## 1.

The Correct Answer is (B) — Subtracting 3 from each side of the inequality gives us $-2\leq&space;-2x$. Dividing each side by -2 and reversing the inequality sign gives us $1&space;\geq&space;x$. Answer choice B is the only line that correctly depicts this relationship.

## 2.

The Correct Answer is (B) — 2.4 x $10^{25}$ is the total number of all the atoms in a cup of water. Since there are 2 hydrogen atoms for 1 oxygen atom, 2/3 or 66.67% of the total atoms are hydrogen atoms. 2/3(2.4 x$10^{25}$) = 1.6 x $10^{25}$.

## 3.

The Correct Answer is (D) — Plugging in (-1, -4) gives us $\small&space;-3\geq&space;5$, which is true. Plugging in (0, 0) gives us $\small&space;0\geq&space;-1$ which is also true. Plugging in (2, 7) gives us $\small&space;6\geq&space;6$, which is also true. At this point, we can go ahead and choose D as our answer, but to check we can see that plugging in (3, 11) would give us $\small&space;9\geq&space;10$ which is not a true statement.

## 4.

The Correct Answer is (B) — We can set up a function for this word problems to predict the shape of its graph. If we use g as the number of gallons of gas, we could set up the function f(g) = 2 + 3.39g that represents the total cost of a transaction. This function is linear, so we can eliminate choices C and D. When g = 0, f(g) = 2 so this function has a y-intercept greater than 0. The correct answer is B.

## 5.

The Correct Answer is (A) — We can set up a system of equations to solve this problem. The total cost of all the hot dogs and hamburgers the group buys is \$20 so we can set up the equation d + (1.5)h = 20, where d is the number of hot dogs and h is the number of hamburgers. We are also told that everyone in the group buys 1 item, so d + h = 15. Subtracting d + h = 15 from d + (1.5)h = 20 gives us (0.5)h = 5. Solving for h gives us h = 10. We are actually solving for the number of hot dogs, so plugging in h into d + h =15 gives us d = 5 hotdogs.

## 6.

The Correct Answer is (C) — Since we are told that the graph represents the function y = mx + b we can just manipulate this equation to solve for x in terms of y. Subtracting b from each side gives us y - b = mx. Then dividing each side by m gives us $\small&space;x&space;=&space;\frac{y-b}{m}$.

## 7.

The Correct Answer is (A) — The amount of money a customer spends per month without a membership can be represented by f(x) = 10 + 7x, where x is the number of times they went to the gym. This function must be greater than 100 for the customer to benefit from purchasing a membership. Solving for x in 10 + 7x > 100, we get x > 12.857 so the customer must go at least 13 times.

## 8.

The Correct Answer is (C) — Looking through our options, we can notice that we can factor out 3 from answer choice C. Doing this we get 3($\small&space;x^{2}$ + 2x + 1) = 0. Now we have a form of the equation that we can easily factor into 3(x +1)(x + 1) = 0. x = -1 for both factors, so this equation has only 1 real solution.

## 9.

The Correct Answer is (D) — If s is the number of students and t is the cost of each ticket, ts is the total amount spent on tickets. We can subtract this from 200 to give us the money remaining to purchase meals. This gives us 200 - ts. Because this is the money that we have to buy meals for s students, we divide the expression by s to find the amount of money we can spend on each meal per student: $\small&space;\frac{200&space;-&space;ts}{s}$.

## 10.

The Correct Answer is (C) — Because 4 x 2 = 8, we can pull out a 4 from underneath the radical in choice B giving us $\small&space;2\sqrt{2x}$. This is the same of choice A, so B is not our answer. $\small&space;2^{4}=16$, so we can pull the 16 out of the radical in choice C to give us $\small&space;2\sqrt{x^{2}}$. This is not the same as A or B so our answer is C.

## 11.

The Correct Answer is (D) — First, we find the slope of the line given to us, which is calculated by $\small&space;\frac{8-0}{0&space;-&space;(-2)}&space;=&space;4$. We know that the slope of the perpendicular line is the negative reciprocal of this calculated slope, so the slope of the perpendicular line must be -1/4. Answer choice D is the only function that has a slope of -1/4.

## 13.

The Correct Answer is (B) — We are looking for the solution to g(2) = b. Since point (2, 6) is found on f(x), we know that f(2) = 6. Since g(x) = 2f(x), we can set up g(2) = 2f(2) = 2(6) = 12.

## 14.

The Correct Answer is (A) — Because the flagpole and its shadow make up the legs of a right triangle, we can use SOHCAHTOA to calculate that the height of the flagpole is 10 sin(x). Similarly, we can calculate that the length of the shadow is 10 cos(x). Taking the difference of these two expressions gives us sin(x) x 1 - cos(x) x 10.

## 15.

The Correct Answer is (C) — We can draw a line BC to get the right triangle BCD. The hypotenuse of BCDis the diameter of the circle, or 2r. We are told that the leg of the triangle made of line CD is r. At this point, we can recognize that this is a 30-60-90 triangle, meaning that line BD = $r&space;\sqrt{3}$. To find the area of the rectangle we multiply and line CD and line BD to get r x $\small&space;r\sqrt{3}&space;=&space;r^{2}\sqrt{3}$.

## 16.

The Correct Answer is (23) — If q is the number of quarters and n is the number of nickels, we can set up the equation 25q + 5n = 690 since we are told that all the quarters and nickels total to 690 cents (the conversion to cents is for the sake of not having to carry around decimals). We are also told that there is the same number of quarters as nickels, so we can set up q = n. Plugging this into the early equation we get, 25q + 5q = 30q = 690 Solving for q gives us q = 23.

## 17.

The Correct Answer is (6) — Subtracting the second equation from the first equation, we get $6&space;=&space;2x^{2}&space;-&space;11x$. Carrying the 6 over to the right side gives us $\small&space;0&space;=&space;2x^{2}&space;-&space;11x&space;-&space;6$. Factoring this we get $\small&space;0&space;=&space;2(x&space;+1)(x-6)$. From this we calculate that x = -1/2 or 6. Since the problem specifies x > 0, the answer is 6.

## 18.

The Correct Answer is (6) — We can find the distance that Carlos and Xiao were apart by calculating the total distance they walked in 20 minutes. 20 minutes is 1/3 of an hour. If Carlos walks at a rate of 15 miles per hour, he must have walked 1/3(15) or 5 miles in 20 minutes. Xiao walks at a rate of 3 miles per hour so she must have walked 1/3(3) or 1 mile in the 20 minutes. Adding both of these distances gives us 5 + 1 = 6 miles.

## 19.

The Correct Answer is (6) — Since the remainder from dividing u by 12 is 8, u/12 = some integer + 8/12 . We can infer from this that $\small&space;\frac{u&space;+&space;10}{12}$ = some integer + 18/12 . However, this is not the proper way to express remainders as 18/12 is greater than 1. We can more correctly write the above expression as $\small&space;\frac{u&space;+&space;10}{12}$ = some integer + 1 + 6/12 . From this, we can see that the remainder is 6.

## 20.

The Correct Answer is (5, 1.5, 3/2) — First, we distribute the 2 on the left side to get $\small&space;2a^{3}&space;+&space;2a^{2}&space;+&space;8a&space;-&space;16&space;=&space;2a^{3}&space;+&space;4a^{2}&space;-&space;5a&space;-1$. Moving all the terms on the left to the right side gives us $\small&space;2a^{3}&space;+&space;2a^{2}&space;+&space;8a&space;-&space;16&space;=&space;2a^{3}&space;+&space;4a^{2}&space;-&space;5a&space;-1$. We can factor this equation into 0 = (2a -3)(a -5). We can then calculate the roots giving us x = 5 or 1.5.