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## Question Explanations For

##
*PRACTICE TEST 1 (No Calculator Math Test)*

## 1.

The Correct Answer is (D) —
If we subtract x from both sides, we get 6 > x + 4; subtracting 4 from both sides gives us 2 > x. So 2 is not a possible value for x.

## 2.

The Correct Answer is (D) —
The graph shows a negative (downward-opening) quadratic function. The equations in (A) and (B) are linear functions, since the variable p has an exponent of 1 (if the exponent is 1 it is not written), so we can eliminate those options. The general form of a quadratic function is , where

*a*,*b*, and*c*are constants. (It is not necessary to expand the equations to solve this question, but if we do, we see that is the same as and is the same as , so both equations fit the general form). If*a*is negative, we call the function a negative quadratic function, and the graph will open downward. In equation (D),*a*= -1, so (D) is the correct answer.## 3.

The Correct Answer is (B) —
To find the next number in the sequence, add 3: -2 + 3 = 1; 1 + 3 = 4, and so on.

## 4.

The Correct Answer is (B) —
If we rearrange the second equation into the form and simplify, we get . We can rearrange the first equation to get . Plugging this in for

*x*in the first equation, we get . Solving for*y*gives us*y*= 1. If we plug this value of*y*into the first equation, we find that*x*= 4. (4, 1) is therefore the point of intersection, and 4 > 1, so*a*>*b*is the correct answer.## 5.

The Correct Answer is (A) —
The slope of this line is -2, since a rise of -1 occurs over a run of ½. The

*y*-intercept is 1. So .## 6.

The Correct Answer is (A) —
Using the FOIL method, we can find that .

## 7.

The Correct Answer is (A) —
The possible ordered pairs are (1, 1) and (1, 2) (zero is neither negative nor positive).

## 8.

The Correct Answer is (B) —
If we plug in 5 for

*x*, we get , which reduces to 3 = 3. If we plug in -6 for*x*, we get , which reduces to .## 9.

The Correct Answer is (C) —
Squaring both sides and rearranging the equation gives us . Factoring gives , so the two possible values for

*y*are 3 and 4. The product of 3 and 4 is 12.## 10.

The Correct Answer is (D) —
The sum of 1 and 1 is 2, which is greater than 0, the absolute value of their difference.

## 11.

The Correct Answer is (D) —

*g*(*x*) is translated by 2 in the positive*x*direction and 5 in the positive*y*direction. This means that*h*must be 2 and*k*must be 5, since*f*(*x*– 2) will translate*f*(*x*) in the positive*x*direction and*f*(*x*) + 5 will translate*f*(*x*) in the positive*y*direction. So*hk*= 2 × 5 = 10.## 12.

The Correct Answer is (B) —
Setting the functions equal to each other gives . Rearranging gives , and factoring gives . This means that the two points of intersection occur when

*x*= -1 and*x*= 3. Since*x*= -1 is not in the first quadrant, we must use*x*= 3. Plugging 3 in for*x*in either equation yields*y*= 29.## 13.

The Correct Answer is (D) —
If we look at the values in the chart, we see that while

*b*increases by one each time,*h*increases by 10, then 14, then 18. This implies that the equation that would represent the relationship is not linear (if it were,*h*would increase by a constant amount each time), so we can eliminate (A) and (B) since they are linear equations. Now, checking the values for*b*and*h*in equation (C), we can see that they do not fit in this function (for example, 29 ≠ 42 + 1). That leaves equation (D), which, if we plug in for*b*and*h*, satisfies all values in the chart.## 14.

The Correct Answer is (6) —
If 2

*f*(*p*) = 8,*f*(*p*) = 4. Plugging this into the original equation, we get 4 = 2 –*p*, so*p*= -2. Plugging -2 into*f*(2*p*) gives*f*(-4) = 2 + 4 = 6.## 15.

The Correct Answer is (1/3) —
To find the smallest value of

*k*, we must find the smallest value for –*x*+ 2, meaning we must find the largest value for*x*(since*x*becomes negative in the equation). The largest value for*x*, given*x*≤ 1, is 1. Plugging 1 in for*x*and solving for*k*gives*k*≥ 1/3. The minimum value of*k*, then, is 1/3.## 16.

The Correct Answer is (5) —
Multiplying each side by the denominators gives -6

*x*=*x*^{2}– 9*x*– 10; simplifying gives 0 =*x*^{2}– 3*x*– 10. Factoring gives 0 = (*x*– 5)(*x*+ 2). The solutions are therefore 5 and -2; 5 is the positive solution.## 17.

The Correct Answer is (29) —
The length of each side can be found using the Pythagorean Theorem:

*x*^{2}+*y*^{2}=*s*^{2}, where*s*is the length of the side of the square. Taking the bottom edge as an example, we can see that*x*= 5 since the difference between the two*x*-coordinates is 5. Similarly,*y*= 2, so we have 5^{2}+ 2^{2}=*s*^{2}. Since the area of a square is*s*^{2}, solving for this term yields 25 + 4 = 29.