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MTTC Mathematics (Elementary) (089) study materials
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MTTC Mathematics (Elementary) (089) practice questions

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Question 1Mathematics (Elementary) content domains (not enumerated in source)

A student writes the number 4,706. What is the place value of the digit 7 in this number?

  1. 7 hundreds Correct answer.
  2. 7 tens
  3. 7 thousands
  4. 7 ones

Explanation

In 4,706 the digits occupy thousands, hundreds, tens, and ones places from left to right. The 7 sits in the hundreds place, so its value is 7 × 100 = 700.

Question 2Mathematics (Elementary) content domains (not enumerated in source)

Which number is equivalent to 3/5?

  1. 0.35
  2. 0.35 repeating
  3. 0.53
  4. 0.6 Correct answer.

Explanation

Dividing the numerator by the denominator gives 3 ÷ 5 = 0.6. Equivalently, multiply numerator and denominator by 2 to get 6/10, which is six tenths.

Question 3Mathematics (Elementary) content domains (not enumerated in source)

A rectangular garden measures 9 meters by 4 meters. What is its area?

  1. 13 square meters
  2. 26 square meters
  3. 36 square meters Correct answer.
  4. 18 square meters

Explanation

The area of a rectangle equals length times width, so 9 × 4 = 36 square meters. Area is reported in square units because two linear dimensions are multiplied.

Question 4Mathematics (Elementary) content domains (not enumerated in source)

Which list shows the numbers ordered from least to greatest?

  1. 0.5, 0.505, 0.55, 0.05
  2. 0.05, 0.505, 0.5, 0.55
  3. 0.5, 0.05, 0.55, 0.505
  4. 0.05, 0.5, 0.505, 0.55 Correct answer.

Explanation

Comparing decimals requires aligning place values: 0.050, 0.500, 0.505, and 0.550. Reading tenths first and then hundredths and thousandths gives 0.05 < 0.5 < 0.505 < 0.55.

Question 5Mathematics (Elementary) content domains (not enumerated in source)

What is the greatest common factor of 24 and 36?

  1. 12 Correct answer.
  2. 72
  3. 6
  4. 4

Explanation

The factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24; the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest shared factor is 12.

Question 6Mathematics (Elementary) content domains (not enumerated in source)

A bag holds 5 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is blue?

  1. 1/3
  2. 5/8
  3. 3/8 Correct answer.
  4. 3/5

Explanation

There are 3 blue marbles out of 8 total marbles, so the probability is 3/8. Probability compares favorable outcomes to all equally likely outcomes.

Question 7Mathematics (Elementary) content domains (not enumerated in source)

Which of the following is a prime number?

  1. 27
  2. 21
  3. 33
  4. 29 Correct answer.

Explanation

A prime number has exactly two positive factors, 1 and itself. The number 29 has no factors other than 1 and 29, whereas 21, 27, and 33 are each divisible by 3.

Question 8Mathematics (Elementary) content domains (not enumerated in source)

A square has a perimeter of 28 centimeters. What is the length of one side?

  1. 14 centimeters
  2. 56 centimeters
  3. 4 centimeters
  4. 7 centimeters Correct answer.

Explanation

A square has four equal sides, so each side equals the perimeter divided by 4. Dividing 28 by 4 gives 7 centimeters per side.

Question 9Mathematics (Elementary) content domains (not enumerated in source)

What is the value of 4 + 3 × (6 − 2)?

  1. 16 Correct answer.
  2. 28
  3. 24
  4. 10

Explanation

Order of operations requires evaluating the parentheses first: 6 − 2 = 4. Then multiply 3 × 4 = 12 and add 4 to get 16.

Question 10Mathematics (Elementary) content domains (not enumerated in source)

A recipe uses 2 1/2 cups of flour for 12 cookies. At this rate, how many cups are needed for 30 cookies?

  1. 5 cups
  2. 6 1/4 cups Correct answer.
  3. 7 1/2 cups
  4. 6 cups

Explanation

The rate is 2.5 cups per 12 cookies, so each cookie needs 2.5/12 cups. Multiplying by 30 gives 2.5 × 30/12 = 6.25 cups, or 6 1/4 cups.

Question 11Mathematics (Elementary) content domains (not enumerated in source)

A shirt originally priced at $40 is on sale for 25% off. What is the sale price?

  1. $15
  2. $10
  3. $35
  4. $30 Correct answer.

Explanation

The discount is 25% of $40, which is 0.25 × 40 = $10. Subtracting the discount from the original price gives $40 − $10 = $30.

Question 12Mathematics (Elementary) content domains (not enumerated in source)

Which expression represents the statement "five less than three times a number n"?

  1. 5n − 3
  2. 3n − 5 Correct answer.
  3. 5 − 3n
  4. 3(n − 5)

Explanation

Three times a number is 3n, and five less than that means subtracting 5 from 3n, giving 3n − 5. The order matters because subtraction is not commutative.

Question 13Mathematics (Elementary) content domains (not enumerated in source)

What is the mean of the data set 4, 8, 6, 10, 12?

  1. 6
  2. 8 Correct answer.
  3. 40
  4. 10

Explanation

The mean is the sum divided by the number of values: (4 + 8 + 6 + 10 + 12) = 40, and 40 ÷ 5 = 8.

Question 14Mathematics (Elementary) content domains (not enumerated in source)

A triangle has two angles measuring 45° and 60°. What is the measure of the third angle?

  1. 105°
  2. 85°
  3. 75° Correct answer.
  4. 45°

Explanation

The interior angles of a triangle sum to 180°. Subtracting the known angles gives 180 − 45 − 60 = 75 degrees.

Question 15Mathematics (Elementary) content domains (not enumerated in source)

Which fraction is equivalent to the repeating decimal 0.444...?

  1. 44/100
  2. 4/10
  3. 1/4
  4. 4/9 Correct answer.

Explanation

Let x = 0.444...; then 10x = 4.444..., and subtracting gives 9x = 4, so x = 4/9. Repeating decimals with a single repeating digit correspond to ninths.

Question 16Mathematics (Elementary) content domains (not enumerated in source)

A rectangular prism has length 5 cm, width 3 cm, and height 4 cm. What is its volume?

  1. 60 cubic centimeters Correct answer.
  2. 24 cubic centimeters
  3. 47 cubic centimeters
  4. 12 cubic centimeters

Explanation

Volume of a rectangular prism equals length × width × height. Multiplying 5 × 3 × 4 gives 60 cubic centimeters.

Question 17Mathematics (Elementary) content domains (not enumerated in source)

A spinner has 4 equal sections numbered 1 through 4. If it is spun twice, what is the probability that both spins land on 3?

  1. 1/4
  2. 1/8
  3. 1/16 Correct answer.
  4. 1/2

Explanation

Each spin is independent, so multiply the probabilities: 1/4 × 1/4 = 1/16. The product rule applies because the outcome of the first spin does not affect the second.

Question 18Mathematics (Elementary) content domains (not enumerated in source)

Which number is the least common multiple of 6 and 8?

  1. 12
  2. 24 Correct answer.
  3. 2
  4. 48

Explanation

Multiples of 6 include 6, 12, 18, 24, and multiples of 8 include 8, 16, 24. The smallest shared multiple is 24.

Question 19Mathematics (Elementary) content domains (not enumerated in source)

A store sells pencils in packs of 6 and erasers in packs of 4. What is the smallest number of each item a teacher can buy so that the number of pencils equals the number of erasers?

  1. 12 Correct answer.
  2. 6
  3. 24
  4. 10

Explanation

The counts must be a common multiple of 6 and 4, and the smallest is the least common multiple. The LCM of 6 and 4 is 12, so buying 2 packs of pencils and 3 packs of erasers gives 12 of each.

Question 20Mathematics (Elementary) content domains (not enumerated in source)

The line y = 3x + 2 is graphed on a coordinate plane. What is the slope of the line?

  1. 5
  2. 1/3
  3. 3 Correct answer.
  4. 2

Explanation

In slope-intercept form y = mx + b, the coefficient m is the slope and b is the y-intercept. Here m = 3, so the line rises 3 units for every 1 unit to the right.

Question 21Mathematics (Elementary) content domains (not enumerated in source)

A cube has a volume of 64 cubic inches. What is the length of one edge?

  1. 8 inches
  2. 4 inches Correct answer.
  3. 16 inches
  4. 32 inches

Explanation

For a cube, volume equals the edge length cubed, so the edge is the cube root of 64. Since 4 × 4 × 4 = 64, the edge is 4 inches.

Question 22Mathematics (Elementary) content domains (not enumerated in source)

A rectangle's length is 3 more than twice its width, and its perimeter is 36 centimeters. What is the width?

  1. 10 centimeters
  2. 5 centimeters Correct answer.
  3. 15 centimeters
  4. 6 centimeters

Explanation

Let w be the width; then the length is 2w + 3. Perimeter gives 2w + 2(2w + 3) = 36, so 6w + 6 = 36 and w = 5 centimeters.

Question 23Mathematics (Elementary) content domains (not enumerated in source)

A data set of five values has a mean of 12. If four of the values are 8, 10, 14, and 15, what is the fifth value?

  1. 11
  2. 20
  3. 13 Correct answer.
  4. 12

Explanation

A mean of 12 across five values means the total is 5 × 12 = 60. The four known values sum to 47, so the fifth value is 60 − 47 = 13.

Question 24Mathematics (Elementary) content domains (not enumerated in source)

A cone and a cylinder share the same base radius and height. If the cylinder's volume is 90 cubic centimeters, what is the cone's volume?

  1. 45 cubic centimeters
  2. 90 cubic centimeters
  3. 30 cubic centimeters Correct answer.
  4. 270 cubic centimeters

Explanation

The volume of a cone is one third of the volume of a cylinder with the same base and height. Dividing 90 by 3 gives 30 cubic centimeters.

Question 25Mathematics (Elementary) content domains (not enumerated in source)

The probability that a student passes a quiz is 0.7, and the probability of passing a second independent quiz is 0.5. What is the probability of passing both quizzes?

  1. 0.35 Correct answer.
  2. 0.6
  3. 0.25
  4. 1.2

Explanation

For independent events, the probability of both occurring is the product of the individual probabilities. Multiplying 0.7 × 0.5 gives 0.35.

Question 26Mathematics (Elementary) content domains (not enumerated in source)

A teacher writes the number 4,706 on the board. What is the value of the digit 7 in this number?

  1. 7,000
  2. 70
  3. 7
  4. 700 Correct answer.

Explanation

In 4,706 the digit 7 sits in the hundreds place, so its place value is 7 × 100 = 700. Reading place values from left to right gives thousands, hundreds, tens, ones, which fixes the position of each digit.

Question 27Mathematics (Elementary) content domains (not enumerated in source)

A student claims that 51 is a prime number. Which statement correctly evaluates this claim?

  1. The claim is false because 51 is an odd number.
  2. The claim is false because 51 = 3 × 17. Correct answer.
  3. The claim is true because 51 has no factor other than 1 and itself.
  4. The claim is true because 51 is not divisible by 2 or 5.

Explanation

A prime number has exactly two factors, 1 and itself. Since 51 = 3 × 17, it has factors 3 and 17 as well, so it is composite. Divisibility by 2 or 5 is neither necessary nor sufficient for primality.

Question 28Mathematics (Elementary) content domains (not enumerated in source)

A rectangular garden measures 9 meters by 6 meters. A fence is built around its entire boundary. How many meters of fencing are needed?

  1. 54
  2. 15
  3. 36
  4. 30 Correct answer.

Explanation

The perimeter of a rectangle is 2(length + width) = 2(9 + 6) = 30 meters. Perimeter measures the distance around the boundary, not the area covered.

Question 29Mathematics (Elementary) content domains (not enumerated in source)

What is the value of 20 − 4 × 3 + 6 ÷ 2?

  1. 3
  2. 11 Correct answer.
  3. 27
  4. 9

Explanation

Following order of operations, multiplication and division come before addition and subtraction: 4 × 3 = 12 and 6 ÷ 2 = 3, so the expression becomes 20 − 12 + 3. Working left to right gives 8 + 3 = 11.

Question 30Mathematics (Elementary) content domains (not enumerated in source)

A class survey shows that 3 out of every 8 students walk to school. If 240 students are surveyed, how many walk to school?

  1. 120
  2. 64
  3. 90 Correct answer.
  4. 45

Explanation

Set up the proportion 3/8 = x/240. Since 240 ÷ 8 = 30, multiply 3 × 30 = 90 students who walk. The ratio stays constant, so scaling both parts by the same factor preserves it.

Question 31Mathematics (Elementary) content domains (not enumerated in source)

An item costs $80, and the sales tax rate is 6%. What is the total cost including tax?

  1. $84.80 Correct answer.
  2. $86.00
  3. $74.80
  4. $80.60

Explanation

The tax is 6% of $80, or 0.06 × 80 = $4.80. Adding the tax to the price gives $80 + $4.80 = $84.80.

Question 32Mathematics (Elementary) content domains (not enumerated in source)

Which expression correctly represents the phrase "twice a number x, decreased by seven"?

  1. 2(x − 7)
  2. 2x + 7
  3. 7 − 2x
  4. 2x − 7 Correct answer.

Explanation

"Twice a number x" is 2x, and "decreased by seven" means subtract 7 from that quantity, giving 2x − 7. Order matters: the subtraction applies to the doubled number, not to 7.

Question 33Mathematics (Elementary) content domains (not enumerated in source)

A data set consists of the values 7, 9, 9, 12, and 13. What is the median of this data set?

  1. 10
  2. 9.5
  3. 12
  4. 9 Correct answer.

Explanation

The values are already in order, and there are five of them, so the median is the middle (third) value, which is 9. The median is a positional measure and is not affected by the size of the extreme values.

Question 34Mathematics (Elementary) content domains (not enumerated in source)

A quadrilateral has three interior angles measuring 85°, 95°, and 100°. What is the measure of the fourth angle?

  1. 80° Correct answer.
  2. 100°
  3. 170°
  4. 90°

Explanation

The interior angles of any quadrilateral sum to 360°. The three known angles total 85 + 95 + 100 = 280°, so the fourth angle is 360 − 280 = 80°.

Question 35Mathematics (Elementary) content domains (not enumerated in source)

Which decimal is equivalent to the fraction 5/8?

  1. 0.85
  2. 0.58
  3. 0.625 Correct answer.
  4. 0.125

Explanation

Dividing the numerator by the denominator gives 5 ÷ 8 = 0.625. Equivalently, multiply numerator and denominator by 125 to obtain 625/1000, which is 0.625.

Question 36Mathematics (Elementary) content domains (not enumerated in source)

A cylindrical can has a radius of 3 centimeters and a height of 10 centimeters. Using π ≈ 3.14, what is the approximate volume of the can?

  1. 31.4 cubic centimeters
  2. 282.6 cubic centimeters Correct answer.
  3. 188.4 cubic centimeters
  4. 94.2 cubic centimeters

Explanation

The volume of a cylinder is V = πr²h. Substituting gives 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cubic centimeters.

Question 37Mathematics (Elementary) content domains (not enumerated in source)

Two fair six-sided dice are rolled. What is the probability that the sum of the two numbers is 7?

  1. 1/36
  2. 1/6 Correct answer.
  3. 1/12
  4. 7/36

Explanation

There are 6 × 6 = 36 equally likely outcomes. The sums equal to 7 come from (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which is 6 outcomes, so the probability is 6/36 = 1/6.

Question 38Mathematics (Elementary) content domains (not enumerated in source)

What is the greatest common factor of 36 and 60?

  1. 180
  2. 12 Correct answer.
  3. 6
  4. 4

Explanation

The prime factorizations are 36 = 2² × 3² and 60 = 2² × 3 × 5. Taking the lowest power of each shared prime gives 2² × 3 = 12, the greatest common factor.

Question 39Mathematics (Elementary) content domains (not enumerated in source)

A student must choose one book from a shelf with 5 novels and 4 biographies, then choose one bookmark from 3 designs. How many different book-and-bookmark combinations are possible?

  1. 27 Correct answer.
  2. 12
  3. 60
  4. 20

Explanation

By the multiplication principle, choosing a book gives 5 + 4 = 9 options, and each pairs with 3 bookmark designs, so 9 × 3 = 27 combinations. The two categories of books are combined by addition because the student picks exactly one book.

Question 40Mathematics (Elementary) content domains (not enumerated in source)

A number line shows a point located 3 units to the left of −2. What number does this point represent?

  1. 1
  2. −5 Correct answer.
  3. −6
  4. 5

Explanation

Moving left on a number line means subtracting, so the point is at −2 − 3 = −5. Moving left always decreases the value, regardless of whether the starting point is positive or negative.

Question 41Mathematics (Elementary) content domains (not enumerated in source)

A triangle has side lengths of 6 centimeters, 8 centimeters, and 10 centimeters. Which classification is correct?

  1. It is an obtuse triangle.
  2. It is a right triangle. Correct answer.
  3. It is an acute triangle.
  4. It is an equilateral triangle.

Explanation

Check the Pythagorean relationship: 6² + 8² = 36 + 64 = 100, and 10² = 100. Since the squares of the two shorter sides sum to the square of the longest side, the triangle is right.

Question 42Mathematics (Elementary) content domains (not enumerated in source)

The line 2y = 6x − 8 is graphed on a coordinate plane. What are the slope and y-intercept of this line?

  1. slope 2, y-intercept −4
  2. slope 3, y-intercept −8
  3. slope 3, y-intercept −4 Correct answer.
  4. slope 6, y-intercept −8

Explanation

Divide every term by 2 to write the equation in slope-intercept form: y = 3x − 4. The coefficient of x gives the slope 3, and the constant term gives the y-intercept −4.

Question 43Mathematics (Elementary) content domains (not enumerated in source)

A right circular cone has a base radius of 3 inches and a height of 8 inches. Using π ≈ 3.14, what is the approximate volume of the cone?

  1. 226.08 cubic inches
  2. 150.72 cubic inches
  3. 75.36 cubic inches Correct answer.
  4. 25.12 cubic inches

Explanation

The volume of a cone is V = (1/3)πr²h. Substituting gives (1/3) × 3.14 × 9 × 8 = 3.14 × 24 = 75.36 cubic inches. The factor of one-third reflects that a cone fills one-third of the cylinder with the same base and height.

Question 44Mathematics (Elementary) content domains (not enumerated in source)

A bag contains 4 green tiles and 6 yellow tiles. One tile is drawn and not replaced, then a second tile is drawn. What is the probability that both tiles are green?

  1. 8/20
  2. 4/25
  3. 2/15 Correct answer.
  4. 1/5

Explanation

The first draw is green with probability 4/10 = 2/5. Because the tile is not replaced, the second draw is green with probability 3/9 = 1/3. Multiplying gives (2/5) × (1/3) = 2/15.

Question 45Mathematics (Elementary) content domains (not enumerated in source)

A data set has a mean of 15 and a median of 20. Which statement best describes the shape of the distribution?

  1. It is symmetric, because the mean and median are both measures of center.
  2. It is bimodal, because the mean and median differ.
  3. It is skewed to the right, because the mean is less than the median.
  4. It is skewed to the left, because the mean is less than the median. Correct answer.

Explanation

In a left-skewed distribution, a long tail of low values pulls the mean below the median. Here the mean of 15 is less than the median of 20, which is consistent with left skew. Comparing the mean and median is a standard way to judge skew direction.

Question 46Mathematics (Elementary) content domains (not enumerated in source)

Which number is irrational?

  1. 0.75
  2. √2 Correct answer.
  3. √16
  4. 22/7

Explanation

An irrational number cannot be written as a ratio of two integers, and √2 has a nonterminating, nonrepeating decimal expansion. The value √16 = 4, 0.75, and 22/7 are all rational.

Question 47Mathematics (Elementary) content domains (not enumerated in source)

A pattern begins 2, 6, 12, 20, 30, ... and continues with the same rule. What is the next term?

  1. 42 Correct answer.
  2. 40
  3. 36
  4. 44

Explanation

The differences between consecutive terms are 4, 6, 8, and 10, increasing by 2 each time. The next difference is 12, so the next term is 30 + 12 = 42. Equivalently, each term equals n(n + 1) for n = 1, 2, 3, ...

Question 48Mathematics (Elementary) content domains (not enumerated in source)

A rectangular prism is 4 centimeters long, 5 centimeters wide, and 6 centimeters high. What is its total surface area?

  1. 148 square centimeters Correct answer.
  2. 120 square centimeters
  3. 74 square centimeters
  4. 60 square centimeters

Explanation

Surface area is 2(lw + lh + wh) = 2(20 + 24 + 30) = 2(74) = 148 square centimeters. Each of the three distinct face shapes appears twice on the prism.

Question 49Mathematics (Elementary) content domains (not enumerated in source)

A student simplifies the expression 3(x + 4) − 2x and gets x + 12. Which statement about the student's work is accurate?

  1. The simplification is correct because 3x + 12 − 2x = x + 12. Correct answer.
  2. The simplification is incorrect because −2x cannot be combined with 3x.
  3. The simplification is incorrect because the 3 should be distributed only to x.
  4. The simplification is incorrect because the result should be x + 4.

Explanation

Distributing gives 3x + 12, and combining like terms with −2x yields 3x − 2x + 12 = x + 12. The distributive property requires multiplying the 3 by both terms inside the parentheses.

Question 50Mathematics (Elementary) content domains (not enumerated in source)

A store discounts a jacket by 20%, then takes an additional 10% off the reduced price. What single percent discount is equivalent to these two successive discounts?

  1. 28% Correct answer.
  2. 30%
  3. 18%
  4. 25%

Explanation

After a 20% discount the price is 80% of the original, and the extra 10% off leaves 90% of that, so the final price is 0.8 × 0.9 = 0.72 of the original. The total discount is 1 − 0.72 = 0.28, or 28%. Successive percent changes multiply rather than add.