NCSSM PLACEMENT TEST PRACTICE EXAM QUESTIONS AND CORRECT ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES 2025

NCSSM PLACEMENT TEST
PRACTICE EXAM QUESTIONS AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2025

1. What is the value of xxx if 3x−7=2x+53x - 7 = 2x + 53x−7=2x+5?
A. 2
B. 5
C. 12
D. -12
Subtracting 2x2x2x from both sides gives x−7=5x - 7 = 5x−7=5; add 7 to
both sides: x=12x = 12x=12.
2. Simplify: (2x2y)(3xy2)(2x^2y)(3xy^2)(2x2y)(3xy2)
A. 5x3y35x^3y^35x3y3
B. 6x3y36x^3y^36x3y3
C. 6x2y26x^2y^26x2y2
D. 5x2y25x^2y^25x2y2
Multiply coefficients and add exponents: 2⋅3=6,x2⋅x=x3,y⋅y2=y32 \cdot 3 =
6, x^2 \cdot x = x^3, y \cdot y^2 = y^32⋅3=6,x2⋅x=x3,y⋅y2=y3.
3. Solve for xxx: x+2x−3=2\frac{x + 2}{x - 3} = 2x−3x+2=2
A. 0
B. 4
C. 5
D. 8
Cross-multiplying gives ( x + 2 = 2(x - 3) \Rightarrow x + 2 = 2x - 6
\Rightarrow -x = -8 \Rightarrow x = 8.
4. What is the solution to the inequality 5−2x>115 - 2x > 115−2x>11?
A. x<−3x < -3x<−3
B. x>−3x > -3x>−3
C. x>3x > 3x>3

, D. x<3x < 3x<3
Subtract 5: −2x>6⇒x<−3-2x > 6 \Rightarrow x < -3−2x>6⇒x<−3
5. Factor: x2−9x+20x^2 - 9x + 20x2−9x+20
A. (x−4)(x−5)(x - 4)(x - 5)(x−4)(x−5)
B. (x−4)(x−5)(x - 4)(x - 5)(x−4)(x−5)
C. (x+4)(x−5)(x + 4)(x - 5)(x+4)(x−5)
D. (x+5)(x−4)(x + 5)(x - 4)(x+5)(x−4)
Factors of 20 that sum to -9 are -4 and -5.
6. What is the domain of the function f(x)=1x2−4f(x) = \frac{1}{x^2 -
4}f(x)=x2−41?
A. All real numbers
B. x≠0x \neq 0x =0
C. x≠±2x \neq \pm 2x =±2
D. x>0x > 0x>0
Denominator zero when x2−4=0⇒x=±2x^2 - 4 = 0 \Rightarrow x = \pm
2x2−4=0⇒x=±2
7. Solve: x+1=4\sqrt{x + 1} = 4x+1=4
A. 15
B. 16
C. 17
D. 18
Square both sides: x+1=16⇒x=15x + 1 = 16 \Rightarrow x =
15x+1=16⇒x=15
8. Which of the following is equivalent to log⁡232\log_2 32log232?
A. 4
B. 5
C. 6
D. 2
Since 25=322^5 = 3225=32, log⁡232=5\log_2 32 = 5log232=5
9. If f(x)=3x2+2x−1f(x) = 3x^2 + 2x - 1f(x)=3x2+2x−1, find f(−1)f(-1)f(−1)
A. -2
B. 0
C. 1
D. 4
Substitute: 3(−1)2+2(−1)−1=3−2−1=03(-1)^2 + 2(-1) - 1 = 3 - 2 - 1 =
03(−1)2+2(−1)−1=3−2−1=0
10.Find the slope of the line passing through (2, 3) and (5, 11).
A. 3
B. 2
C. 83\frac{8}{3}38

, D. 38\frac{3}{8}83
Slope = 11−35−2=83\frac{11 - 3}{5 - 2} = \frac{8}{3}5−211−3=38



11.What is the equation of a line with slope 2 and y-intercept -4?
A. y=2x+4y = 2x + 4y=2x+4
B. y=−2x−4y = -2x - 4y=−2x−4
C. y=2x−4y = 2x - 4y=2x−4
D. y=−2x+4y = -2x + 4y=−2x+4
Use slope-intercept form: y=mx+b⇒y=2x−4y = mx + b \Rightarrow y = 2x
- 4y=mx+b⇒y=2x−4
12.Simplify: 2x2−84x\frac{2x^2 - 8}{4x}4x2x2−8
A. x−2x\frac{x - 2}{x}xx−2
B. x+2x\frac{x + 2}{x}xx+2
C. x2−4x\frac{x^2 - 4}{x}xx2−4
D. x2+4x\frac{x^2 + 4}{x}xx2+4
Factor numerator: 2(x2−4)=2(x−2)(x+2)2(x^2 - 4) = 2(x - 2)(x +
2)2(x2−4)=2(x−2)(x+2); cancel with denominator.
13.What is the value of sin⁡(30∘)\sin(30^\circ)sin(30∘)?
A. 0
B. 12\frac{1}{2}21
C. 32\frac{\sqrt{3}}{2}23
D. 1
From unit circle: sin⁡(30∘)=1/2\sin(30^\circ) = 1/2sin(30∘)=1/2
14.The graph of y=∣x−3∣y = |x - 3|y=∣x−3∣ is a:
A. V-shaped graph shifted 3 units right
B. V-shaped graph shifted 3 units left
C. Parabola
D. Line
Absolute value graphs are V-shaped; x−3x - 3x−3 shifts right.
15.If a2=49a^2 = 49a2=49, then:
A. a=7a = 7a=7
B. a=±7a = \pm 7a=±7
C. a=−7a = -7a=−7
D. a=0a = 0a=0
Square roots have both positive and negative values.
16.Convert 0.25 to a fraction:
A. 13\frac{1}{3}31
B. 15\frac{1}{5}51