of 50 dollars and sales tax is 8.25%. What is the total cost of the shirt?
• A ratio of apples to oranges is 3:5. If there are 48 fruits total, how many apples?
• Solve for x: 2x + 5 = 17.
• Average daily temperatures are most likely calculated using which method of central tendency?
• If the mean of five numbers is 7, what is their sum?
• In a survey of 400 students about gifts for mom, Mother's Day accounts for 48 responses. What is the probability that a randomly selected response is Mother's Day?
• The triple (3, 4, 5) demonstrates what in a right triangle?
• What is 0.6 times 0.3?
• Calculate the area of a trapezoid with bases 2 and 6 and height 4.
• In a measurement-focused activity aligned with TEKS, a teacher instructs students to use a ruler to measure objects. If a student does not complete the activity successfully, what should the teacher plan next?
• Convert 0.5 to a fraction.
• If two events are independent, how do you find the probability of both occurring?
• What is the sum of the interior angles of a pentagon?
• What is the perimeter of a square with side length s?
• Sea-Tac Airport has a flight to Dallas every 2 hours and a flight to Washington, D.C. every 45 minutes. If both depart at 5:00 AM, when is the next time they will depart at the same time?
• Expand (x + 2)(x + 5).
• What is 3/8 plus 1/3?
• If a circle's diameter is d, which statement is true about the radius?
• Using P(color) = 0.53, P(haircut) = 0.40, and P(both) = 0.17, what is P(color OR haircut)?
• Using inductive reasoning, what is the next bottom layer in the pattern: 1; 1+2; 1+3+3; 1+3+7+4; 1+3+7+15+5; ?
• Manipulatives can be used as concrete representations of mathematical ideas. To learn mathematics from manipulatives, what must students perceive?
• Which property states that a + b = b + a for all numbers a and b?
• How many faces does a hexagonal pyramid have?
• A cylinder has diameter 16 inches and height 20 inches. A label covers the lateral surface area (the side) only. What is the area of the label?
• What is the mean of the data set 2, 4, 6, 8, 10?
• Round 2.468 to the nearest tenth.
• Which equation demonstrates the commutative property of addition?
• On a target board with scores 0, 1, 3, and 5, is it possible to obtain a score of 12 or 14 with exactly three coins?
• Which two properties of numbers did Jamie use to solve 15 + 12 + 28 + 45 = 100 by grouping and adding pairs to get 60 and 40, then 60 + 40?
• A teacher has students match numerical values such as 3.25%, 18(degrees), 1/3, 0, 3 5/8, 13.24, and -220 with descriptions like distance, freezing point, and money. This activity is assessing which mathematical concept?
• Which choice is a real number?
• What is the value of 12 + (7 × 2) − 2(5 + 3)?
• In a population problem, 40% buy iPods and 35% of those enjoy country music. If N people are in the group, how many will enjoy country music on their iPods?
• In the loan example, what is the next step after computing total amount paid (monthly payment times number of payments) to find the interest accrued?
• In the data set 1, 2, 2, 3, 3, 3, 4, what is the mode?
• Which statement describes the TEKS expectation for measuring length using standard units?
• Convert 19/4 to a mixed number.
• If a triangle has angles 30° and 60°, what is the third angle?
• Which expression demonstrates the commutativity of addition for the terms -3^0, a, and 4?
• If a fair die is rolled, probability of getting an even number is what?
• If the mean of 10 numbers is 7, what is their sum?
• How many vertices does a hexagonal pyramid have?
• In 0.004, the digit 4 is in which place value?
• If 20 students each require 12 ounces of plaster for an impression, how many pounds of plaster are needed in total?
• Which expression correctly gives the area of a rectangle?
• Which instructional activity best aligns with teaching students to find the length of objects using concrete models?
• Which axis is parallel to a line with slope 0?
• If triangles ABC and DEF are similar with AB corresponding to DE and AC to DF, and AB = 8, DE = 4, AC = 10, DF = 5, what is the similarity scale factor from DEF to ABC?
• In 0.0074, the digit 7 is in which place value?
• Which expression is an explicit rule for a mathematical sequence?
• How many total monthly payments are made on a 30‑year loan?
• Which expression represents reducing the fraction 40/100 to lowest terms?
• From the five-occasion chart, what is the combined percentage for Christmas and Birthday?
• Which of the following is a standard unit for length?
• In the division problem 56 ÷ 7, which number is the divisor?
• What is the greatest common divisor of 630 and 36?
• What is the name of a polyhedron whose faces are all triangles?
• After analyzing benchmark assessment results, which of the following could be part of a re-teach plan?