1) Points A, B, and C lie on a line in that order, as shown below. The ratio of the length of AB to the length of AC is 7 to 10. What is the ratio of the length of AB to the length of BC, if it can be determined?

2) Which of the following expressions is equivalent to

$$\left(3x^2-2x+4\right)+\left(2x-1\right)-\left(x^2-3x+2\right)?$$

3) The following statements are true of the players of a game that uses cards numbered 1–10. I. George has none of the same cards as Ian.

II. George has all the cards that Fiona has.

III. Ian has all the cards that Hailey has.

Which of the following statements must be true?

4) Which of the following expressions is equivalent to $$\frac{p^2-3p}{2p}+\frac{1}{p^2}?$$

5) The students in a math class are asked to determine the equation of an unknown linear function, f. The teacher tells the class that the output of the function is 7 when the input is 4. The teacher also says that the output of the function is 28 when the input is 16. Which of the following equations correctly expresses the function f, where x is the input and f(x) is the output?

6) A salesman earns $600 per week in base salary. For each successful sale, he receives $125 in commission. Which of the following represents the amount of money, in dollars, the salesman earns in a given week in which he makes s successful sales?

7) The expression (n² – 6n + 5)(n + 4) is equivalent to

8) If $$f\left(a\right)=a^2+3\ ,\ g\left(a\right)=3a-1,\$$ which of the following is an expression for g(f(a))?

9) Which of the following expressions is equivalent to (y – 4)^–50 ?

10) In a professional sports league consisting of x teams, y represents the number of teams that qualify for the playoffs in a given season. Which of the following could be used to determine the fraction of teams that does NOT make the playoffs in a given season?

11) For positive real numbers x, y, and z such that 3x = 4y and $$\frac{2}{3}y=\frac{1}{3}z$$ , which of the following inequalities is true?

12) If x>y, then $$-\left|y-x\right|$$ is equal to?

13) What is the LEAST possible integer value of a + b, if 6 < b < a ?

14) If –1 < x < 0, then which of the following must be true

15) Consider all pairs of positive integers a and b whose sum is 6. For how many values of a does $$a^b=b^a$$ ?