Algebra/Arithmetic
Solve for x: 3x + 7 = 22.
x = 5
What is the sum of the interior angles of a triangle?
180°
Find sin(7π/6)
-1/2
Find the limit as x approaches infinity of 1/x^7
0
Which ancient civilization developed a number system based on 60, which still influences how we measure time?
The Babylonians
Simplify: (2x³)(3x²).
6x⁵
What is the area of a circle with radius 6?
36π square units
Find the amplitude of y = −4cos(3x) + 2.
4
Find the equation of the line tangent to the function f(x) = 5x³ − 2x + 7 at the (1,10).
(Tell your answer in the form y=mx+b)
y=13x-3
Name the theorem:
a2+b2=c2
Pythagorean theorem
If x + y = 10 and xy = 21,
find x² + y².
58
A right triangle has legs of 6 and 8. Find its hypotenuse.
10
If f(x) = x² + 1 and g(x) = 3x − 2, find f(g(2)).
17
Find the derivative of
f(x)=(3x5)(e7x)
15(x4)(e7x)+21(x5)(e7x)
Which mathematician is credited with introducing the Cartesian coordinate system?
René Descartes
Solve: |2x − 5| = x + 1.
x = 6 or x = 4/3.
Each interior angle of a regular polygon is 150°. How many sides does it have?
12 sides
Solve for x on 0 <= x < 2π
(Hint there are 4 answers)
x= π/4, 3π/4, 5π/4, 7π/4
Find the derivative of 8^x
8xln(8)
Which two mathematicians independently developed calculus?
(Name 1 and you get points)
Isaac Newton and Gottfried Wilhelm Leibniz
Express your answer as a power of 3:
(33^3)/(33)(33)2(33)3
39
A sector has radius 6 and central angle 60°. Find its area.
6π square units
Solve for x:
log2(x)+log2(x-2)=3
4
Integral of tan(x) dx
ln|sec(x)| + C or ln|1/cos(x)| + C
Which mathematician is famous for proving Fermat's Last Theorem in 1994?
Andrew Wiles