All SAT II Math I Resources
Example Questions
Example Question #271 : Sat Subject Test In Math I
Decrease by 30%. Which of the following will this be equal to?
The correct answer is not among the other responses.
A number decreased by 30% is equivalent to 100% of the number minus 30% of the number. This is taking 70% of the number, or, equivalently, multiplying it by 0.7.
Therefore, decreased by 30% is 0.7 times this, or
Example Question #12 : Simplifying Expressions
The polynomial is divisible by the linear binomial
. Evaluate
.
None of the other choices gives the correct answer.
By the factor theorem, a polynomial is divisible by the linear binomial
if and only if
. Therefore, we want the value of
that makes the polynomial equal to 0 when evaluated at
.
Example Question #13 : Simplifying Expressions
Factor:
can be rewritten as
and is therefore the sum of two cubes. As such, it can be factored using the pattern
where .
Example Question #121 : Single Variable Algebra
Factor completely:
The grouping technique works here:
The first factor is the difference of squares and can be factored further accordingly:
Example Question #11 : Simplifying Expressions
Factor completely:
The polynomial is prime.
The polynomial is prime.
Since the first term is a perfect cube, the factoring pattern we are looking to take advantage of is the difference of cubes pattern. However, 243 is not a perfect cube of an integer , so the factoring pattern cannot be applied. No other pattern fits, so the polynomial is a prime.
Example Question #121 : Single Variable Algebra
Exponentiate:
Vertical multiplication is perhaps the easiest way to multiply trinomials.
Example Question #123 : Single Variable Algebra
Exponentiate:
The difference of two terms can be cubed using the pattern
Where :
Example Question #124 : Single Variable Algebra
How many of the following are prime factors of ?
I)
II)
III)
IV)
Four
None
Three
Two
One
Three
Factor all the way to its prime factorization.
can be factored as the difference of two perfect square terms as follows:
is a factor, and, as the sum of squares, it is a prime.
is also a factor, but it is not a prime factor - it can be factored as the difference of two perfect square terms. We continue:
Therefore, of the given four choices, only is not a factor, so the correct response is three.
Example Question #1 : Multiplying And Dividing Rational Expressions
For all values , which of the following is equivalent to the expression above?
First, factor the numerator. We need factors that multiply to and add to
.
We can plug the factored terms into the original expression.
Note that appears in both the numerator and the denominator. This allows us to cancel the terms.
This is our final answer.
Example Question #126 : Single Variable Algebra
Simplify the following expression:
When simplifying an equation,you must find a common factor for all values in the equation, including both sides.
and,
can all be divided by
so divide them all at once
.
This leaves you with
.
Certified Tutor
All SAT II Math I Resources
