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
A factor of a number n is any integer that divides n without leaving a remainder. How many positive factors does the number 36 have?
- A
- B
- C
- D
Explanation
The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, which is 9 factors. To verify using prime factorization: 36 = 2² × 3², so the number of factors is (2+1)(2+1) = 9. 7 would miss two factors. 8 would miss one factor. 10 would incorrectly count a non-factor.
Question 2 · Number Theory
The Least Common Multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers. What is the LCM of 8 and 12?
- A
- B
- C
- D
Explanation
Multiples of 8 are 8, 16, 24, 32... and multiples of 12 are 12, 24, 36... The smallest common multiple is 24. 48 and 96 are common multiples but not the least. 4 is a common factor, not a common multiple.
Question 3 · Number Theory
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Which of the following numbers is prime?
- A
- B
- C
- D
Explanation
61 is prime because it has no divisors other than 1 and 61. 51 = 3 × 17, so it is not prime. 57 = 3 × 19, so it is not prime. 91 = 7 × 13, so it is not prime.
Question 4 · Number Theory
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Which of the following numbers is prime?
- A
- B
- C
- D
Explanation
61 is prime because its only divisors are 1 and 61. 51 = 3 × 17, so it is composite. 57 = 3 × 19, so it is composite. 91 = 7 × 13, so it is composite.
Question 5 · Number Theory
The Greatest Common Divisor (GCD) of two integers is the largest positive integer that divides both numbers without a remainder. What is the GCD of 48 and 36?
- A
- B
- C
- D
Explanation
The GCD of 48 and 36 is 12 because 48 = 12 × 4 and 36 = 12 × 3, and no larger number divides both. 6 divides both but is not the greatest. 18 does not divide 48 evenly (48 ÷ 18 ≈ 2.67). 24 divides 48 but does not divide 36 evenly (36 ÷ 24 = 1.5).
Question 6 · Number Theory
The Least Common Multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers. What is the LCM of 8 and 12?
- A
- B
- C
- D
Explanation
The LCM of 8 and 12 is 24 because 24 = 8 × 3 = 12 × 2, and no smaller positive integer is divisible by both. 48 is a common multiple but not the least. 96 is also a common multiple but much larger. 4 is a common factor, not a common multiple.
Question 7 · Number Theory
A composite number is a positive integer 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
49 = 7 × 7, so it has divisors 1, 7, and 49, making it composite. 37 is prime (no divisors other than 1 and 37). 41 is prime (no divisors other than 1 and 41). 53 is prime (no divisors other than 1 and 53).
Question 8 · Number Theory
The Euclidean algorithm is an efficient method for computing the GCD of two integers. Using the Euclidean algorithm, what is the GCD of 56 and 98?
- A
- B
- C
- D
Explanation
Using the Euclidean algorithm: 98 = 1 × 56 + 42; 56 = 1 × 42 + 14; 42 = 3 × 14 + 0. The last nonzero remainder is 14, so GCD(56, 98) = 14. 7 divides both numbers but is not the greatest common divisor since 14 also divides both. 21 does not divide 56 (56 ÷ 21 ≈ 2.67). 28 does not divide 98 (98 ÷ 28 ≈ 3.5).
Question 9 · Number Theory
Two integers are said to be relatively prime (or coprime) if their greatest common divisor is 1. Which of the following pairs of numbers is relatively prime?
- A
- B
- C
- D
Explanation
GCD(8, 15) = 1 because 8 = 2³ and 15 = 3 × 5 share no common prime factors. GCD(12, 18) = 6 because both are divisible by 6. GCD(15, 25) = 5 because both are divisible by 5. GCD(14, 21) = 7 because both are divisible by 7.
Question 10 · Number Theory
An even integer is any integer that is divisible by 2, and an odd integer is any integer that is not divisible by 2. Which statement about the sum of two odd integers is always true?
- A
- B
- C
- D
Explanation
The sum of two odd integers is always even because an odd number can be written as 2k+1, and (2k+1)+(2m+1) = 2(k+m+1), which is divisible by 2. The sum is not always odd; for example, 3+5=8, which is even. The sum is not always prime; 3+5=8 is not prime. The sum is not always negative; two positive odd numbers give a positive sum.
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.