Elementary Algebra - One Line Questions
1.
If x = -1, what is the value of 3x^3 - 2x^2 + 5x - 4? —
-10
2.
What is the product of the roots of the quadratic equation 2x^2 - 5x + 3 = 0? —
3/2
3.
Factorize: 4x^2 - 25y^2. —
(2x - 5y)(2x + 5y)
4.
Which algebraic identity is used to find the difference of two squares? —
a^2 - b^2 = (a-b)(a+b)
5.
Which of the following is NOT a factor of x^3 - 8? —
(x + 2)
6.
Factorize the expression x^2 - 9. —
(x - 3)(x + 3)
7.
What is the solution set for the equation |x| = 7? —
{7, -7}
8.
What is the value of (x + y)^2 - (x - y)^2? —
4xy
9.
If a:b = 1:2 and b:c = 3:4, what is the ratio a:b:c? —
3:6:8
10.
If y = 3x - 2, what is the value of y when x = 4? —
10
11.
Solve for x: sqrt(x) = 5. —
25
12.
What is the value of the expression 5a + 3b when a=2 and b=4? —
22
13.
If x/3 = 5, what is the value of x? —
15
14.
If x = 2, y = 3, what is the value of 2x^2 + 3y? —
25
15.
What is the average of the first 5 natural numbers? —
3
16.
Solve for x: 2^x = 8. —
3
17.
If x = 3, what is the value of (x^2 - 1) / (x + 1)? —
4
18.
If (x - 2)(x + 3) = 0, what are the possible values of x? —
2 and -3
19.
If x:y = 2:3 and y:z = 4:5, what is the ratio x:z? —
8:15
20.
Solve for x: 1/x + 1/2x = 3/4. —
2/3
21.
If a = 5, b = -2, what is the value of a^2 - b^2? —
29
22.
What is the value of the expression (a^2 + b^2) if a + b = 7 and ab = 10? —
29
23.
If a number is multiplied by 5 and then 3 is added to the result, the answer is 18. The number is: —
3
24.
If two angles of a triangle are x and 2x, and the third angle is 60 degrees, what is the value of x? —
30
25.
If three consecutive integers are x, x+1, and x+2, their sum is: —
3x + 3
26.
If x is an integer such that 5 < x < 10, how many possible values of x are there? —
4
27.
If a number is increased by 20% and then decreased by 20%, the net change is: —
4% decrease
28.
What is the value of 'x' in the equation 2x + 5 = 15? —
5
29.
Solve for 'y' in the equation 3y - 7 = 8. —
5
30.
Solve for x: 4x - 3 = 2x + 7. —
5
31.
What is the value of 'k' if (x - 2) is a factor of x^2 + kx + 6? —
-5
32.
Solve for x: log_2(x) = 3. —
8
33.
If a + b = 10 and a - b = 4, what is the value of 'a'? —
7
34.
If x + 1/x = 3, what is the value of x^2 + 1/x^2? —
7
35.
If x + y = 12 and xy = 35, what is the value of x^2 + y^2? —
74
36.
What is the value of the expression (a+b)(a-b) when a=5 and b=3? —
16
37.
What is the formula for the nth term of an arithmetic progression? —
a + (n-1)d
38.
Simplify: (a^m * a^n) / a^p —
a^(m+n-p)
39.
What is the formula for the sum of a geometric progression? —
a(r^n - 1) / (r - 1)
40.
What is the value of the determinant of a 2x2 matrix [[a, b], [c, d]]? —
ad - bc
41.
What is the general form of a linear equation in two variables? —
ax + by + c = 0
42.
What is the discriminant of the quadratic equation ax^2 + bx + c = 0? —
b^2 - 4ac
43.
If the cost price of an item is 'C' and the selling price is 'S', the profit is given by: —
S - C
44.
What is the sum of the roots of the quadratic equation ax^2 + bx + c = 0? —
-b/a
45.
What is the sum of the first 'n' odd natural numbers? —
n^2
46.
If the perimeter of a square is 4s, what is its area? —
s^2
47.
What is the value of x^0, where x is any non-zero number? —
1
48.
Simplify the expression: 3(x + 2) - 2(x - 1). —
x + 8
49.
Solve the inequality 2x < 10 for x. —
x < 5
50.
Expand the expression (x + y)^2. —
x^2 + 2xy + y^2