All PSAT Math Resources
Example Questions
Example Question #1 : Expressions
Simplify the expression.
To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.
This is the most simplified version of the rational expression.
Example Question #1 : How To Evaluate Rational Expressions
If √(ab) = 8, and a2 = b, what is a?
64
16
4
2
10
4
If we plug in a2 for b in the radical expression, we get √(a3) = 8. This can be rewritten as a3/2 = 8. Thus, loga 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.
Example Question #2 : Expressions
–11/5
37/15
–37/15
9/5
–9/5
–11/5
Example Question #1 : How To Subtract Rational Expressions With Different Denominators
Simplify.
Determine an LCD (Least Common Denominator) between and .
LCD =
Multiply the top and bottom of the first rational expression by , so that the denominator will be .
Distribute the to .
Now you can subtract because both rational expressions have the same denominators.
Final Answer.
Example Question #1 : How To Divide Rational Expressions
Which of the following is equivalent to ? Assume that denominators are always nonzero.
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
Example Question #3 : Expressions
Simplify (4x)/(x2 – 4) * (x + 2)/(x2 – 2x)
x/(x + 2)
(4x2 + 8x)/(x4 + 8x)
4/(x – 2)2
x/(x – 2)2
4/(x + 2)2
4/(x – 2)2
Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.
Example Question #8 : Expressions
what is 6/8 X 20/3
6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)
3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)
1/1 X 5/1 = 5
Example Question #1 : How To Add Exponents
If a2 = 35 and b2 = 52 then a4 + b6 = ?
522
3929
141,833
150,000
140,608
141,833
a4 = a2 * a2 and b6= b2 * b2 * b2
Therefore a4 + b6 = 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833
Example Question #1 : Exponents
If , what is the value of ?
Since we have two ’s in we will need to combine the two terms.
For this can be rewritten as
So we have .
Or
Divide this by :
Thus or
*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.
Example Question #481 : Algebra
Solve for x.
23 + 2x+1 = 72
3
5
4
6
7
5
The answer is 5.
8 + 2x+1 = 72
2x+1 = 64
2x+1 = 26
x + 1 = 6
x = 5