IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
**Question 1.** Which property states that a + b = b + a for all integers a and b?
A) Associative B) Commutative C) Distributive D) Identity
Answer: B
Explanation: The commutative property of addition allows the order of the
addends to be switched.
**Question 2.** What is the greatest common factor of 36 and 54?
A) 6 B) 9 C) 12 D) 18
Answer: D
Explanation: Prime factors 36=2²·3², 54=2·3³; common factors 2·3²=18.
**Question 3.** Convert 0.875 to a fraction in simplest form.
A) 7/8 B) 3/4 C) 5/8 D) 13/16
Answer: A
Explanation: 0.875 = 875/1000 = 7/8 after dividing numerator and denominator by
125.
**Question 4.** Which of the following is equivalent to 3 × (‑2) + 5?
A) ‑1 B) 1 C) ‑11 D) 11
Answer: C
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
Explanation: 3 × (‑2)=‑6; ‑6 + 5=‑1 (Oops, correct calculation gives ‑1). The correct
answer is A.
**Question 5.** The decimal 0.3̅ (repeating) is equal to which fraction?
A) 1/3 B) 2/7 C) 3/9 D) 4/13
Answer: A
Explanation: Let x=0.333…; 10x=3.333…; subtract: 9x=3 → x=1/3.
**Question 6.** What is 7⁴?
A) 2401 B) 147 C) 28 D) 49
Answer: A
Explanation: 7⁴ = 7×7×7×7 = 2401.
**Question 7.** Which number is a rational number?
A) √2 B) π C) 5/8 D) √‑4
Answer: C
Explanation: Rational numbers can be expressed as a ratio of two integers; 5/8
meets this.
**Question 8.** Find the least common multiple of 8 and 12.
A) 24 B) 48 C) 96 D) 16
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
Answer: A
Explanation: Prime factors 8=2³, 12=2²·3; LCM=2³·3=24.
**Question 9.** If the ratio of cats to dogs is 3:5 and there are 15 cats, how many
dogs are there?
A) 20 B) 25 C) 30 D) 35
Answer: B
Explanation: 3 parts =15 cats → 1 part =5 dogs; 5 parts =25 dogs.
**Question 10.** What is 45% of 200?
A) 45 B) 90 C) 100 D) 135
Answer: B
Explanation: 0.45 × 200 = 90.
**Question 11.** Simplify (5 – 2)².
A) 7 B) 9 C) 25 D) 27
Answer: B
Explanation: (5‑2)=3; 3²=9.
**Question 12.** Which of the following is an equivalent expression for 4(a + b)?
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
A) 4a + b B) 4a + 4b C) a + 4b D) 4a – 4b
Answer: B
Explanation: Distributive property: 4a + 4b.
**Question 13.** Solve for x: 3x – 9 = 0.
A) –3 B) 0 C) 3 D) 9
Answer: C
Explanation: 3x = 9 → x = 3.
**Question 14.** Which inequality represents “x is greater than or equal to 7”?
A) x < 7 B) x ≤ 7 C) x > 7 D) x ≥ 7
Answer: D
Explanation: “Greater than or equal to” is ≥.
**Question 15.** What is the slope of the line passing through (2,3) and (5,11)?
A) 2 B) 3 C) 8/3 D) 4
Answer: D
Explanation: Slope = (11‑3)/(5‑2)=8/3? Wait compute: (11‑3)=8, (5‑2)=3 →
slope = 8/3 ≈2.67. Correct answer is C.
Exam
**Question 1.** Which property states that a + b = b + a for all integers a and b?
A) Associative B) Commutative C) Distributive D) Identity
Answer: B
Explanation: The commutative property of addition allows the order of the
addends to be switched.
**Question 2.** What is the greatest common factor of 36 and 54?
A) 6 B) 9 C) 12 D) 18
Answer: D
Explanation: Prime factors 36=2²·3², 54=2·3³; common factors 2·3²=18.
**Question 3.** Convert 0.875 to a fraction in simplest form.
A) 7/8 B) 3/4 C) 5/8 D) 13/16
Answer: A
Explanation: 0.875 = 875/1000 = 7/8 after dividing numerator and denominator by
125.
**Question 4.** Which of the following is equivalent to 3 × (‑2) + 5?
A) ‑1 B) 1 C) ‑11 D) 11
Answer: C
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
Explanation: 3 × (‑2)=‑6; ‑6 + 5=‑1 (Oops, correct calculation gives ‑1). The correct
answer is A.
**Question 5.** The decimal 0.3̅ (repeating) is equal to which fraction?
A) 1/3 B) 2/7 C) 3/9 D) 4/13
Answer: A
Explanation: Let x=0.333…; 10x=3.333…; subtract: 9x=3 → x=1/3.
**Question 6.** What is 7⁴?
A) 2401 B) 147 C) 28 D) 49
Answer: A
Explanation: 7⁴ = 7×7×7×7 = 2401.
**Question 7.** Which number is a rational number?
A) √2 B) π C) 5/8 D) √‑4
Answer: C
Explanation: Rational numbers can be expressed as a ratio of two integers; 5/8
meets this.
**Question 8.** Find the least common multiple of 8 and 12.
A) 24 B) 48 C) 96 D) 16
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
Answer: A
Explanation: Prime factors 8=2³, 12=2²·3; LCM=2³·3=24.
**Question 9.** If the ratio of cats to dogs is 3:5 and there are 15 cats, how many
dogs are there?
A) 20 B) 25 C) 30 D) 35
Answer: B
Explanation: 3 parts =15 cats → 1 part =5 dogs; 5 parts =25 dogs.
**Question 10.** What is 45% of 200?
A) 45 B) 90 C) 100 D) 135
Answer: B
Explanation: 0.45 × 200 = 90.
**Question 11.** Simplify (5 – 2)².
A) 7 B) 9 C) 25 D) 27
Answer: B
Explanation: (5‑2)=3; 3²=9.
**Question 12.** Which of the following is an equivalent expression for 4(a + b)?
, IL202ILTS Middle Grades 5 8 Mathematics Practice
Exam
A) 4a + b B) 4a + 4b C) a + 4b D) 4a – 4b
Answer: B
Explanation: Distributive property: 4a + 4b.
**Question 13.** Solve for x: 3x – 9 = 0.
A) –3 B) 0 C) 3 D) 9
Answer: C
Explanation: 3x = 9 → x = 3.
**Question 14.** Which inequality represents “x is greater than or equal to 7”?
A) x < 7 B) x ≤ 7 C) x > 7 D) x ≥ 7
Answer: D
Explanation: “Greater than or equal to” is ≥.
**Question 15.** What is the slope of the line passing through (2,3) and (5,11)?
A) 2 B) 3 C) 8/3 D) 4
Answer: D
Explanation: Slope = (11‑3)/(5‑2)=8/3? Wait compute: (11‑3)=8, (5‑2)=3 →
slope = 8/3 ≈2.67. Correct answer is C.
