We publish practice problems on our social media pages. Here's where you can find the correct answers—and explanations.

THE CORRECT ANSWER IS D.

The question asks for the value of an expression for a certain value of the variable. Plug in the number given for a in the expression to find the value: –2 + (–2)^{2} – (–2)^{3} + (–2)^{4} – (–2)^{5}. Remember PEMDAS, the order of operations: The first thing to do here is deal with the Exponents, then we can take care of the Addition and Subtraction: –2 + 4 – (–8) + 16 – (–32), which simplifies to –2 + 4 + 8 + 16 + 32 = 58. The correct answer is (D).

THE CORRECT ANSWER IS B.

The question asks for the value of *n*. First, simplify the equation 4* ^{x}* •

THE CORRECT ANSWER IS D.

The question asks for the value of *t*. To figure out how much you need to add to 2.74 to get to 4.22, take 4.22 – 2.74 on your calculator. The difference between the two numbers is 1.48. This increase reflects the same number, *t*, added to each of the four numbers on the list. Divide 1.48 by 4 to find that *t* = 0.37. The correct answer is (D).

THE CORRECT ANSWER IS D.

The question asks for the value of 24/*x* . First, solve for *x*. Divide both sides of the equation by 3, and you get *x* = 4. Then divide 24 by 4, which gives you 6. The correct answer is (D).

THE CORRECT ANSWER IS C.

The zero of *g *is the value of the variable, in this case *x*, when the equation is set to 0. This is also called the root or solution of an equation. Set the equation to 0 to get 0 = 2*x*2 – *dx *– 6. Plug 6 in for *x *to get 0 = 2(62) – *d*(6) – 6. Simplify the equation to get 0 = 72 – 6*d *– 6, or 0 = 66 – 6*d*. Solve for *d *to get –66 = –6*d*, so 11 = *d*. Plug 11 in for *d *and set the quadratic to 0 to get 0 = 2*x*2 – 11*x *– 6. Factor the equation to get 0 = (*x *– 6)(2*x *+ 1). The other zero of the equation is when 2*x* + 1 = 0. Solve for *x* to get 2*x* = –1, or *x* = –1/2. The correct answer is (C).

THE CORRECT ANSWER IS B.

The question asks for the value of *f*(3) + *f*(5), so find the values of *f*(3) and f(5) separately: *f*(3) = 2(3)2 + 4 = 22 and f(5) = 2(5)2 + 4 = 54. So *f*(3) + *f*(5) = 76. Now evaluate the answers to see which one will give a result of 76. You can tell that *f*(4) will be between 22 and 54, so you can cross out (A). If you Ballpark (C) and (D), putting 10 or 15 in the function will give you a number bigger than 100, and you’re looking for 76, so (C) and (D) are too big. The correct answer is (B).

THE CORRECT ANSWER IS C.

The question asks for the equation that best models the ball’s acceleration. Figure out the points that will be on the graph from the data given: (0, 0), (1, 5), (2, 10), (3, 15), (4, 20). Draw a line through or close to these points to get an idea of what the graph will look like. Then use POE. The line is linear, not quadratic, so you can eliminate (D). It is also clear that the line begins at the origin, so the y-intercept will be 0. This will eliminate (A). A slope of 25 is far too big—Ballpark—so you can eliminate (B). The correct answer is (C).

THE CORRECT ANSWER IS B.

The question asks for the value of *c*. Start by plugging in what you know into the given function. If *f *( *x *) = *x *2 – *c*, and *f *(–2) = 6, then plug in –2 for *x *in the function: *f *(–2) = (–2) 2 – *c*. Solve and replace *f *(–2) with 6: 6 = 4 – *c *; 2 = – *c*; and *c *= –2. If you picked (A), you forgot that (–2) 2 is positive 4. The correct answer is (B).

THE CORRECT ANSWER IS D.

The question asks for the difference in minutes between Steve’s time and Adam’s time. Use a Rate Pie to calculate the time for each runner. To find Steve’s time, divide his distance by his rate, which means that he runs for 1 1/2 hours (or 1.5 if you’re using your calculator). Adam runs the same 12 miles at 6 miles per hour. This means that Adam runs for 2 hours. Adam takes half an hour longer to complete the race, and half an hour is 30 minutes. The correct answer is (D).

THE CORRECT ANSWER IS C.

The question asks for an expression that is equivalent to the given one. There are variables in the answer choices, which means this is a perfect Plug In problem. Since you can’t use a calculator, make up an easy value for *x*, such as 2. Therefore, 9* ^{x} *+ 3

THE CORRECT ANSWER IS D.

The question asks for the ratio of *a *to *c *and defines both in terms of *x*. Since you are never told what *x *is, and there is no way to find it, plug in for *x*. Say that *x *= 100. Then, 63% of 100 is 63, and 3/8 of 100 is 37.5. The ratio of *a *to *c *is *a */ *c*. So, 63/37.5 = 1.68. To save time, you can Ballpark the answer, since *a* > *c* and (D) is the only choice greater than 1. The correct answer is (D).

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