## 1.

The Correct Answer is (B) — Because the scientist took a random sample, we can assume that all other squares have approximately 15 cells. To get the total number of cells, we can multiply the number of cells per square by the total number of squares, giving us 15n.

## 2.

The Correct Answer is (C) — The equation y=-2x+1 is in the form y=ax+b, meaning that the slope is -2 and the y-intercept is 1. Therefore, we expect the graph to have a negative slope and a positive y-intercept. Answer choice (C) is the only graph that satisfies these criteria.

## 3.

The Correct Answer is (A) — When we plug in 10 for x in f(x), we get 1000/(10-20)=1000/(-10)=-100.

## 4.

The Correct Answer is (A) — When we plug in 10 for y in y = 0.75x + 10, we get 10 = 0.75x + 10. Subtracting 10 from each side gives us 0 = 0.75x. Dividing each side by 0.75 gives us x = 0.

## 5.

The Correct Answer is (C) — The probability that the first marble drawn will be blue is 6/13. Since we do not replace this marble, the probability that the second marble drawn will be blue is 5/12. Multiplying 6/13 and 5/12 gives us 5/26.

## 6.

The Correct Answer is (D) — When we plug in the second equation for y in the first equation, we get 10x - 2(5x - 4) + 3 = 11. Distributing the 2 into the parentheses gives us 10x - 10x + 8 + 3 = 11, which simplifies to 11 = 11. Since this statement is always true, there are infinite solutions to the system of equations.

## 7.

The Correct Answer is (B) — Taking the square root of both sides of the equation gives us x + 20 = 70 - x. Adding x and subtracting 20 from both sides gives us 2x = 50. Dividing each side by 2 gives us x = 25.

## 8.

The Correct Answer is (A) — Average speed is calculated by dividing the total distance traveled by the total time. Driver 1 traveled 300 miles in 10 hours so his average speed is 30 miles per hour. Driver 2 traveled 200 miles in 10 hours so his average speed is 20 miles per hour. The difference in the two average speeds is 10 miles per hour.

## 10.

The Correct Answer is (C) — Because density is calculated by dividing mass by volume, we can calculate volume by dividing mass by density. We first need to convert 2.4 kilograms to grams, giving us 2400 grams of palladium. Dividing mass by density gives us
$\frac{2400g}{12\frac{g}{cm^{^{3}}}}&space;=&space;200&space;cm^{3}$

## 11.

The Correct Answer is (B) — Solving the second equation for y, we get y = 34 - x. Plugging this value for y into the first equation, we get 1.5x + 2(34 - x) = 58. Distributing the 2 into the parentheses gives us 1.5x + 68 - 2x = 58. Combining the x terms and subtracting 68 from each side gives us -0.5x = -10. Dividing each side by -0.5 gives us x = 20.

## 12.

The Correct Answer is (D) — Since 10 out of the 100 butterflies caught were tagged, we can assume that 10% of the entire butterfly population has been tagged. This would mean that 50 (the original number of tagged butterflies) is 10% of the entire population, and 500 would be a good estimate for the total number of butterflies.

## 13.

The Correct Answer is (B) — Using exponent rules, we get that the equation given is equal to $a^{7+x}&space;=&space;a^{8}$. We can then set the exponents equal to each other, giving us 7 + x = 8. Solving for x gives us x = 1.

## 15.

The Correct Answer is (D) — Moving all the terms to the right side gives us $0&space;=&space;x^{2}&space;-2x&space;-&space;8$. Factoring this equation gives us (x - 4)(x + 2) = 0. Since these represent the roots of the equation, x can equal 4 or -2. -2 is not one of the options, so the answer is (D).

## 17.

The Correct Answer is (A) — The ratio for the solution is 10 mg/80 uL. When we equate this to the ratio that we want to solve, we get 10 mg/80 uL = 300 mg/x . Solving for x we get x = 2400 uL. Converting this to liters, we get 2400 uL(L/1,000,000uL) = 0.0024 L which converts to 2.4 mL.

## 18.

The Correct Answer is (D) — The remaining distance can be calculated by subtracting the total distance traveled from 600 miles. The distance traveled is speed multiplied by time, which in this case is 50t. Subtracting this from 600 gives us f(t) = 600 - 500t.

## 19.

The Correct Answer is (D) — Plugging in -1 for x in the inequality gives us 4y > -8 which simplifies to y > -2. This eliminates answer choices (A) and (B). Plugging in choice (C) gives us 4(-2) > 3(1) - 5 which simplifies to -8> -2 which is an untrue statement. This leaves us with answer choice (D).