### All SAT Math Resources

## Example Questions

### Example Question #1 : Simplifying Expressions

If *x* + *y* = 4, what is the value of *x* + *y* – 6?

**Possible Answers:**

4

0

6

–2

2

**Correct answer:**

–2

Substitute 4 for *x* + *y *in the expression given.

4 minus 6 equals –2.

### Example Question #1 : Simplifying Expressions

If 6 less than the product of 9 and a number is equal to 48, what is the number?

**Possible Answers:**

4

3

6

5

**Correct answer:**

6

Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.

### Example Question #1 : Simplifying Expressions

If x y = (5x - 4y)/y , find the value of y if 6 y = 2.

**Possible Answers:**

5

4

10

2

**Correct answer:**

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 #1 : Simplifying Expressions

Simplify the following expression: x^{3} - 4(x^{2} + 3) + 15

**Possible Answers:**

x5 + 3

x3 – 4x2 + 3

x3 – 3x2 + 15

x3 – 12x2 + 15

**Correct answer:**

x3 – 4x2 + 3

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x^{2 }and -4 by 3.

x^{3} - 4x^{2} -12 + 15

You can then add -12 and 15, which equals 3.

You now have x^{3} - 4x^{2} + 3 and are finished. Just a reminder that x^{3} and 4x^{2 }are not like terms as the x’s have different exponents.

### Example Question #1 : Simplifying Expressions

Evaluate: (2x + 4)(x^{2} – 2x + 4)

**Possible Answers:**

4x^{2} + 16x + 16

2x^{3} – 8x^{2} + 16x + 16

2x^{3} + 16

2x^{3} + 8x^{2} – 16x – 16

2x^{3} – 4x^{2} + 8x

**Correct answer:**

2x^{3} + 16

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x^{2} – 2x + 4) = 2x^{3} – 4x^{2} + 8x + 4x^{2} – 8x + 16 = 2x^{3} + 16

### Example Question #21 : Simplifying Expressions

Which of the following is equivalent to ?

**Possible Answers:**

ab^{5}c

b^{5}/(ac)

a^{2}/(b^{5}c)

ab/c

abc

**Correct answer:**

b^{5}/(ac)

First, we can use the property of exponents that x^{y}/x^{z} = x^{y–z}

Then we can use the property of exponents that states x^{–y} = 1/x^{y}

a^{–1}b^{5}c^{–1 }= b^{5}/ac

### Example Question #1 : Simplifying Expressions

Solve for x: 2y/3b = 5x/7a

**Possible Answers:**

6ab/7y

7ab/6y

15b/14ay

14ay/15b

5by/3a

**Correct answer:**

14ay/15b

Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.

### Example Question #2 : 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*.

**Possible Answers:**

3*m* – 3

3*m* + 3

3*m* + 6

3*m* – 6

3*m*

**Correct answer:**

3*m* – 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* = 3*m* – 3

### Example Question #2 : How To Do Distance Problems

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.

**Possible Answers:**

*g* + *f*

*g* + *f* + 30

**Correct answer:**

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

=

### Example Question #7 : Simplifying Expressions

If *a* + *b* = 10 and *b* + *c* = 15, then what is the value of (*c* – *a*)/(*a* + 2*b* +* c*)?

**Possible Answers:**

1/5

3/2

2/3

5

150

**Correct answer:**

1/5

Add the two equations:

*a* + *b* = 10

*b* + *c* = 15

------------

*a* + *b* + *b* + *c* = 10 + 15

*a* + 2*b* + *c* = 25 (this is the denominator of the answer)

Subtract the two equations:

*b* + *c* = 15

*a* + *b* = 10

------------

*b* + *c* – (*a* +* b*) = 15 – 10

*c* – *a* = 5 (this is the numerator of the answer)

5/25 = 1/5

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