Functions
If f(x) = 3x + 4, what is f(2)?
10
Simplify: (x + 2)(x + 3)
x^2 + 5x + 6
Solve: x^2 - 6x + 9 = 0
What is sin(30°)?
1/2
Solve for x: 3x-5=10
5
If f(x) = x^2 - 5x, what is f(3) + f(-2)?
-6
What is the degree of the polynomial: x^3 + 4x^2 - 7x + 1?
3
Factor completely: x^3 + 3x^2 - x - 3
(x + 3)(x - 1)(x + 1)
In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?
3/5
Simplify: (x^2 - 9) / (x + 3)
x-3
(Note: Factor numerator as (x - 3)(x + 3))
If f(x) = 2x + 1 and g(x) = x - 3, what is f(g(4))?
3
Factor: x^2 - 16
(x - 4)(x + 4)
Divide: (x^3 + 2x^2 - x - 2) ÷ (x + 1)
x^2 + x - 2
What is the period of y = sin(2x)?
π
Solve the system:
2x + y = 7
x - y = 1
x = 2, y = 3
The function f(x) = ax + b passes through the points (2, 5) and (4, 9). Find a.
2
Simplify: (2x - 3)^2
4x^2 - 12x + 9
If x^3 + px^2 + qx + 6 has roots 1, 2, and -3, find p and q.
p = 0, q = -5
If tan(θ) = 3 and sec(θ) = √10 / 3, find sin(θ).
(3√10) / 10
Simplify the expression: √50-√18
5√2 - 3√2 = 2√2
Let f(x) = x^2 - 6x + 10. What is the minimum value of f(x)?
1
If x^2 + bx + 25 = (x + 5)^2, find the value of b.
10
Find all real roots of f(x) = x^3 - 2x^2 - x + 2
x = -1, 1, 2
Solve: 2sin(x) - √2 = 0 for 0 ≤ x ≤ 2π
x = π/4, 3π/4
The quadratic equation x^2+bx+16=0 has one real solution. Find the value of b.