PRAXIS MATH (practice 1)

Elisa's number: 5,723,683 Troy's number: 2,678,533 Both Elisa and Troy wrote a number, as shown. The 7 digit in Elisa's number represents how many times what the digit 7 represent in Troy's number? A. 10 B. 100 C. 1,000 D. 10,000

A: The question requires an understanding of place value systems. The value of the number represented by the 7 in Elisa's number is 700,000, or 7 X 10 ^5, while the value of the number represented by the 7 in Troy's number is 70,000 or 7 X 10 ^4, Therefore, the value of the former is 10 times as great as the value of the latter.

(0 x 10 ^4) + (4 x 10 ^3) + (0 x 10^2) + (5 x 10^1) + (2 x 10^0) What number is represented by the bast 10 expression shown?

(4,052) The question requires an understanding of how to write numbers using base 10 numerals, number names, and expanded form. Since 10^3 = 1,000 10^2 = 100, and 10^0 = 1, the expression shown is equivalent to (0) + (4 x 1,000) + (0) + (5 x 10) + (2 x 1) = 4,000 + 50 + 2 which equals 4,052

Tom's company has to ship 1,944 boxes of shoes. If a truck can hold 450 boxes, how many trucks does he need to ship all the boxes?

(5) 1,944/450 =4.32 Round up to 5 as there is no "partial" trucks

Kyle's father set up a savings account for him with an initial balance of $100. Since then, Kyle has been depositing $28 into the account each week. Kyle represents the amount of money he has saved after x weeks by the expression 28x + 100. Which of the following is equivalent to Kyle's expression? (equivalent =another way of saying it) A. 4( 7x + 25) B. 7(4x + 100) C. 7(4x + 25) D. 4(7x + 100)

(A) The question requires an understanding of algebraic expression and the ability to manipulate them. Since both 28 and 100 are divisible by 4, 4 is a factor of the expression 28x + 100. To arrive at the equivalent expression in (A), the distributive property was applied to 28x + 100. In fact 28x + 100 = 4 x 7x + 4 x 25 = 4(7x + 25)

3x^5 + 7x^3 - 5 Which of the following lists the coefficients and degrees of the terms in the polynomial shown? A. Coefficients: 3, 7, -5 ; Degrees: 5, 3, 0 B. Coefficients: 3, 7, -5 ; Degrees: 5, 3, 1 C. Coefficients: 5, 3, 0 ; Degrees: 3, 7, -5 D. Coefficients: 5, 3, 1 ; Degrees: 3, 7, -5

(A) The question requires an understanding of algebraic terminology. The coefficients of the terms of a polynomial are the numbers by which the variables are multiplied. The degrees of the terms of a polynomial are the exponents to which the variables are raised. Therefore, the coefficients are 3, 7, and -5 and the degrees are 5, 3, and 0.

Which of the following is an algebraic expression? (An algebraic expression is made of constants, variables, and algebraic operations) A. 6x - 4 B. 6y < 4 C. 6z = 4 D. 6 + 4

(A) The question requires an understanding of how to differentiate between algebraic expressions and equations. An algebraic expression is made of constants, variables, and algebraic operations. While (A) is an algebraic expression, (B) is an algebraic inequality, (C) is an algebraic equation, and (D) is a numerical expression.

25x^2 + 6y^3 + 4x - 25y + 3x^2 - 4y^2 Which of the following shows all like terms of the expression above? A. 25x^2 and 3x^2 B. 25x^2 and 25y C. 25x^2, 3x^2, and 4y^2 D. 6y^3, 25y, and 4y^2

(A) The question requires an understanding of how to use mathematical terms to identify parts of expressions. In an expression, like terms are terms that meet two conditions. First the terms contain identical products of variables. Second, the exponent of a variable in a term is identical to the exponent of the same variable in the other terms. The only terms in the expression shown that meet these two conditions are 25x^2 and 3x^2, since the variable x is identical in each term and the exponent of 2 on the x is identical in each term.

Which of the following is an algebraic "equation"? (equation equals something) A. 3x - 5 = 2 B. 4x - 2y + 8 C. 3(9 - 4) = 5(4 - 1) D. 7 + 5 - 12/3

(A) The question requires an understanding of the difference between algebraic expressions and equations. Neither option (B) nor (D) shows and equation since there is no equal sign in either option; these are instead both expressions. Options (A) and (C) both show equations, but the equation is option (C) is not algebraic since it does not contain any variables. Only the equation in option (A) is algebraic, since it is an equation that contains at least one variable.

15(4 + 3) = 15 x 4 + 15 x 3 A. The distributive property of multiplication over addition (foil) B. The commutative property of multiplication C. The associative property of multiplication D. The additive inverse and additive identity properties

(A) The question requires and understanding of the basic properties of real numbers. The distributive property of multiplication over addition states that for any real numbers a, b, and c, a(b + c) is equal to ab + ac.

In a bag there are 28 candies, of which 17 are peppermints and the rest are caramel chews. What is the ratio of the number of caramel chews to the number of peppermints in the bag? A. 11 : 17 B. 17 : 11 C. 17 : 28 D. 28 : 17

(A) The question requires an understanding of how to apply the concepts of ratios and unit rates to describe relationships between two quantities. The total number of candies is 28, and 17 of them are peppermint. Therefore 27-17 = 11, or 11 caramel chews. The ratio of chews to peppermints is 11 : 17.

Carlos makes an annual salary of $65, 295. Which of the following is Carlos' salary rounded to the nearest thousand? A. $65,000 B. $65,300 C. $66,000 D. $70,000

(A) The question requires and understanding of how to round multi digit numbers to any place value. To round to the nearest thousand, one must look at the digit in the hundreds place first. The digit in the hundreds place is 2, which is less than 5. Therefore, the digit in the thousands place is not changed when rounding in the nearest thousand.

Which of the following are equivalent to dividing 288 by 24? Select all that apply. (288/24=12 so look for all that equal 12) A. (288/4) / 6 B. 2(144/24) C. (144/12) + (144/12) D. (240/24) + (48/24)

(A, B, and D) The question requires and understanding of the order of operations in basic computations. Operations within the parenthesis must be solved first. A. 72/6 = 12 B. 2*6 = 12 C. 12 + 12 = 24 D. 10 + 2 = 12

2y^2 + 17x^2 + 14x^2y + 8xy^2 + 1 Which THREE of the following statements are correct about the algebraic expression shown? A. The coefficients are 2, 17, 14, 8, and 1 B. The variables are x and y C. There are like terms D. There are 4 terms E. The degree of the expression is 3

(A, B, and E) The question requires and understanding of how to use mathematical terms to identify parts of expressions and describe expression. A term is an expression consists of the product of a coefficient, which is a number, and one or more variables raised to a positive exponents. The coefficients of the terms in the expression are 2, 17, 14, 8 and 1 so option (A) is correct. The consistent term, 1, is a simplified version of 1x^0y^0, and if written this way, each of the five terms can be seen to contain x and y as variables; so option (B) is correct. The degrees of the monomials are 2, 2, 3, 3, and 0, so the degree of the expression is 3 and hence option (E) is correct.

If one cup of soup costs $2, which one of the following represents the number of cups of soup that can be purchased with d dollars? A. 2d B. d/2 C. d/100 x 2 D. 100 X d/2

(B) The question requires an understanding of algebraic representation. The number of dollars spent divided by the number of dollars per cup of soup gives the number of cups of soup purchased. Therefore, the number of cups of soup that can be purchased with d dollars is d/2.

If r is a real number, which of the following illustrates the commutative property of multiplication? (communicative is all the same "talking together") A. (32) (r) = (3) (2r) B. (32) (r) = (r) (32) (correct answer) C. (32) (r) = (30) (r) + (2) (r) D. (32) (r) = (32) (r) (1)

(B) The question requires an understanding of how to identify properties of operations. The commutative property of multiplication states that given any two numbers A and B, A x B = B x A that is, the order of the factors in a multiplication problem does not affect the product.

2/3 / 4/3 + 3/5 x (5/3)^2 Which of the following is equivalent to the expression shown? A. 2/9 B. 13/6 C. 5/9 D. 12/16

(B) The question requires an understanding of how to solve problems using the order of operations. By using the order of operations and the fact that dividing is equivalent to multiplying by the inverse, the expression, 2/3 / 4/3 + 3/5 x (5/3)^2 can be simplified to: 2/3 x 3/4 + 3/5 x 25/9 Performing both multiplications equals: 1/2 + 5/3, which equals 13/6

462,359 In the number shown, the value represented by the 6 x b, where b is a constant. Which of the following equals b? A. 10^3 B. 10^4 C. 10^5 D. 10^6

(B) The question requires an understanding of how to use whole-number exponents to denote powers of 10. The number 462,359 can be written as 4 x 10^5 + 6 + 10^4 + 2 x 10^3 + 3 x 10^2 + 5 x 10^1 + 9 x 10^0 The value represented by the digit 6 is 6 x 10^4, so b = 10^4

Which of the following is equal to 4(5 - 2)^2 - 2^3 ? A. 16 B. 28 C. 76 D. 136

(B) The question requires an understanding of the order of operations (PEMDAS). 1. Simplify the expression in parenthesis 4(5 - 2)^3 - 2^3 which equals: 4 x 3^2 - 2^3 2. Evaluate the powers: 4 x 9 - 8 3. Multiply: 36 - 8 = 28

Which of the following has the greatest value? A. 5 thousands B. 53 hundreds C. 506 tens D. 5,100 ones

(B) The question requires and understanding of place value. By writing each of the answer choices as a numeral, you can compare the four numbers and decide which is the greatest. 5 thousands is the same as 5 X 1,000 or 5,000. 53 hundreds is the same as 53 X 100 or 5,300. 506 tens is the same as 506 X 10 or 5,060. 5,100 ones is the same as 5,100 X 1 or 5,100.

3y + 2y What is the value of the algebraic expression shown when y = 5? A. 15 B. 25 C. 60 D. 85

(B) The question requires an understanding of algebraic expressions and the ability to manipulate them. To find the value of the given algebraic expression when y = 5, 5 must be substituted for y in the expression. Therefore, 3y + 2y = 3 x 5 + 2 x 5 = 25

If y = 2, what is the value of 4 - 2(4y) + 5y? A. -22 B. -2 C. 22 D. 26

(B) The question requires an understanding of how to evaluate simple algebraic expressions. The first step is to substitute 2 in place of the variable y, which yields 4 - 2(4 x 2) + 5 x2 (use the order of operations to solve) 4 - 2 x 8 + 10 4 - 16 + 10 4 - 6 = -2

Which is the expanded form of 3,056.45? A. (3 x 1,000) + (5 x 10) + (6 x 1) + (4 x 1/100) + (5 x 1/10) B. (3 x 1,000) + (5 x 10) + (6 x 1) + (4 x 1/10) + (5 x 1/100) C. (3 x 1,000) + (5 x 100) + (6 x 10) + (4 x 1/10) + (5 x 1/100)

(B) The question requires an understanding of place value and how to write numbers in expanded form. Expanded form is a decomposition of a number into a sum, where the add ends are the values represented by the digits in a number. Therefore, 3,056.45 = 3,000 + 6 + 0.4 + 0.05 = (3 x 1,000) + (5 X 10) + (6 x 1) + (4 x 1/10) + (4 x 1/10) + (5 x 1/100)

Which of the following numbers is least? A. 0.103 B. 0.1041 C. 0.1005 D. 0.11

(C) Is the least, being equal to 1,005 ten-thousandths. (Moves away from zero and the decimal point to the right or smaller increments)

County Population Brookhaven 74,702 Columbus 70,472 Davidson 74,072 Washington 74,720 The chart shows the populations of four neighboring counties. Bob lives in the county with a population of 70,000 + 4000 + 70 + 2. In which county does Bob live? A. Brookhaven B. Columbus C. Davidson

(C) The question requires an understanding of how to compose and decompose multidigit numbers. The expanded form 70,000 + 4,000 +70 + 2 corresponds to the number 74,072, which is the population of Davidson County.

"3 less than 4 times the sum of the number x and 15" Which of the following expressions best represents the verbal phrase shown? A. 4x + 15 - 3 B. 3 —4x + 15 C. 4(x + 15) - 3 D. 3 - 4(x + 15)

(C) The question requires an understanding of how to translate between verbal statements and algebraic expressions or equations. The product of a number and a sum requires parentheses around the sum. Therefore "4 times the sum of the number x and 15" can be represented by the expression 4(x + 15). "Less than" can be translated as subtraction, where what comes before "less than" is taken aways from what comes after it. Therefore, the verbal phrase can be represented by the expression 4(x + 15) - 3

Jamal bought a pair of headphones priced at $17.99. If the sales tax rate is 8%, which of the following proportions can be used to find the amount of sales tax x, in dollars, for the headphones? A. 8/17.99 = x/100 B. 8/17.99 = 100/x C. 8/100 = x/17.99

(C) The question requires an understanding of how to use proportional relationships to solve ratio and percent problems. The taxes are 8% of the price; that is, the ratio x : 17.99 is equal to 8 : 100. Therefore 8/100 = x/17.99

3 x 2 + 7 x 2 The expression shown results when the distributive property of multiplication over addition is applied to which of the following expressions? A. 3 + 3 + 7 + 7 B. 6 + 14 C. (3 + 7) x 2 D. 56 / 23

(C) The question requires an understanding of properties of operations. The distributive property of multiplication over addition states that ; (A + B) x C = (A x C) + (B x C) so (3 + 7) x 2 = 3 x 2 + 7 x 2

If 125 + 4x = 7y, what is x in terms of y? A. x = 4(7y - 125) B. x= 4(7y + 125) C. x = (7y - 125) / 4 D. x = (7y + 125) / 4

(C) The question requires an understanding of solving an equation for a given variable. To find x in terms of y, the equation 125 + 4x = 7y must be transformed so that the variable x is by itself on one side of the equal sign. 1. Subtract 125 from both sides (4x = 7y - 125) 2. Divide both sides by 4 equals x = (7y - 125) / 4

———-A———-B———C——-> Which of the following can be used to name the ray that has endpoint A and goes in the direction of C in the figure shown? A.-—> AB only B. —->AC only C.—>AC and —>AB D. —>CA and —>AC

(C) The question requires an understanding of the definition of a ray. Since a ray is apart of a line that has one endpoint and extends in one direction without ending, then both ray AC and ray AB represents the same ray that has endpoint A and extends in the direction of C.

Which of the following is an example of the associative property of multiplication? (3 or more and the same thing is done to all) A. AB + C = BA + C B. AB + C = C + AB C. (AB)C = A(BC) D. A(B + C) = AB + AC

(C) This question requires an understanding of algebraic properties. The associative property of multiplication concerns the order in which the multiplications are preformed when three or more numbers are multiplied, which can be changed by inserting or removing grouping symbols such as parenthesis. The same thing must be done to both sides so that they remain equal.

Which of the following is equal to 5 (10^0)? A. 0 B. 1 C. 5 D. 50

(C) This question requires an understanding of the place value system and powers of 10. Since 10^0 = 1, the expression 5(10^0) is equal to 5 x 1, or 5.

8a - 3b What is the value of the expression shown when a = 2 and b = 5? A. -46 B. -31 C. 1 D. 31

(D) The question requires an understanding of how to evaluate simple algebraic expressions. Substituting a = 2 and b = -5 into the expression yields 8(2) - 3(-5) = 16 - (-15) = 16 + 15 = 31 (remember to carry over the negative sign in the problem and multiplication)

Which of the following represents the calculation -7 - (- 2)

(D) The question requires an understanding of how to represent rational numbers and their operations in different ways, using drawings, models, number lines, and arrays. One must first plot -7 on the number line. Since -(-2) is equivelent to +2, one must next move two steps to the right, which yields an answer of -5.

Which of the following pairs of numbers estimates the number 3.27461 to the nearest tenth, and to the nearest thousandths, respectively? A. 3.2 and 3.274 B. 3.2 and 3.275 C. 3.3 and 3.274 D. 3.3 and 3.275

(D) The question requires an understanding of how to round multi digit numbers to any place value. The tenths place is the first digit after the decimal and would be rounded to 3 based on the next digit, 7, which is in the hundredths place. The thousandths place is the third digit after the decimal and would be rounded to 5 based on the next digit, 6, which is in the ten-thousandths place.

4x (3x + 2y) What does 2y represent in the expression shown? (Remember Monomial means ONE) A. A binomial B. A factor C. A coefficient D. A monomial

(D) The question requires an understanding of how to use mathematical terms to identify parts of expressions and describe expressions. A monomial is an algebraic expression that consists of ONE TERM that is a number, a variable, or a product of a number and a variable, where all exponents are whole numbers.

Which of the following expressions is equivalent to -4(3 - 2x) ? A. -2x - 12 B. 2x - 12 C. -8x - 12 D. 8x - 12

(D) The question requires an understanding of how to use the distributive property to generate equivalent linear algebraic expressions. Using the distributive property of multiplication over addition, -4(3 -2x) = -12 + 8x or using the commutative property of addition it equals 8x - 12

In a certain number, a and b represent digits, and a represents 10^4 times what b represents. Which of the following could be the place value of a and b? A. a is in the thousandths place, and be is in the tens place B. a is in the tenths place, and b is in the hundreds place C. a is in the ones place, and b is in the hundredths place D. a is in the tens place, and b is in the thousandths place

(D) The question requires an understanding of place value and how a digit in one place represents ten times what it represents in the place to its right and one-tenth what it represents in the place to its left. A digit in the tens place is 10^4 times what a digit in the thousandths place represents. In option (A), a would be 10^2 what b represents. In option (B), a would be 1/10^3 times what b represents. In option (C), a would be 10^2 what b represents.

The digit 5 is in what place in the number 3.14159 A. Thousands place B. Thousandths place C. Hundredths place D. Ten-thousandths place

(D) The question requires an understanding of place value. The digit 5 is in the fourth place to the right of the decimal point, and the places in order from the decimal point to the right are the tenths, the hundredths, the thousandths, and the ten thousandths.

What value does the 8 represent in the number 5,836,303 A. Eight hundred B. Eight thousand C. Eighty thousand D. Eight hundred thousand

(D) The question requires an understanding of how to identify the place a digit is in and its value in that place. The digit 8 is in the fifth place to the left of the ones place, so its value is 8 x 10^5 or 800,000, that is, eight hundred thousand.

In the number 567,894, what is the value of the digit 6? A. Sixty B. Ten thousand C. Six thousand D. Sixty thousand

(D) The question requires an understanding of place value systems. Reading 567,894 from left to right, the digit 4 is in the ones position and has a value of 4. The digit 9 is in the tens position and has a value of 90. The digit 8 is in the hundreds position and has a value of 800. The digit 7 is in the thousands position and has a value of 7,000. The digit 6 is in the ten-thousands position and has a value of 60,000.

(X - 2) (y + 1) + (y - 1) (x - 2) Which of the following expressions is equivalent to the expression shown? A. 2y B. (X - 2) C. 2(x - 2) D. 2y(x - 2)

(D) the question requires an understanding of how to use the distributive property to generate equivalent linear expressions. (X - 2) is the common factor so... (X - 2) (y +1 + y - 1) 2y(X - 2)

Consider the algorithm shown Step 1. Select a numerical value for the variable K Step 2. Add 3 to K Step 3. Multiply the result by 8 Step 4. Cube the result Step 5. End

Executing the algorithm shown is equivalent to evaluating which of the following algebraic expressions? A. (8k + 3)^3 B. 8(k + 3)^3 C. 8^3(k + 3) D. 8^3(k + 3)^3 (D)