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## Question Explanations For

##
*PRACTICE TEST 2 (No Calculator Math Test)*

## 1.

The Correct Answer is (C) —
Subtracting

*x*from both sides gives us 2*x*+ 5 = 15; subtracting 5 from both sides gives us 2*x*= 10.## 2.

The Correct Answer is (B) —
This is the only equation that satisfies

*f*(*x*) for all values of*x*. To quickly solve this type of problem, try plugging in one of the values for*x*from the table for each answer option, and cross out any that don’t produce the correct result for*f*(*x*). If you can’t eliminate three of the options with one row from the table, try plugging in a second row for any remaining options.## 3.

The Correct Answer is (D) —
-2

*x*+ 12 = 2*y*can be rewritten as –*x*+ 6 =*y*or 6 =*y*+*x*.## 4.

The Correct Answer is (A) —
Setting the equations equal to each other gives 10

*x*+ 2 = -2(8 – 2*x*) or 5*x*+ 1 = -8 + 2*x*. Rearranging gives 3*x*= -9, so*x*= -3. Plugging this back into either equation gives*y*= -28.## 5.

The Correct Answer is (C) —
The graph is a parabola translated in the positive

*x*direction and negative*y*direction. The basic form of a parabola is*y*=*x*^{2}. To translate in the positive*x*direction, we must subtract from*x*:*y*= (*x*–*a*)^{2}. To translate in the negative*y*direction, we must subtract from outside the function:*y*= (*x*–*a*)^{2}–*c*. The only equation that is in this form is (C).## 6.

The Correct Answer is (D) —
4

*y*– 4 > 8 can be rewritten as 4*y*> 12, and dividing both sides by 4 gives*y*> 3.## 7.

The Correct Answer is (D) —
This equation is in fact equal to

*ax*+*x*^{2}.## 8.

The Correct Answer is (C) —
A student who is 9 or 15 would not be allowed to participate, so we can test the values 9 and 15 in each equation. In equation (A), plugging in 9 gives 1 ≤ 4, so (A) is incorrect. In equation (B), plugging in 15 give 5 ≥ 4, so (B) is incorrect. In equation (D), plugging in 15 gives 1 ≤ 2, so (D) is incorrect.

## 9.

The Correct Answer is (C) —
If 6 residents moved out, we now have 40 residents. If there are 3 times as many female residents as male residents, we can write

*f*= 3*m*and*f*+*m*= 40. Plugging in to the second equation, we get 3*m*+*m*= 40, or*m*= 10. Since*f*= 3*m*, there are 30 female residents in the building.## 10.

The Correct Answer is (C) —
Factoring the numerator gives (7

*x*+ 4)(2*x*– 3). Plugging this back into the fraction gives us (7*x*+ 4)(2*x*– 3)/(2*x*– 3). This allows us to cancel the term (2*x*– 3), leaving us with 7*x*+ 4.## 11.

The Correct Answer is (B) —
At every interval, the population grows by a factor of 3. This means that the population is growing exponentially, so the equation must have the form

*P*(*t*) =*c*(*g*)^{t}, where*c*is a constant (the value at time 0) and*g*is the growth rate. (B) is the only exponential function given.## 12.

The Correct Answer is (B) —
Setting the equations equal to each other gives

*x*^{2}– 4*x*+ 9 = -2*x*+ 17. Rearranging gives*x*^{2}– 2*x*– 8 = 0, and factoring gives (*x*– 4)(*x*+ 2), so the possible values of*x*are 4 and -2. Since (*a*,*b*) is in the first quadrant, we must use the positive value for*x*. Plugging 4 back into either equation gives*y*= 9, so*a*+*b*= 13.## 13.

The Correct Answer is (B) —
Factoring the numerator gives (3

*x*+ 2)(2*x*+*y*); plugging this back in gives (3*x*+ 2)(2*x*+*y*)/(3*x*+ 2). We can cancel the term (3*x*+ 2), leaving us with 2*x*+*y*.## 14.

The Correct Answer is (12) —
4

^{1}× 4^{1}= 16 or 4^{0}× 4^{2}= 16. Plugging these values into the second equation gives 6 + 6 or 0 + 12, respectively.## 15.

The Correct Answer is (4) —
The

*x*-intercept is the point at which*y*= 0, as given in the ordered pair. To find this point, we need to factor this equation – that is, finding two numbers that add up to -8 and whose product is 16. These numbers are both -4, so the factored equation is (*x*– 4)(*x*– 4) or (*x*– 4)^{2}. This means that*x*= 4.## 16.

The Correct Answer is (1) —
We can represent the area of the frame not taken up by the picture (equal to 112 in

^{2}– 72 in^{2}= 40 in^{2}) as the sum of the areas of the corners (each is*x*^{2}in^{2}), the areas of the vertical spans (each is 6*x*in^{2}), and the areas of the horizontal spans (each is 12*x*in^{2}): 40 = 4*x*^{2}+ 2(6*x*) + 2(12*x*). Solving for*x*gives 1.## 17.

The Correct Answer is (3) —
Set the equations to zero: -

*c*+ 5*x*/3 +*y*= 0, -*c*+ 4*x*+ 2*y*= 0. Subtract them to get -7*x*/3 –*y*= 0. So*y*= -7*x*/3. Plug this into*x*+*y*= 6:*x*-7*x*/3 = 6, so*x*= -9/2. Since*x*+*y*= 6,*y*= 6 + 9/2 = 21/2. Plugging these values into either equation gives*c*= 3.