CSS - PMS - CCE - PCS - Mathematics
Algebra
A positive number plus its square is 72. What is the number?
A. 8
B. 9
C. 6
D. 12
Correct Answer: A
Let number=x. x²+x−72=0=(x−8)(x+9). Positive solution is 8.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 2x+y=11 and y=x−1, find y.
A. 2
B. 4
C. 3
D. 5
Correct Answer: C
Substitute y=x−1: 3x−1=11, x=4 and y=3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Which quadratic equation has roots 3 and 5?
A. x² − 8x + 15 = 0
B. x² + 8x + 15 = 0
C. x² + 2x − 15 = 0
D. x² − 15x + 8 = 0
Correct Answer: A
Equation is x²−(sum)x+(product)=0. Sum=8 and product=15.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What are the roots of x² + 2x − 8 = 0?
A. 4 and 2
B. −2 and 4
C. −2 and −4
D. 2 and −4
Correct Answer: D
x²+2x−8=(x+4)(x−2), so roots are −4 and 2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: x² = 49.
A. x = −7 only
B. x = 7 only
C. x = 49
D. x = ±7
Correct Answer: D
Both 7 and −7 have square 49.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify: (a²b³)/(ab).
A. a²b²
B. ab²
C. ab³
D. a/b²
Correct Answer: B
Subtract exponents: a²/a=a and b³/b=b².
CSS - PMS - CCE - PCS - Mathematics
Algebra
Simplify: (x² − y²)/(x − y), where x ≠ y.
A. x² + y²
B. x − y
C. 1
D. x + y
Correct Answer: D
x²−y²=(x−y)(x+y); cancel x−y.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If x−y=6 and xy=16, find x²+y².
A. 68
B. 52
C. 84
D. 36
Correct Answer: A
x²+y²=(x−y)²+2xy=36+32=68.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If a+b=10 and ab=21, find a²+b².
A. 79
B. 42
C. 58
D. 100
Correct Answer: C
a²+b²=(a+b)²−2ab=100−42=58.
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.