The Problem with Words
A rectangle has a length of 3 more than its width. If the area is 40 square units, what is the width?
5 units
x2-5x+6=0
x=2, x=3
Complete the square:
x2+6x + ? = 0
9
0.75
Rational
What famous Greek mathematician is known for the theorem: a2+b2=c2
Pythagoras
The product of two consecutive integers is 56. What are the integers?
7 and 8 or -7 and -8
2x2+3x-2=0
x=0.5, x=-2
Solve by completing the square:
x2+8x=20
x=2,-10
√49
Rational
What number is called the “additive identity” because adding it to a number does not change the value?
0
A ball is thrown upward from the ground. Its height after t seconds is modeled by
h(t)=−16t2+48t
When does the ball hit the ground?
t = 3
3x2-4x+7 = 0
no solutions
Rewrite in vertex form by completing the square:
y=x2-4x+1
y=(x-2)2-3
√18
Irrational
What is the only even prime number?
2
A farmer wants to build a rectangular pen with an area of 96 square feet. The length is 4 feet longer than the width. Find the dimensions.
Width = 8 feet, Length = 12 feet
x2-2x+7=0
x=-1+2√2, x=-1-2√2
Solve by completing the square:
x2-10x+7=0
x=5+3√2, x=5-3√2
True or False: The sum of a rational and irrational number is always rational.
False
The symbol "pi" represents the ratio of a circle’s circumference to what?
Diameter
The sum of two numbers is 15 and their product is 44. Find the numbers.
11 and 4
2x2-6x-5=0
x=(3+√19)/2, x=(3-√19)/2
Rewrite in vertex form:
y = 2x2+12x+5
y = 2(x+3)2-13
Simplify: √72
6√2
A chessboard has 64 squares. If 1 grain of rice is placed on the first square, 2 on the second, 4 on the third, and the pattern continues doubling each time, what type of growth does this represent?
Exponential