### 1. If x + 3 = n, then 2x + 6 = ?

## Correct Wrong

To answer this question, solve the first equation for *x*:

*x* + 3 = *n*

*x* = *n* – 3

Next, substitute *n* – 3 for x in the second equation:

2(*n* – 3) + 6

= 2*n* – 6 + 6

= 2*n*

### 2. The expression a(b – 2c) is equivalent to:

## Correct Wrong

This question tests your ability to recognize and apply the distributive property. According to the distributive property, for any numbers *a*, *b*, and *c*, *c*(*a* + *b*) = *ca* + *cb*. If you distribute the *a* value, you get *ab* – *a*2*c*, or *ab* – 2*ac*.

### 3. What is the slope intercept form of -3x + y + 8 = 0?

## Correct Wrong

The slope-intercept form is expressed as *y *= *mx* + *b*. The equation given is -3*x* + *y *+ 8 = 0. Isolate *y *on the left side of the equation, and you get *y* = 3*x* – 8.

### 4. The expression 4c – 2d is equivalent to which of the following?

## Correct Wrong

This is another problem that tests your ability to recognize and apply the distributive property; however, in this one you must work backward. Again, for any numbers *a*, *b*, and *c*, *c*(*a* + *b*) = *ca* + *cb*. In this problem, since 2 is the common factor for both 4 and 2, you can “factor out” 2. Eliminate answer choices A and D, which have incorrectly factored out 4. Once you factor out 2, the expression will look like this: 2(2*c* – *d*).

### 5. What is the median of the data given below? 9, 13, 27, 22, 20, 31, 13

## Correct Wrong

The median is the middle value in a list that is either in ascending order or descending order. Your first step is to put the data in order, as follows:

9, 13, 13, 20, 22, 27, 31

Because the list includes an odd number of values, simply pick the middle value which is 20.

### 6. If 4(a + b)(a – b) = 40 and a – b = 20, then a + b =?

## Correct Wrong

The first step in solving this problem is to simplify the equation by dividing both sides by 4:

4(*a* + *b*)(*a* – *b*) = 40

(*a* + *b*)(*a* – *b*) = 10

Next, substitute 20 for *a* – *b* and solve for *a* + *b*:

(*a* + *b*)20 = 10

*a* + *b* = 10/20 = 1/2

### 7. Which of the following degree measures is equivalent to 4.25π radians?

## Correct Wrong

Because there are 2π radians in the circumference of every circle and a circle consists of 360°, π radians = 180°. Divide 4.25π radians by π to get 4.25, multiply 4.25(180°) to get the degree measure of the angle, 765°.

### 8. The ratio of L to M is 3 to 4, and the ration of P to M is 1 to 2. What is the ratio of L to P?

## Correct Wrong

You are given that L/M = ¾ and P/M = ½. The ratio of L/P is equivalent to ¾ x 2/1, or 6/4, which can be reduced to 3/2.

### 9. If the sum of the consecutive integers from -22 to n, inclusive, is 72, then n = ?

## Correct Wrong

To solve this problem, you can apply some logic: because each number between -22 and 22 will cancel each other out, you can start with the next consecutive integer, 23. Now simply begin adding consecutive integers until you reach 72: 23 + 24 + 25 = 72. Therefore, *n* must equal 25. You can also solve this problem mathematically by using the following formula:

(-22 + *n*)(23 + *n*) = 72

2

By expanding this equation and simplifying it, you can reach the equation (2*n* + 1)[squared] = 2,601. Therefore, 2*n* + 1 = 51 and *n* = 25.

### 10. In a set of 13 different numbers, which of the following CANNOT affect the value of the median?

## Correct Wrong

The median is the middle number in an ordered list of numbers. Therefore, the value of the median can be changed by increasing each number by 10 or by doubling each number, so eliminate choices D and E. Likewise, if you increase the smallest number or decrease the largest number, you could potentially change the order of the numbers in the list, thereby potentially changing the value of the median, eliminate choices B and C. However, if you increase the largest number, it will still remain in the last position in the list, so the value of the median will not change.

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#### 10 Practice Math Questions for the ACT

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