CSS - PMS - CCE - PCS - Mathematics
Algebra
Which expression has x − 1 as a factor?
A. x² + 2x + 2
B. x³ − 2x + 4
C. x³ + x + 1
D. x³ − 4x² + x + 2
Correct Answer: D
By the Factor Theorem, substitute x=1. Only 1−4+1+2=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Find the remainder when x² + 3x + 5 is divided by x − 2.
A. 9
B. 13
C. 11
D. 15
Correct Answer: D
By the Remainder Theorem, remainder=f(2)=4+6+5=15.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify: 2√3 × 3√6.
A. 12√3
B. 18√3
C. 6√2
D. 18√2
Correct Answer: D
2×3×√18=6×3√2=18√2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Rationalize 1/(√5 − √2).
A. (√5 + √2)/7
B. (√5 − √2)/3
C. (√5 + √2)/3
D. √5 + √2
Correct Answer: C
Multiply numerator and denominator by √5+√2. Denominator becomes 5−2=3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify √50.
A. 5√2
B. 2√5
C. 10√5
D. 25√2
Correct Answer: A
√50=√(25×2)=5√2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Evaluate √9.
A. 3
B. 6
C. −3
D. 9
Correct Answer: A
The principal square root of 9 is 3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 3ˣ = 81, find x.
A. 6
B. 5
C. 3
D. 4
Correct Answer: D
81=3⁴, so x=4.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Evaluate: (2³)⁴.
A. 4096
B. 2048
C. 512
D. 64
Correct Answer: A
(2³)⁴=2¹²=4096.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify: (x³ × x⁴)/x².
A. x⁷
B. x⁶
C. x⁵
D. x⁹
Correct Answer: C
Add exponents when multiplying and subtract when dividing: 3+4−2=5.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Factorize x² − 16.
A. (x − 8)(x + 2)
B. (x + 8)(x − 2)
C. (x − 4)(x + 4)
D. (x − 4)²
Correct Answer: C
This is a difference of squares: x²−4²=(x−4)(x+4).
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify: (a + b)² − (a − b)².
A. 4ab
B. a²+b²
C. 4a²b²
D. 2ab
Correct Answer: A
Expanding both expressions and subtracting leaves 4ab.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If x + 1/x = 5, find x² + 1/x².
A. 21
B. 25
C. 23
D. 27
Correct Answer: C
Square: x²+2+1/x²=25, so x²+1/x²=23.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the product of the roots of 2x² − 7x + 3 = 0?
A. 7/2
B. 3/2
C. 2/3
D. −3/2
Correct Answer: B
Product of roots=c/a=3/2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the sum of the roots of x² − 8x + 15 = 0?
A. 15
B. -8
C. 23
D. 8
Correct Answer: D
For ax²+bx+c, sum of roots=−b/a=8.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the discriminant of x² − 4x + 4 = 0?
A. 8
B. 0
C. 16
D. 4
Correct Answer: B
Discriminant b²−4ac=16−16=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Factorize x² + 7x + 12.
A. (x + 1)(x + 12)
B. (x + 3)(x + 4)
C. (x − 3)(x − 4)
D. (x + 2)(x + 6)
Correct Answer: B
Two numbers whose sum is 7 and product is 12 are 3 and 4.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the positive root of x² − 9 = 0?
A. 9
B. −3
C. 3
D. 6
Correct Answer: C
x²=9, so x=±3. The positive root is 3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What are the roots of x² − 5x + 6 = 0?
A. −2 and −3
B. 1 and 6
C. 2 and 3
D. 3 and 6
Correct Answer: C
x²−5x+6=(x−2)(x−3), so roots are 2 and 3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 3x − 2y = 4 and x + y = 8, find x.
A. 5
B. 3
C. 2
D. 4
Correct Answer: D
y=8−x. Substitute: 3x−2(8−x)=4, so 5x=20 and x=4.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 2x + 3y = 13 and x + y = 5, find y.
A. 4
B. 1
C. 2
D. 3
Correct Answer: D
From x=5−y. Substitute: 2(5−y)+3y=13, so y=3.