OSAT Middle Level Mathematics (225)

Free OSAT Middle Level 225 Practice Questions

10 sample questions for the OSAT Middle Level Mathematics (225), with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.

Sections covered on the exam: Number Properties and Number Sense, Relations, Functions, and Algebra, Measurement and Geometry, Probability, Statistics, and Discrete Mathematics, Pedagogical Content Knowledge.

Question 1 · Number Properties and Number Sense
Section 1: Number Properties and Number Sense
Which of the following demonstrates the distributive property of multiplication over addition?
- A.a+b=b+a
- B.a(b+c)=ab+ac
- C.(a+b)+c=a+(b+c)
- D.ab=ba
Show answer and explanation
Answer: B. a(b+c)=ab+ac
The distributive property states that multiplying a number by a sum is the same as multiplying by each addend individually and then adding the products. Hence, a(b+c)=ab+ac.
Question 2 · Relations, Functions, and Algebra
Simplify the expression: 3x+4x−2
- A.7x−2
- B.7x+2
- C.x−2
- D.12x
Show answer and explanation
Answer: A. 7x−2
Combine like terms: 3x+4x=7x; final expression: 7x−2
Question 3 · Measurement and Geometry
How many centimeters are in 2.5 meters?
- A.250
- B.25
- C.2.5
- D.0.025
Show answer and explanation
Answer: A. 250
1 meter = 100 centimeters, so 2.5×100=250 cm.
Question 4 · Probability, Statistics, and Discrete Mathematics
What is the mean of the data set: 4, 7, 9, 10, 10?
- A.8
- B.9
- C.10
- D.7
Show answer and explanation
Answer: A. 8
Mean = (4+7+9+10+10)/5=40/5=8
Question 5 · Pedagogical Content Knowledge
Which strategy best promotes conceptual understanding in mathematics?
- A.Memorizing formulas
- B.Repeating practice problems
- C.Using manipulatives
- D.Assigning extra homework
Show answer and explanation
Answer: C. Using manipulatives
Manipulatives help students visualize abstract math concepts and strengthen conceptual understanding.
Question 6 · Number Properties and Number Sense
Which of the following equations shows the associative property of addition?
- A.(3+4)+5=3+(4+5)
- B.3+5=5+3
- C.3×(4+5)=3×4+3×5
- D.3÷1=3
Show answer and explanation
Answer: A. (3+4)+5=3+(4+5)
The associative property states that the grouping of numbers doesn't affect the sum: (a+b)+c=a+(b+c)
Question 7 · Relations, Functions, and Algebra
Simplify the expression: 6x−4x+9
- A.2x+9
- B.10x+9
- C.2x−9
- D.6x+9
Show answer and explanation
Answer: A. 2x+9
Combine like terms: 6x−4x=2x; Final: 2x+9
Question 8 · Measurement and Geometry
Convert 2.75 liters to milliliters.
- A.275 mL
- B.0.275 mL
- C.27.5 mL
- D.2750 mL
Show answer and explanation
Answer: D. 2750 mL
1 liter = 1000 milliliters. 2.75×1000=2750 mL
Question 9 · Probability, Statistics, and Discrete Mathematics
Which measure of central tendency is most affected by extreme values?
- A.Mean
- B.Median
- C.Mode
- D.Range
Show answer and explanation
Answer: A. Mean
The mean includes all data values, so it is most influenced by outliers.
Question 10 · Pedagogical Content Knowledge
Which instructional method emphasizes discovery and problem-solving in mathematics?
- A.Direct instruction
- B.Inquiry-based learning
- C.Memorization drills
- D.Summative testing
Show answer and explanation
Answer: B. Inquiry-based learning
Inquiry-based learning encourages students to explore, question, and build understanding through discovery.

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