Praxis 5003 Practice Test
Question 1 of 5.
Extract:5,743.12
Which of the following statements must be true about the preceding number?
A. The place value of the digit 5 is the greatest place value of all the digits.
B. The place value of the digit 7 is ten times what the place value of the digit 3 is.
C. The place value of the digit 4 is one thousand times what the place value of the digit 2 is.
D. The place value of the digit 1 is the least place value of all the digits.
E. The place value of the digit 2 is one-hundredth times what the place value of the digit 3 is.
Explanation: Digit 5 is in thousands place, which is greatest. Digit 7 is in hundreds place, digit 3 is in ones place, and hundreds is ten times tens? Actually, hundreds is 100, ones is 1, so 100 is not ten times 1. Wait, option B: place value of 7 is hundreds (100), place value of 3 is ones (1), and 100 is not ten times 1. So false. Option C: place value of 4 is tens (10), place value of 2 is hundredths (0.01), and 10 is not 1000 times 0.01 (which is 0.01*1000=10). Actually, 10 = 1000 * 0.01, so true. Option D: place value of 1 is tenths (0.1), which is not the least; hundredths (0.01) is less. Option E: place value of 2 is hundredths (0.01), place value of 3 is ones (1), and 0.01 is not one-hundredth of 1 (which is 0.01), so true? 0.01 = (1/100)*1, so yes. But only A, C, E are true? But the question says 'select all that apply'. So A, C, E. But option B is false. So correct answers are A, C, E.
Question 2 of 5.
Which of the following is an equation?
A. x = 2
B. x²+xy-y
C. 3x - 4 = 20y^2
D. 13y = y + 1
E. x/5 = 9
Explanation: An equation is a statement that two expressions are equal, containing an equals sign. x=2 is an equation. x²+xy-y is an expression, not an equation. 3x-4=20y^2 is an equation. 13y=y+1 is an equation. x/5=9 is an equation. Therefore, the equations are A, C, D, and E.
Question 3 of 5.
Extract:5x ^ 2 + 2x - 2
Which of the following best describes the expression shown?
A. The expression has two terms, none of which are constants.
B. The expression has two terms, one of which is a constant.
C. The expression has three terms, one of which is a constant.
D. The expression has three terms, all of which are constants.
Explanation: The expression has three terms: 5x², 2x, and -2. The term -2 is a constant. Option A is incorrect because there are three terms and one is a constant. Option B is wrong as there are three terms. Option D is incorrect because not all terms are constants; 5x² and 2x are variable terms.
Question 4 of 5.
Which of the following lists contains all the coefficients of the expression 12x^3 + 7x^2 + 24x?
A. 2, 3
B. 7, 12
C. 7, 12, 24
D. 2, 3, 7, 12, 24
Explanation: Coefficients are the numerical factors of the terms. For 12x³, the coefficient is 12; for 7x², it is 7; for 24x, it is 24. So the coefficients are 12, 7, and 24. Option A lists digits from the exponents. Option B misses 24. Option D includes digits that are not coefficients.
Question 5 of 5.
In terms of x, what is the sum of the lengths of the sides of the preceding polygon?
A. 18x-22
B. 21x-5
C. 23x+32
D. 19x-2
Explanation: To find the sum of the lengths of the sides of the polygon, we first identify the given side lengths: AB = 10- 2x, BC = x+3, CD=4x-5, DE = 6x-7, EF = 62-5, and FA = 42 +2. Next, we add these expressions together: (10-2)+(x+3)+(4x-5)+(6x-7)+(6x-5)+(4x+2). Combining like terms, we group all coefficients of a and constant values: (-2x+x+4x+6x+6x+ 4x)+(10+3-5-7-5+2). Simplifying further, the coefficient of adds up to 192, while the constants simplify to -2. Therefore, the total sum of the lengths of all the sides of the polygon is 19 - 2. This expression represents the perimeter of the polygon in terms of 2.