Algebra Adventures
Factor x2−5x+6x
(x-3)(x-2)
A right triangle has legs of length 6 and 8. Find the length of the hypotenuse.
10
Simplify sin2(x)+cos2(x)
1
If an item costs $120 and is on sale for 25% off, what is the sale price?
$90
In the 16th century, Gerolamo Cardano conceived these numbers to solve certain cubics. Numbers of this type multiplied by their conjugate will always result in real numbers. Every one of these has a real part and an imaginary part.
Complex numbers
Solve the system of equations:
2x+y=10
x−y=4
x= 14/3 and y= 2/3
a logical argument that uses known facts, axioms, and postulates to demonstrate the truth of a given statement by following a series of steps and deductions
Proof
Use the unit circle to find tan(60°)
Square root 3
The average of five numbers is 8. If four of the numbers are 6, 9, 12, and 7, what is the fifth number?
6
Identify the transformation of the graph of f(x)=x2 to f(x)=(x−3)2 + 4
Right by 3 units and up 4 units
Find the roots of the quadratic equation 2x2−7x+3=0
(7±5)/4
A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 10 cm. What is the volume of the prism?
400cm3
From a point 100 meters away from the base of a tower, the angle of elevation to the top of the tower is 45°. Find the height of the tower.
100m
Define mode
The mode is the value that appears most frequently in a data set
What is the number of ways to arrange the letters in the word "MATH"?
24
solve for x: log2(x+3)=5
A pyramid has a square base with a side length of 6 units and a height of 9 units. Find the volume of the pyramid. (v= 1/3Bh)
108 square units
What are the side lengths of a 30, 60, 90 triangle?
x, 2x, and xsquare root 3
What is the product of 6, x2+3x, and x-10
6x3 - 78x2 + 180x
Andrey Markov’s namesake one of these can be used to prove Chebyshev’s one of these, though that one is also sometimes called Chebyshev’s, since it preceded Markov’s work. In engineering sciences, some of these are used to rationalize the neglect of a variable based on several orders of magnitude in relation to another variable. These notations can be read “a is much greater than b” or “a is much less than b”. Name these relations between two or more expressions which are not equal.
Inequalities
The origin of algebra came from Muhammad ibn Musa Al-Khwarizmi. The word algebra is derived from his book called what? (You can either name the book or the language in which it was written)
Al-Jabr (arabic)
The length of a rectangle is twice its width. If the area of the rectangle is 200 square units, find the dimensions of the rectangle.
10x20
A ladder is leaning against a wall. The angle between the ladder and the ground is 60°, and the distance between the base of the ladder and the wall is 5 meters. How tall is the wall?
5 x sin(60°) or 4.33 m
Liam can type faster than any of his classmates. He took a test that showed he can type 700 words in 5 minutes. At this rate, how long does Liam need to type a 20 page paper with 250 words on each page? Round your answer to the nearest whole minute.
36 mins
While it is not the polar coordinate system, this system does contain x and y reference axes. Name this coordinate system with each point being a unique ordered pair.
Cartesian coordinate system