All SAT II Math I Resources
Example Question #63 : Number Theory
Which of the following is not an irrational number?
A root of an integer is one of two things, an integer or an irrational number. By testing all five on a calculator, only comes up an exact integer - 5. This is the correct choice.
Example Question #1 : Irrational Numbers
Simplify by rationalizing the denominator:
Multiply the numerator and the denominator by the conjugate of the denominator, which is . Then take advantage of the distributive properties and the difference of squares pattern:
Example Question #2 : Irrational Numbers
Example Question #3 : Irrational Numbers
Use the FOIL technique:
Example Question #4 : Irrational Numbers
We can set in the cube of a binomial pattern:
Example Question #5 : Irrational Numbers
You cannot divide by complex numbers
To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem, is our denominator, so we will multiply the expression by to obtain:
We can then combine like terms and rewrite all terms as . Therefore, the expression becomes:
Our final answer is therefore
Example Question #62 : Classifying Algebraic Functions
Simplify the following product:
Multiply these complex numbers out in the typical way:
and recall that by definition. Then, grouping like terms we get
which is our final answer.
Example Question #6 : Irrational Numbers
Identify the real part of
none of the above.
A complex number in its standard form is of the form: , where stands for the real part and stands for the imaginary part. The symbol stands for .
The real part in this problem is 1.
Example Question #7 : Irrational Numbers
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
Example Question #63 : Classifying Algebraic Functions
Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.
Remember that , so .
Substitute in for