All High School Math Resources
Example Questions
Example Question #1 : Number Theory
Without using a calculator, which of the following is the best estimate for
?
We know that
and .
Because 90 falls is approximately halfway between 81 and 100, the square root of 90 is approximately halfway between 9 and 10, or 9.5.
Example Question #2 : Number Theory
Place in order from smallest to largest:
To place in order, first we must find a common denominator and convert all fractions to that denominator.
have a common denominator of .
have a common denominator of .
have a common denominator of .
Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.
Example Question #1 : Understanding Real Numbers
What number is
of ?
For percent problems there are verbal cues:
"IS" means equals and "OF" means multiplication.
Then the equation to solve becomes:
Example Question #4 : Number Theory
Which of the following is NOT a real number?
We are looking for a number that is not real.
, , and are irrational numbers, but they are still real.
Then,
is equivalent to by the rules of complex numbers. Thus, it is also real.That leaves us with:
which in fact is imaginary (since no real number multiplied by itself yields a negative number) and simplifies to .Example Question #2 : Understanding Real Numbers
Which of the following are considered real numbers?
Real numbers can be found anywhere on a continuous number line ranging from negative infinity to positive infinity; therefore, all of the numbers are real numbers.
Example Question #2 : Number Theory
If a card is drawn randomly from a regular shuffled 52 card deck, what is the probability that the card is either a spade or a 3?
How many cards in the deck are either a spade or a 3?
There are thirteen spades, including a 3 of spades.
There are four 3's, including a 3 of spades.
Since we are counting the same card (3 of spades) twice, there are actually
distinct cards that fit the criteria of being either a spade or a 3.
Since any of the 52 cards is equally likely to be drawn, the probability that it is a spade or a 3, is
Example Question #3 : Number Theory
Find the distance between
and on a number line.
To find the distance on a number line: