Q.1 If x + y = 10 and x - y = 4, what is the value of x?
3
7
6
5
Explanation - Adding the two equations: (x+y) + (x-y) = 10 + 4 ⇒ 2x = 14 ⇒ x = 7.
Correct answer is: 7
Q.2 The quadratic equation x^2 - 5x + 6 = 0 has roots:
2 and 3
1 and 6
3 and 2
2 and 4
Explanation - Factorizing: x^2 - 5x + 6 = (x-2)(x-3) = 0, so roots are x=2,3.
Correct answer is: 2 and 3
Q.3 If (x-2)(x+3) = 0, what are the roots of the equation?
x=2 and x=-3
x=-2 and x=3
x=2 only
x=-3 only
Explanation - Setting each factor to zero: x-2=0 ⇒ x=2, x+3=0 ⇒ x=-3.
Correct answer is: x=2 and x=-3
Q.4 Solve for x: 2x - 7 = 5
6
1
5
2
Explanation - 2x - 7 = 5 ⇒ 2x = 12 ⇒ x = 6.
Correct answer is: 6
Q.5 The sum of the roots of x^2 - 9x + 20 = 0 is:
9
20
29
5
Explanation - Sum of roots of ax^2+bx+c=0 is -b/a = -(-9)/1 = 9.
Correct answer is: 9
Q.6 If 3x + 2 = 11, then x = ?
3
2
5
4
Explanation - 3x + 2 = 11 ⇒ 3x = 9 ⇒ x = 3.
Correct answer is: 3
Q.7 Factorize: x^2 - 16
(x-4)(x+4)
(x-8)(x+2)
(x-2)(x+8)
Cannot factorize
Explanation - Difference of squares: a^2 - b^2 = (a-b)(a+b).
Correct answer is: (x-4)(x+4)
Q.8 If x^2 + x - 6 = 0, then one root is:
2
-3
Both 2 and -3
1
Explanation - Factorizing: x^2 + x - 6 = (x+3)(x-2)=0 ⇒ x=2, x=-3.
Correct answer is: Both 2 and -3
Q.9 Solve: 5x - 3 = 2x + 9
4
5
6
7
Explanation - 5x - 3 = 2x + 9 ⇒ 3x = 12 ⇒ x = 4.
Correct answer is: 4
Q.10 The roots of x^2 - 4x + 3 = 0 are:
1 and 3
2 and 2
3 and 1
Both 1 and 3
Explanation - Factorizing: x^2 -4x +3 = (x-1)(x-3)=0 ⇒ x=1,3.
Correct answer is: Both 1 and 3
Q.11 Simplify: (x^2 + 2x + 1)
(x+1)^2
(x-1)^2
(x+1)(x-1)
Cannot simplify
Explanation - x^2 + 2x + 1 = (x+1)^2 (perfect square trinomial).
Correct answer is: (x+1)^2
Q.12 If 2x + 3y = 12 and x = 3, then y = ?
1
2
3
0
Explanation - 2*3 + 3y = 12 ⇒ 6 + 3y = 12 ⇒ 3y=6 ⇒ y=2
Correct answer is: 2
Q.13 Solve: x^2 - 7x + 10 = 0
x=2,5
x=5,2
x=1,10
x=-2, -5
Explanation - Factorizing: x^2 -7x +10 = (x-2)(x-5)=0 ⇒ x=2,5.
Correct answer is: x=2,5
Q.14 If (x+3)(x-4)=0, x = ?
-3,4
3,-4
4 only
-3 only
Explanation - Set each factor to zero: x+3=0 ⇒ x=-3, x-4=0 ⇒ x=4.
Correct answer is: -3,4
Q.15 Solve for x: 4x - 7 = 9
4
3
5
2
Explanation - 4x - 7 = 9 ⇒ 4x = 16 ⇒ x = 4.
Correct answer is: 4
Q.16 Factorize: x^2 + 5x + 6
(x+2)(x+3)
(x+1)(x+6)
(x+3)(x+2)
(x+2)(x+4)
Explanation - x^2 + 5x + 6 = (x+2)(x+3).
Correct answer is: (x+2)(x+3)
Q.17 The roots of 2x^2 - 8x = 0 are:
0 and 4
0 and 2
2 and 4
0 and -4
Explanation - Factor: 2x(x-4)=0 ⇒ x=0,4.
Correct answer is: 0 and 4
Q.18 Solve: 3x + 4 = 19
5
4
6
7
Explanation - 3x + 4 =19 ⇒ 3x=15 ⇒ x=5.
Correct answer is: 5
Q.19 Factorize: x^2 - 9x + 18
(x-3)(x-6)
(x-2)(x-9)
(x-1)(x-18)
(x-6)(x-3)
Explanation - Find two numbers that multiply to 18 and add to -9: -3 and -6.
Correct answer is: (x-3)(x-6)
Q.20 Solve for x: x/2 + 3 = 7
8
6
4
2
Explanation - x/2 +3=7 ⇒ x/2=4 ⇒ x=8.
Correct answer is: 8
Q.21 If x^2 = 16, then x = ?
4 only
-4 only
4 or -4
0
Explanation - x^2 =16 ⇒ x=±4.
Correct answer is: 4 or -4
Q.22 Simplify: (x+2)^2
x^2 + 4x + 4
x^2 + 2x + 4
x^2 + 2x +2
x^2 + 4x +2
Explanation - (x+2)^2 = x^2 + 2*2*x + 2^2 = x^2 +4x +4.
Correct answer is: x^2 + 4x + 4
Q.23 Solve for x: 7x - 5 = 16
3
2
4
5
Explanation - 7x -5=16 ⇒ 7x=21 ⇒ x=3.
Correct answer is: 3
Q.24 If x - y = 3 and x + y = 9, x = ?
6
3
9
12
Explanation - Adding equations: 2x = 12 ⇒ x=6.
Correct answer is: 6
Q.25 Factorize: x^2 - 5x + 6
(x-2)(x-3)
(x+2)(x-3)
(x-1)(x-6)
(x-3)(x-2)
Explanation - x^2 -5x +6 = (x-2)(x-3).
Correct answer is: (x-2)(x-3)