## 1.

The Correct Answer is (C) — Madison’s dad begins (10 miles/hour)(2 hours) or 20 miles from Madison. He is traveling at 15 miles per hour and Madison is traveling at 10 miles per hour. He is traveling 5 miles per hour faster than Madison, so it will take him 20 miles/(5 miles/hour), or 4 hours to reach Madison.

## 2.

The Correct Answer is (B) — The values for x that make this equation true are -4 and 1, as both of these x values result in a value of 0.

## 3.

The Correct Answer is (C) — The sound wave travels the 525 meters to the tree in 525 meters/350 meters/second, or 1.5 seconds.

## 4.

The Correct Answer is (B)h = 9, therefore w = 9/3 or 3, according to the equation h = 3w. w = l/8, according to the first equation. Therefore, l = 3 × 8, or 24.

## 5.

The Correct Answer is (C)n + (n + 1) = 15, therefore 2n + 1 = 15. Solving the equation, n = 7. The product of the two integers is n(n + 1) or n2 + n. Substituting 7 for n, 49 + 7 = 56.

## 6.

The Correct Answer is (C) — Substituting 0 into x, f(x) would be 0 for A) and D), so A) and D) are incorrect. Substituting -1 into x, f(x) would be -2 for B), so this is incorrect. The remaining answer C) is the correct answer.

## 7.

The Correct Answer is (D) — The cost to sequence DNA base pairs is 10 cents/1000 pairs. One gene with 120,000 base pairs would cost (120,000/1000)($0.10) or$12.00. 100 samples would cost $12 × 100 or$1200.

## 8.

The Correct Answer is (A) — The equation can be rearranged as 2x2x – 15 = 0. Substituting the answer choices, A) = 18 – 3 – 15 = 0. This is the correct answer. B) yields, 8 – 2 – 15 or -9, C) yields, 8 + 2 – 15 or -5, D) yields, 32 + 4 – 15, or 43.

## 9.

The Correct Answer is (A) — When v = 0, the velocity of the ball is equal to zero. The equation 0 = -5t2 – 20t + 60 can be rewritten as -5(t2 + 4t – 12). The bracketed equation can be factored as (t – 2)(t + 6). Solving for t gives us either -6 or 2. Since it is not possible to have negative values for time, 2 is the only answer.

## 10.

The Correct Answer is (C) — Combining the two equations, we arrive at x + y = 4y – 2x. This simplifies to 3x = 3y, or x = y. Substituting x, we arrive at x = -2x – 3 for the second equation. Thus arranging our terms, this results in 3x = -3, or x = -1. Since x = y, xy = -1(-1) or 1.

## 11.

The Correct Answer is (C) — The graph shows a distance of 6 on the x axis between the two x–intercepts. The vertex of the graph is found in the middle, or 3 from either x–intercept. The x-value for this would be therefore -2 + 3 or 4 – 3; both of these result in 1. C) is the only equation that shows a quadratic equation with a shift one unit to the right, and for which the x-values of -2 and 4 both result in a y value of 0.

## 12.

The Correct Answer is (C) — 27 can be written as 33. With a common base the two exponents (2x + 2) and (3)(2) can be equated and solved. The solution of x for 2x + 2 = 6 is 2.

## 13.

The Correct Answer is (D) — We can rewrite this expression as 12½ × k¼ = 6a. This simplifies to $\inline&space;\frac{6a}{12^{\frac{1}{2}}}&space;=&space;k^{\frac{1}{4}}$. Squaring both sides gives $\inline&space;\frac{36a}{12}&space;=&space;k^{\frac{1}{2}}$. Squaring this again gives the answer 9a4 = k.

## 14.

The Correct Answer is (6) — 2 + 4 + 6 = 12. 2 × 6 = 12.

## 15.

The Correct Answer is (8) — Since we know that 1a2a + a31 = 2659, 1 + a = 9. Solving for this, a = 8. Checking for the second value, 2a=16, so a = 8 here too.

## 16.

The Correct Answer is (16)g(2) = 2(22) = 8. f(8)/f(2) = 4. Since f(x) = x2 = d, this simplifies to 64 + d = 16 + 4d. Simplifying this, 48 = 3d and d = 16.

## 17.

The Correct Answer is (320) — We can figure out that angle BAC is equal to 60 degrees, because angle BCA is equal to 30 degrees and the figure shows a right triangle (180 – 30 – 90 = 60). These angles are defined by a 1, 3½, 2 triangle, where 1 is the side opposite the 30 degree angle (AB) and 2 is the hypotenuse (AC). Since we know that side AB is equal to 160, side AC is equal to 320.