SAT Math : SAT Mathematics
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Example Questions
Example Question #1 : Algebra
If 4xs = v, v = ks , and sv ≠ 0, which of the following is equal to k ?
xv
x
4xv
4x
2xv
4x
This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.
Example Question #3 : Linear / Rational / Variable Equations
If 2x2(5-x)(3x+2) = 0, then what is the sum of all of the possible values of x?
Since we are told that 2x2(5-x)(3x+2) = 0, in order to find x, we must let each of the factors of our equation equal zero. The equation is already factored for us, which means that our factors are 2x2, (5-x), and (3x+2). We must let each of these equal zero separately, and these will give us the possible values of x that satisfy the equation.
Let's look at the factor 2x2 and set it equal to zero.
2x2 = 0
x = 0
Then, let's look at the factor 5-x.
5-x = 0
Add x to both sides
5 = x
x = 5
Finally, we set the last factor equal to zero.
(3x+2) = 0
Subtract two from both sides
3x = -2
Divide both sides by three.
x = -2/3
This means that the possible values of x are 0, 5, or -2/3. The question asks us to find the sum of these values.
0 + 5 + -2/3
5 + -2/3
Remember to find a common denominator of 3.
15/3 + -2/3 = 13/3.
The answer is 13/3.
Example Question #3 : Algebra
If bx + c = e – ax, then what is x?
To solve for x:
bx + c = e – ax
bx + ax = e – c
x(b+a) = e-c
x = (e-c) / (b+a)
Example Question #2 : Algebra
√( x2 -7) = 3
What is x?
To solve, remove the radical by squaring both sides
(√( x2 -7)) 2 = 32
x2 -7 = 9
x2 = 16
x = 4
Example Question #4 : Algebra
√(3x) = 9
What is x?
–3
27
3
9
–27
27
To solve, remove the radical by squaring both sides
(√3x) 2 = 92
3x = 81
x = 81/3 = 27
Example Question #2 : Algebra
√(8y) + 18 = 4
What is y?
First, simplify the equation:
√(8y) + 18 = 4
√(8y) = -14
Then square both sides
(√8y) 2 = -142
8y = 196
y = 196/8 = 24.5
Example Question #111 : Gre Quantitative Reasoning
If y = 4 and 6y = 10z + y, then z = ?
30
6
4
2
24
2
- Substitute y in the equation for 4.
- You now have 6 * 4 = 10z + 4
- Simplify the equation: 24 = 10z + 4
- Subtract 4 from both sides: 24 – 4 = 10z + 4 – 4
- You now have 20 = 10z
- Divde both sides by 10 to solve for z.
- z = 2.
Example Question #112 : Gre Quantitative Reasoning
A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?
59
55
61
50
56
59
This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.
Example Question #113 : Gre Quantitative Reasoning
The first four numbers of a sequence are 5, 10, 20, 40. Assuming the pattern continues, what is the 6th term of the sequence?
160
60
50
140
80
160
Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get An = 5(2)n–1. Setting n = 6, you get 160 as the 6th term.
Example Question #111 : Gre Quantitative Reasoning
Given f(x) = x2 – 9. What are the zeroes of the function?
0, 3
–3, 3
0
–3, 0, 3
3
–3, 3
The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x2 = 9. Since a square makes a negative number positive, x can be equal to 3 or –3.
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