NCSSM PLACEMENT TEST STUDY GUIDE 2026 100 Complete Practice Questions with Correct Detailed Answers (Recent Version – High-Yield Preparation)

NCSSM PLACEMENT TEST STUDY GUIDE 2026
100 Complete Practice Questions with Correct
Detailed Answers
(Recent Version – High-Yield Preparation)

SECTION A: ALGEBRA & NUMBER SENSE (1–25)

1. Solve: 𝟑𝒙 − 𝟕 = 𝟏𝟏

• A. 4

• B. 5

• C. 6

• D. 7

Answer: Add 7 to both sides: 3𝑥 = 18, so 𝑥 = 6



2. Simplify: 𝟓(𝟐𝒙 − 𝟑) − 𝟒𝒙

• A. 6𝑥 − 15

• B. 10𝑥 − 15

• C. 6𝑥 − 3

• D. 10𝑥 − 3

Answer: 10𝑥 − 15 − 4𝑥 = 6𝑥 − 15


𝒙
3. Solve: 𝟒 = 𝟔

• A. 10

• B. 24

, • C. 12

• D. 18

Answer: Multiply both sides by 4 → 𝑥 = 24



4. What is the slope of the line 𝒚 = 𝟑𝒙 − 𝟓?

• A. −5

• B. 3

• C. 5

• D. −3

Answer: The slope is the coefficient of 𝑥



5. Evaluate: (−𝟑)𝟐 + 𝟒

• A. −5

• B. 13

• C. 1

• D. 7

Answer: 9 + 4 = 13



6. Factor: 𝒙𝟐 − 𝟗

• A. (𝑥−3)2

• B. (𝑥 + 9)(𝑥 − 1)

• C. (𝑥 − 3)(𝑥 + 3)

• D. Prime

Answer: Difference of squares



7. Solve: 𝟐𝒙 + 𝟓 = 𝟏𝟕

, • A. 5

• B. 6

• C. 7

• D. 8

Answer: 2𝑥 = 12, so 𝑥 = 6



𝟏𝟐𝒙𝟐
8. Simplify:
𝟑𝒙

• A. 4𝑥

• B. 9𝑥

• C. 4𝑥 2

• D. 3𝑥

Answer: Divide coefficients and subtract exponents



9. Solve: 𝒙𝟐 = 𝟏𝟔

• A. 4

• B. −4

• C. ±4

• D. 8

Answer: Square roots produce two solutions



10. Which is a linear equation?

• A. 𝑦 = 𝑥 2

• B. 𝑦 = 2𝑥 + 1
1
• C. 𝑦 = 𝑥

• D. 𝑦 = √𝑥

, Answer: Linear equations have degree 1



11. Simplify: 𝟕𝒙 − 𝟐𝒙 + 𝟗

• A. 5𝑥 + 9

• B. 9𝑥

• C. 7𝑥 + 9

• D. 5𝑥



12. Solve: 𝟒𝒙 − 𝟑 = 𝟐𝒙 + 𝟓

• A. 2

• B. 4

• C. 6

• D. 8

Answer: 2𝑥 = 8



13. What is the y-intercept of 𝒚 = −𝟐𝒙 + 𝟕?

• A. −2

• B. 7

• C. 2

• D. −7



14. Simplify: (𝒙𝟑 )(𝒙𝟐 )

• A. 𝑥 5

• B. 𝑥 6

• C. 𝑥 9

• D. 𝑥1