NCSSM PLACEMENT TESTQuestions And Answers
Latest Updates 2025/2026 With Correct Answers
100% With Complete Solutions Pass Guaranteed |
Graded A+ |
NCSSM PLACEMENT
NCSSM Practice Placement Test (Sample 2025/2026)
(All questions are original practice examples.)
1. Solve for ( x ):
( 3(x - 2) = 2x + 5 )
Answer: ( x = 11 )
Rationale:
Expand: ( 3x - 6 = 2x + 5 )
Subtract ( 2x ): ( x - 6 = 5 )
Add 6: ( x = 11 )
2. Which expression is equivalent to ( (x^3)^4 )?
A. ( x^7 )
B. ( x^{12} )
C. ( x^{81} )
D. ( x^{3/4} )
, Answer: B. ( x^{12} )
Rationale: Multiply exponents when raising a power to a power → (
(x^a)^b = x^{a \times b} ).
3. The graph of ( y = 2x + 3 ) intersects the y-axis at:
A. (0, 2)
B. (0, 3)
C. (3, 0)
D. (2, 0)
Answer: B. (0, 3)
Rationale: The y-intercept is the constant term when ( x = 0 ).
4. Simplify: ( \dfrac{2x^2y}{4xy^3} )
Answer: ( \dfrac{x}{2y^2} )
Rationale:
Cancel common factors:
( \frac{2x^2y}{4xy^3} = \frac{2}{4} \times \frac{x^{2-1}}{y^{3-1}} =
\frac{1}{2} \times \frac{x}{y^2} ).
5. If ( f(x) = 3x^2 - 2x + 4 ), find ( f(-1) ).
Answer: ( 9 )
Rationale: Substitute: ( 3(-1)^2 - 2(-1) + 4 = 3(1) + 2 + 4 = 9 ).
,6. A right triangle has legs 6 cm and 8 cm. Find the
hypotenuse.
Answer: ( 10 \text{ cm} )
Rationale: Use Pythagorean theorem: ( c = \sqrt{6^2 + 8^2} = \sqrt{36
+ 64} = \sqrt{100} = 10. )
7. Which of the following represents direct variation?
A. ( y = 3x + 2 )
B. ( y = \frac{4}{x} )
C. ( y = 7x )
D. ( y = x^2 + 4 )
Answer: C. ( y = 7x )
Rationale: Direct variation means ( y = kx ), where ( k ) is a constant.
8. Simplify: ( \sqrt{50} )
Answer: ( 5\sqrt{2} )
Rationale: ( 50 = 25 \times 2 ), and ( \sqrt{25} = 5 ).
9. If ( \sin(\theta) = \frac{3}{5} ), what is ( \cos(\theta) )
(acute angle)?
Answer: ( \frac{4}{5} )
Rationale: Use ( \sin^2 + \cos^2 = 1 ).
( \cos = \sqrt{1 - (3/5)^2} = \sqrt{1 - 9/25} = \sqrt{16/25} = 4/5 ).
, 10. Which of these is a function?
A. ( x^2 + y^2 = 9 )
B. ( y = \pm \sqrt{x} )
C. ( y = 2x - 1 )
D. ( x = 4 )
Answer: C. ( y = 2x - 1 )
Rationale: A function gives only one y-value for each x-value.
( y = 2x - 1 ) passes the “vertical line test.”
Science Section
11. Which subatomic particle determines the element’s
identity?
A. Neutron
B. Proton
C. Electron
D. Isotope
Answer: B. Proton
Rationale: The atomic number equals the number of protons —
unique for each element.
12. What happens to the kinetic energy of molecules as
temperature increases?
A. It decreases
B. It increases
Latest Updates 2025/2026 With Correct Answers
100% With Complete Solutions Pass Guaranteed |
Graded A+ |
NCSSM PLACEMENT
NCSSM Practice Placement Test (Sample 2025/2026)
(All questions are original practice examples.)
1. Solve for ( x ):
( 3(x - 2) = 2x + 5 )
Answer: ( x = 11 )
Rationale:
Expand: ( 3x - 6 = 2x + 5 )
Subtract ( 2x ): ( x - 6 = 5 )
Add 6: ( x = 11 )
2. Which expression is equivalent to ( (x^3)^4 )?
A. ( x^7 )
B. ( x^{12} )
C. ( x^{81} )
D. ( x^{3/4} )
, Answer: B. ( x^{12} )
Rationale: Multiply exponents when raising a power to a power → (
(x^a)^b = x^{a \times b} ).
3. The graph of ( y = 2x + 3 ) intersects the y-axis at:
A. (0, 2)
B. (0, 3)
C. (3, 0)
D. (2, 0)
Answer: B. (0, 3)
Rationale: The y-intercept is the constant term when ( x = 0 ).
4. Simplify: ( \dfrac{2x^2y}{4xy^3} )
Answer: ( \dfrac{x}{2y^2} )
Rationale:
Cancel common factors:
( \frac{2x^2y}{4xy^3} = \frac{2}{4} \times \frac{x^{2-1}}{y^{3-1}} =
\frac{1}{2} \times \frac{x}{y^2} ).
5. If ( f(x) = 3x^2 - 2x + 4 ), find ( f(-1) ).
Answer: ( 9 )
Rationale: Substitute: ( 3(-1)^2 - 2(-1) + 4 = 3(1) + 2 + 4 = 9 ).
,6. A right triangle has legs 6 cm and 8 cm. Find the
hypotenuse.
Answer: ( 10 \text{ cm} )
Rationale: Use Pythagorean theorem: ( c = \sqrt{6^2 + 8^2} = \sqrt{36
+ 64} = \sqrt{100} = 10. )
7. Which of the following represents direct variation?
A. ( y = 3x + 2 )
B. ( y = \frac{4}{x} )
C. ( y = 7x )
D. ( y = x^2 + 4 )
Answer: C. ( y = 7x )
Rationale: Direct variation means ( y = kx ), where ( k ) is a constant.
8. Simplify: ( \sqrt{50} )
Answer: ( 5\sqrt{2} )
Rationale: ( 50 = 25 \times 2 ), and ( \sqrt{25} = 5 ).
9. If ( \sin(\theta) = \frac{3}{5} ), what is ( \cos(\theta) )
(acute angle)?
Answer: ( \frac{4}{5} )
Rationale: Use ( \sin^2 + \cos^2 = 1 ).
( \cos = \sqrt{1 - (3/5)^2} = \sqrt{1 - 9/25} = \sqrt{16/25} = 4/5 ).
, 10. Which of these is a function?
A. ( x^2 + y^2 = 9 )
B. ( y = \pm \sqrt{x} )
C. ( y = 2x - 1 )
D. ( x = 4 )
Answer: C. ( y = 2x - 1 )
Rationale: A function gives only one y-value for each x-value.
( y = 2x - 1 ) passes the “vertical line test.”
Science Section
11. Which subatomic particle determines the element’s
identity?
A. Neutron
B. Proton
C. Electron
D. Isotope
Answer: B. Proton
Rationale: The atomic number equals the number of protons —
unique for each element.
12. What happens to the kinetic energy of molecules as
temperature increases?
A. It decreases
B. It increases
