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## Question Explanations For

##
*PRACTICE TEST 3 (No Calculator Math Test)*

## 1.

The Correct Answer is (B) —
When

*y*= 3, the equation becomes 3*x*+ 2*x*= 5(3) + 5, or 5*x*= 20. Dividing by 5 gives*x*= 4.## 2.

The Correct Answer is (C) —
Subtracting

*x*from both sides gives*x*+ 6 = 12; subtracting 6 from both sides gives*x*= 6.## 3.

The Correct Answer is (C) —
This question is most quickly solved with guess-and-check, but we can also look for the function that is maximized by (has its greatest value when given) negative numbers – in this case, the function that includes a negative

*x*. (C) is the only such function, since (D) simplifies to*f*(*x*) = -3 +*x*.## 4.

The Correct Answer is (C) —
We can break up the expression

*f*(-*x*) + 2 to make it easier to find the correct graph. First, look at “*f*(-*x*)”. Plugging this into the first equation gives us*f*(-*x*) = -*x*+*b*. Since both equations are linear, they can be written in the form*y*=*mx*+*b*, so we know that the slope of the graph we are looking for is negative, since*m*= -1. Next, look at “+ 2”. Adding 2 means we are shifting the graph in the positive*y*direction by 2, so we need to find the graph with a negative slope, shifted up by 2 relative to the original graph. (C) is the only graph that satisfies these criteria.## 5.

The Correct Answer is (B) —
We can represent the sum of three consecutive even integers as

*n*+ (*n*+ 2) + (*n*+ 4), or 3*n*+ 6. Since this sum must be greater than 20, we can write 3*n*+ 6 > 20. Subtracting 6 from both sides gives 3*n*> 14. Since 14 is not divisible by 3, we can try the closest even numbers that are: 12 and 18. These give us*n*= 4 and*n*= 6. When*n*= 4, 3*n*= 12, which is not greater than 14, so*n*must be 6.## 6.

The Correct Answer is (B) —
We can take the square root of both sides to get (

*x*– 1) = 2. Adding 1 to both sides gives*x*= 3. (Since the original term was squared, -1 is another possible value for*x*, but only positive numbers are given as answer choices).## 7.

The Correct Answer is (C) —
We can write this equation as

*f*(5) –*f*(5 + 1) = 2(5) – 5, or*f*(5) –*f*(6) = 5. Since we know that*f*(6) is 12, we can write*f*(5) – 12 = 5. Adding 12 to both sides gives*f*(5) = 17.## 8.

The Correct Answer is (C) —
Every year, the amount of money increases by 5%. This implies an exponential relationship, so we can eliminate (A) and (B). (D) cannot be correct, since when

*t*= 2,*d*(*t*) = 1200 + (0.05)(12002) = 1200 + (0.05)(1440000) = 73200, which is far greater than the given value of 1323.## 9.

The Correct Answer is (A) —
Let

*x*represent the number of molecules of molecule A and*y*represent the number of molecules of molecule B. Since there are 12 molecules total,*x*+*y*= 12. Since it takes 2 milliseconds to decompose molecule A, the time to decompose molecule A can be written as 2*x*. Similarly, the time to decompose molecule B can be written as*y*. So 2*x*+*y*= 16.## 10.

The Correct Answer is (C) —

*x*^{-2}is the same as , so we can write . Multiplying both sides by*x*^{2}gives*x*^{3}= 1.*x*cannot be -1 (-1^{3}= -1), 0 (0^{3}= 0), or 2 (2^{3}= 8), but 1^{3}= 1.## 11.

The Correct Answer is (B) —
The lowest point of this graph will be at the

*x*value at the midpoint between its*x*-intercepts, which occur when*x*= -2 and*x*= 4. The midpoint of -2 and 4 is 1.## 12.

The Correct Answer is (C) —
At every interval, the population of beetles doubles. This implies an exponential relationship, which eliminates (A) and (B), which are quadratic. (D) does not work when

*t*= 1 (since 20(0.5)^{1+1}= 20(0.25) = 5).## 13.

The Correct Answer is (C) —
Every number in the

*y*column is the square of the number 3 greater than the number in the*x*column. We can represent this relationship as*y*= (*x*+ 3)^{2}. Expanding by the FOIL method gives us*y*=*x*^{2}+ 6*x*+ 9.## 14.

The Correct Answer is (36) —
We can divide both sides by 4 to get , then square both sides to get

*x*= 36.## 15.

The Correct Answer is (1/9) —
We can rewrite this equation as , or . Taking the reciprocal gives , and multiplying by 3 gives

*x*^{3}= 27, so*x*= 3. Plugging in to*x*^{-2}gives 3^{-2}or , which is the same as 1/9.## 16.

The Correct Answer is (4) —
The area of a triangle is ½

*bh*. The height is 4, since the triangle extends from a height of*y*= 0 to the line*y*= 4. The base is the*x*-coordinate of the point where the two lines intersect, that is, the point at which 2*x*= 4. Since*x*= 2,*b*= 2, so the area of the triangle is ½(2)(4) = 4.## 17.

The Correct Answer is (16) —
We can represent Jane’s age now as

*j*and Mark’s age now as*m*. So 10 years ago, Jane’s age was*j*– 10. Since at that time she was twice as old as Mark is now, we can write*j*– 10 = 2*m*. If in two years Jane is three times as old as Mark is now, we can write*j*+ 2 = 3*m*. To find out how old Mark will be in 4 years, we need to find*m*+ 4. We can rewrite our first equation as*j*= 2*m*+ 10. Plugging this into our second equation gives us (2*m*+ 10) + 2 = 3*m*. Simplifying gives us 12 =*m*. This means that Mark is 12 years old, so in 4 years he will be 16.