CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the sum of the first n odd natural numbers?
A. n²+n
B. n²
C. n(n+1)
D. 2n
Correct Answer: B
The identity 1+3+5+…+(2n−1)=n².
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 2x + 5 = 3(x − 2).
A. 13
B. 9
C. 11
D. 7
Correct Answer: C
2x+5=3x−6, so x=11.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 2a = 3b, what is a:b?
A. 3:2
B. 2:3
C. 1:3
D. 3:1
Correct Answer: A
2a=3b implies a/b=3/2, so a:b=3:2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
y varies inversely as x. If y=10 when x=4, find y when x=8.
A. 20
B. 2.5
C. 5
D. 8
Correct Answer: C
xy=k=40. When x=8, y=40/8=5.
CSS - PMS - CCE - PCS - Mathematics
Algebra
x varies directly as y. If x=12 when y=3, find x when y=7.
A. 21
B. 28
C. 24
D. 32
Correct Answer: B
x=ky. k=12/3=4, so x=4×7=28.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: |x − 3| = 5.
A. x = 8 or x = −2
B. x = 8 only
C. x = −2 only
D. x = 3 or x = 5
Correct Answer: A
|x−3|=5 gives x−3=5 or x−3=−5.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve the inequality: −2x < 10.
A. x > 5
B. x > −5
C. x < −5
D. x < 5
Correct Answer: B
Dividing by a negative reverses the sign: x>−5.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve the inequality: 3x − 5 > 7.
A. x > 4
B. x < 4
C. x > 2
D. x ≥ 4
Correct Answer: A
3x>12, so x>4.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If f(x)=2x²−3x+1, find f(2).
A. 3
B. 5
C. 1
D. 7
Correct Answer: A
f(2)=2(4)−6+1=3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the coefficient of x² in (x + 2)(x² − 3x + 4)?
A. 2
B. -1
C. -2
D. 1
Correct Answer: B
Expansion gives x³−x²−2x+8, so the coefficient is −1.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the degree of 5x⁴ − 3x + 7?
A. 5
B. 3
C. 1
D. 4
Correct Answer: D
The highest power of x is 4.
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.