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: 6bh (6 x base x height)
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 triangular prism with two identical equilateral triangles on the ends?
Answer: (2 x [(b x h) / 2]) + 3bh
What is the base in: (-10)^3?
The base is -10.
Express the following as a single power (do not evaluate):
(2^3)(2^4)
Answer: 2^7
What is an equivalent fraction to 2/7?
Example: 4/14
How many perfect squares are there 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 -5^2 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):
(3^6)(3^8) / (3^2)(3^3)
Answer: 3^9
(3^6)(3^8) / (3^2)(3^3)
=3^14 / 3^5
=3^9
Which fraction corresponds to 0.171717171717...?
Answer: 17/99
A square parking lot has an area of 5256.25 ft^2. What is the side length of the parking lot?
Answer: 72.5 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 2^3
Answer: -2
6 x 5 - 4 x 2^3
=30 - 4 x 8
=30 - 32
= -2
Evaluate:
(3^2 x 3^3)^2
Answer: 59 049
(3^2 x 3^3)^2
=(3^5)^2
=3^10
=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.
Without using a calculator, benchmark 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 cm^2
Express the following in standard form:
(7 x 10^6) + (5 x 10^4) + (3 x 10^2) + (8 x 10^0)
Answer: 7 050 308
What is the difference between the "quotient of powers" law and the "power of a quotient" law?
The "quotient of powers" law is when two powers with the same base are being divided. To simplify, the exponents of the two powers are subtracted.
The "power of a quotient" law is when an entire fraction is raised to an exponent. The exponent is distributed to both the numerator and the denominator of the fraction.