Linear Equations
Solve the equation 3x + 7 = 16.
x = 3
Simplify 5^3 * 5^4.
5^7
Solve the equation 2x^2 - 5x + 3 = 0.
x = 1, x = 1.5
Find the derivative of f(x) = 3x^2 + 4x - 2.
f'(x) = 6x + 4
A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 36 cookies?
6 cups of flour
Find the slope of the line passing through the points (2, 4) and (6, 10).
Slope = (10-4)/(6-2) = 1
Find the square root of 144.
√144 = 12
Factor the quadratic equation x^2 + 6x + 9.
(x+3)^2
Calculate the integral of 2x^2 + 3x + 5 with respect to x.
∫(2x^2 + 3x + 5)dx = (2/3)x^3 + (3/2)x^2 + 5x + C
If a car travels at a constant speed of 60 miles per hour, how far will it travel in 4 hours?
240 miles
Write the equation of a line with slope 2 and y-intercept 3.
y = 2x + 3
Simplify √32.
4√2
Solve the inequality 3x + 7 > 10.
x > 1
Find the limit of (x^2 - 4)/(x - 2) as x approaches 2.
The limit is 4.
DAILY DOUBLE: If Sarah has twice as many apples as John, and they have a total of 15 apples, how many apples does Sarah have?
Sarah has 10 apples, John has 5 apples.
Solve the system of equations: 2x + y = 4 and x - y = 3.
x = -1, y = 4
DAILY DOUBLE: Evaluate 2^3 * 3^2.
72
Simplify the expression (x^2 + 5x - 7)(2x^2 - 3).
2x^4 + 10x^3 - 3x^2 - 15x + 21
Determine the critical points of the function f(x) = x^3 - 6x^2 + 9x.
The critical points are x = 1 and x = 3.
A store is offering a 20% discount on all items. If a shirt is originally $25, how much is it after the discount?
The shirt is $20 after the discount.
Determine if the lines y = 2x + 1 and y = -2x + 5 are parallel, perpendicular, or neither.
The lines are perpendicular.
Solve for x: x^2 = 49.
x = 7 or x = -7
Solve the system of equations: 2x + 3y = 7 and 5x - 4y = 8.
x = 4, y = 1
Find the area under the curve y = x^2 from x = 0 to x = 2.
The area is 8/3 square units.
A rectangle has a length of 10 units and a width of 5 units. What is the perimeter of the rectangle?
The perimeter is 30 units.