RATIONAL NUMBERS
What is a rational number?
Any number that can be expressed as a fraction.
What is the square root of 9?
Answer: 3
What is the formula for determining the surface area of a cube?
Answer: 6b2 or (6x b x h)
What are the two parts of a power called?
The two parts of a power are the base and the exponent.
Evaluate: (-10 499)0
Answer: 1
What are the "top" and "bottom" numbers in a fraction called?
Numerator and denominator
Is 6.25 a perfect square? Explain.
Yes, 6.25 is a perfect square. It is the result of multiplying the same number by itself, 2.5 x 2.5.
What is the formula for determining the surface area of a rectangular prism with side lengths of L, W , H ?
Answer: 2(L x H) + 2(L x W) + 2(W x H)
What is the base in: -103?
The base is 10.
Express the following as a single power (do not evaluate):
(23) x (24)
Answer: 27
What is an equivalent fraction to -2/7?
Example: The negative can be on the top, on the bottom or in the middle
What are the perfect squares between 1 and 100, including 1 and 100? (Do not count fractions or decimal numbers.)
There are 10 perfect squares between 1 and 100, including 1 and 100:
1, 4, 9, 16, 25, 36, 49, 64, 81 and 100
What does the term "overlap" mean regarding surface area of composite 3D objects?
Overlap occurs when two or more 3D objects are connected. For every overlap, two faces are removed from the surface area calculation.
How are (-5)2 and -52 different?
The base in the first power is -5 whereas the base in the second power is 5. When evaluated, the answer to the first power is 25, and the answer to the second power is -25.
Express the following as a single power (do not evaluate):
(36) x (38) /(32)x (33)
Answer: 39
(36) x (38) /(32)x (33)
=314 / 35
=39
Which fraction corresponds to 0.125?
Answer: 125/1000
A square parking lot has an area of 1.96 ft2. What is the side length of the parking lot?
Answer: 1.4 ft
Two identical cubes are joined together. How many visible faces does this composite 3D object have?
There are 10 visible faces.
[(2 cubes x 6 faces) - (1 overlap x 2 faces)]
Evaluate:
6 x 5 - 4 x 23
Answer: -2
6 x 5 - 4 x 23
=30 - 4 x 8
=30 - 32
= -2
Evaluate:
(32 x 33)2
Answer: 59 049
(32 x 33)2
=(35)2
=310
=59 049
Is "pi" (3.1415926535...) a rational number? Explain.
No, "pi" is not a rational number. It is an irrational number because it is a non-terminating, non-repeating decimal number.
Using benchmark =, what is the square root of 79.5.
Because 79.5 falls between the perfect squares 64 and 81, its square root would be between 8 and 9. Because 79.5 is only 1.5 units less than 81, its square root would be approximately 8.9.
A 10 cm cube is connected to a 20 cm cube. What is the total surface area of this composite 3D object?
Answer: 2 800 cm^2
[(6 x 10 x 10) + (6 x 20 x 20)] - (2 x 10 x 10)
=(600 + 2 400) - 200
=3 000 - 200
=2 800 cm2
Express the following in standard form:
(7 x 105) + (5 x 104) + (3 x 102) + (8 x 100)
Answer: 750 308
Who can list all 6 exponent laws?
1) x0 = 1
2) (am) x (an) = am+n
3) (am) / (an) = am-n
4) (am)n = a mxn
5) [(am) x (bn)]r = (amr) x (bnr)
5) [(am) / (bn)]r = (amr) / (bnr)