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.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If x + y = 10 and x − y = 4, find x.
A. 7
B. 6
C. 8
D. 3
Correct Answer: A
Adding the equations gives 2x=14, so x=7.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If 2/x = 1/4, find x.
A. 8
B. 4
C. 6
D. 10
Correct Answer: A
Cross multiplication gives x=8.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: (x − 2)/5 = 3.
A. 13
B. 20
C. 15
D. 17
Correct Answer: D
x−2=15, hence x=17.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 3(x + 2) − 2(x − 1) = 13.
A. 5
B. 3
C. 6
D. 4
Correct Answer: A
3x+6−2x+2=13, so x+8=13 and x=5.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 7 − 2x = −9.
A. 7
B. -8
C. 8
D. 9
Correct Answer: C
−2x=−16, so x=8.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 4x + 3 = 2x + 15.
A. 9
B. 8
C. 6
D. 4
Correct Answer: C
2x=12, so x=6.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 2(x − 3) = 14.
A. 10
B. 7
C. 11
D. 8
Correct Answer: A
x−3=7, hence x=10.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: x/3 + 4 = 10.
A. 21
B. 14
C. 12
D. 18
Correct Answer: D
x/3=6, so x=18.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 5x − 7 = 3x + 9.
A. 8
B. 6
C. 9
D. 7
Correct Answer: A
2x=16, so x=8.