– 14i^2 . Simplify the result by multiplying through where you can to get 2 – 8i + i – 14i^2 . To
combine the i terms, multiply 8 by to get . Now the expression is 2 – i + i – 14i^2 ,
which can be further simplified to 2 – i – 14i^2 . Substitute –1 for i^2 and combine like terms: 2 –
i + 14i = 16 – i, which is (A).
14. A The first step to answering this question is to get the equation into the standard form of a
quadratic equation by moving all the terms to the left or right side of the equation and setting it
equal to zero, like this: rx^2 – x − 3 = 0. Now that you have the equation in standard form, you
can begin to solve for the roots. Since you are given variables instead of numbers, factoring this
quadratic would require higher-level math, if it were even possible. You may have noticed the
familiar form of the answer choices. They are in a form similar to the quadratic equation.
Remember that a quadratic in standard form is represented by the equation ax^2 + bx + c = 0, and
the quadratic formula is x = . In this equation, a = r, b = – , and c = –3.
Therefore, x = . This exact format is not present in the
answer choices, but the root part only matches the one in (A), so that is likely the answer. You
will have to do a little more manipulation before you can get the equations to match exactly. The
fractions need to be split up, so rewrite the equation as x = or x =
.
Algebra Drill 2: Calculator-Permitted Section
4. A Solve the first inequality by subtracting 6 from each side so that x > –6. You are looking for
values that won’t work for x, and x cannot equal –6. Therefore, the answer must be (A). Just to
be sure, solve the next inequality by subtracting 1 from each side to get –2x > –2. Divide by –2,
remembering to switch the sign because you are dividing by a negative number, to get x < 1. The
values in (B), (C), and (D) fit this requirement as well, so they are values for x and not the
correct answer.
