Praxis 5165
Mathematics: Content Knowledge
Maryland Passing Score
160
MSDE Score Code
7403
Retake Wait
28 days
Score Valid
10 years
10 Free Practice Questions
Question 1 · Number Theory
Modular arithmetic involves computing remainders after division by a fixed modulus. What is 23 mod 5?
- A
- B
- C
- D
Explanation
23 mod 5 means the remainder when 23 is divided by 5. Since 23 = 4 × 5 + 3, the remainder is 3. A remainder of 1 would mean 23 = 4×5+1 = 21, which is false. A remainder of 2 would mean 23 = 4×5+2 = 22, which is false. A remainder of 4 would mean 23 = 3×5+4 = 19, which is false.
Question 2 · Number Theory
The relationship between the GCD and LCM of two positive integers a and b is given by the formula GCD(a, b) × LCM(a, b) = a × b. If GCD(12, 18) = 6, what is LCM(12, 18)?
- A
- B
- C
- D
Explanation
Using the formula: LCM(12, 18) = (12 × 18) / GCD(12, 18) = 216 / 6 = 36. 18 is a factor of 36 but is not the LCM. 24 is a multiple of 12 but not of 18. 72 would result from incorrectly multiplying 12 × 6, rather than using the correct formula.
Question 3 · Number Theory
A factor of an integer n is any integer that divides n evenly with no remainder. How many positive factors does the number 24 have?
- A
- B
- C
- D
Explanation
The positive factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, giving a total of 8 factors. 4 factors would be too few and does not account for all divisors of 24. 6 factors is incorrect; there are more divisors. 12 is itself a factor of 24 but is not the count of all factors.
Question 4 · Number Theory
The number 1 is a special integer that is neither prime nor composite. Which of the following correctly explains why 1 is not considered a prime number?
- A
- B
- C
- D
Explanation
A prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 has only one positive divisor (itself), so it fails this criterion. Being odd (A) is not the reason; 3, 5, 7 are odd and prime. Being less than 2 (C) is a consequence of the definition but not the core reason. Option D is misleading because primality is defined by the count of divisors, not divisibility by primes.
Question 5 · Number Theory
A multiple of an integer n is any integer that can be expressed as n times another integer. Which of the following is NOT a multiple of 7?
- A
- B
- C
- D
Explanation
45 is not a multiple of 7 because 45 ÷ 7 ≈ 6.43, which is not an integer. 14 = 7 × 2, so it is a multiple of 7. 35 = 7 × 5, so it is a multiple of 7. 42 = 7 × 6, so it is a multiple of 7.
Question 6 · Number Theory
The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be expressed uniquely as a product of prime numbers, up to the order of the factors. What is the prime factorization of 60?
- A
- B
- C
- D
Explanation
The prime factorization of 60 is 2² × 3 × 5 = 4 × 3 × 5 = 60, using only prime factors. Option B (2 × 3 × 10) is not a prime factorization because 10 is not prime. Option C (2² × 15) is not fully factored because 15 = 3 × 5 is not prime. Option D (4 × 3 × 5) uses 4, which is not prime.
Question 7 · Number Theory
Divisibility rules provide quick ways to determine whether one integer divides another without performing full division. Which of the following numbers is divisible by 9?
- A
- B
- C
- D
Explanation
A number is divisible by 9 if the sum of its digits is divisible by 9. For 342: 3+4+2 = 9, which is divisible by 9, so 342 is divisible by 9. For 235: 2+3+5 = 10, not divisible by 9. For 412: 4+1+2 = 7, not divisible by 9. For 514: 5+1+4 = 10, not divisible by 9.
Question 8 · Number Theory
A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. Which of the following is a composite number?
- A
- B
- C
- D
Explanation
15 is composite because 15 = 3 × 5, giving it divisors other than 1 and itself. 2 is prime (divisors are only 1 and 2). 7 is prime (divisors are only 1 and 7). 11 is prime (divisors are only 1 and 11).
Question 9 · Number Theory
Integers can be classified as positive, negative, or zero. The absolute value of an integer is its distance from zero on the number line. What is the absolute value of −17?
- A
- B
- C
- D
Explanation
The absolute value of −17 is 17 because absolute value represents distance from zero, which is always non-negative. −17 is the original number, not its absolute value. 0 is the absolute value of 0 only. 289 is (−17)², which is the square of −17, not its absolute value.
Question 10 · Number Theory
An integer is divisible by 3 if the sum of its digits is divisible by 3. Which of the following numbers is divisible by 3?
- A
- B
- C
- D
Explanation
For 231: 2+3+1 = 6, which is divisible by 3, so 231 is divisible by 3. For 124: 1+2+4 = 7, not divisible by 3. For 214: 2+1+4 = 7, not divisible by 3. For 251: 2+5+1 = 8, not divisible by 3.
Frequently Asked Questions
What is the Maryland passing score for Praxis 5165?
The Maryland passing score for the Praxis 5165 (Mathematics: Content Knowledge) is 160. This is set by MSDE and differs from other states. Always verify current requirements at msde.maryland.gov.
What is the MSDE score recipient code for Maryland?
The Maryland State Department of Education (MSDE) score recipient code is 7403. Select this code at every Praxis registration to have your scores sent directly to MSDE for licensure processing.
How long do I have to wait to retake the Praxis 5165?
Maryland requires a 28-day wait between Praxis 5165 attempts. This wait applies regardless of your score. Plan your test dates accordingly.
How many questions are on the Praxis 5165?
The Praxis 5165 contains 120 selected-response questions plus 2 constructed-response items (for PLT exams). You have 2 hours to complete the exam.
What domains does the Praxis 5165 cover?
The Praxis 5165 covers content knowledge specific to Mathematics: Content Knowledge. See the official ETS test framework for the complete domain breakdown.
How long are Praxis 5165 scores valid in Maryland?
Praxis scores are valid for 10 years from the test date in Maryland. Scores do not expire for the purposes of Maryland teacher certification within this window.
Can I use a calculator on the Praxis 5165?
No on-screen calculator is provided for the Praxis 5165.
Does PraxisPass tell me when I'm ready to book the Praxis 5165?
Yes. PraxisPass is the only platform that tells you exactly when to book your exam. When your Pass Probability Score (PPS) for the 5165 reaches 90%, sustained over 7 consecutive days with 2 passing mock exams, PraxisPass declares you ready and prompts you to schedule.
Is PraxisPass free to use for the Praxis 5165?
PraxisPass offers a permanent free tier that includes your Exam Readiness Score diagnostic, Pass Probability Score baseline, and your first complete 25-minute study mission for the 5165. The Individual plan at $19/month unlocks unlimited study sessions across all 50+ Maryland Praxis exams.