SAT Math : Algebra
Study concepts, example questions & explanations for SAT Math
All SAT Math Resources
Example Questions
Example Question #64 : Expressions
Given a right triangle 
To solve for 
The question states that 
Therefore, to calculate 
and since 
Example Question #761 : Algebra
In terms of 
None of these
Subtracting 1 from both sides:
Subtracting 8 from both sides:
Squaring both sides, and applying the binomial square pattern to the right expression:
Example Question #1 : Simplifying Expressions
If x + y = 4, what is the value of x + y – 6?
4
0
2
–2
6
–2
Substitute 4 for x + y in the expression given.
4 minus 6 equals –2.
Example Question #1 : How To Simplify An Expression
If 6 less than the product of 9 and a number is equal to 48, what is the number?
3
5
4
6
6
Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.
Example Question #2 : How To Simplify An Expression
If x 
y = (5x - 4y)/y , find the value of y if 6 y = 2.
5
2
10
4
5
If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 -->2y =30 -4y --> 6y =30 --> y=5. We could also work from the answers and substitute each answer in and solve.
Example Question #2 : Simplifying Expressions
Evaluate: (2x + 4)(x2 – 2x + 4)
2x3 + 16
2x3 + 8x2 – 16x – 16
2x3 – 8x2 + 16x + 16
4x2 + 16x + 16
2x3 – 4x2 + 8x
2x3 + 16
Multiply each term of the first factor by each term of the second factor and then combine like terms.
(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x + 4x2 – 8x + 16 = 2x3 + 16
Example Question #92 : Expressions
Which of the following is equivalent to 
?
ab5c
a2/(b5c)
ab/c
b5/(ac)
abc
b5/(ac)
First, we can use the property of exponents that xy/xz = xy–z
Then we can use the property of exponents that states x–y = 1/xy
a–1b5c–1 = b5/ac
Example Question #2 : Simplifying Expressions
Solve for x: 2y/3b = 5x/7a
5by/3a
14ay/15b
6ab/7y
15b/14ay
7ab/6y
14ay/15b
Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.
Example Question #1 : How To Simplify An Expression
Three consecutive positive integers are added together. If the largest of the three numbers is m, find the sum of the three numbers in terms of m.
3m – 6
3m
3m – 3
3m + 6
3m + 3
3m – 3
Three consecutive positive integers are added together. If the largest of the three numbers is m, find the sum of the three numbers in terms of m.
If m is the largest of three consecutive positive integers, then the integers must be:
m – 2, m – 1, and m, where m > 2.
The sum of these three numbers is:
m - 2 + m – 1 + m = 3m – 3
Example Question #1 : Simplifying Expressions
Sophie travels f miles in g hours. She must drive another 30 miles at the same rate. Find the total number of hours, in terms of f and g, that the trip will take.
g + f + 30
g + f
Using d = rt, we know that first part of the trip can be represented by f = rg. The second part of the trip can be represented by 30 = rx, where x is some unknown number of hours. Note that the rate r is in both equations because Sophie is traveling at the same rate as mentioned in the problem.
Solve each equation for the time (g in equation 1, x in equation 2).
g = f/r
x = 30/r
The total time is the sum of these two times
Note that, from equation 1, r = f/g, so
=
All SAT Math Resources
