This is a compound-function question, in which you'll have to apply two functions in combination. The most important rule to remember is that you have to work from the inside out. Start by finding g(2.3). That means putting the number 2.3 in place of the x in the definition of g(x), g(2.3) = + 1 = (1.52) + 1 = 0.76 + 1 = 1.76. Once you know that g(2.3) = 1.76, you know that f(g(2.3)) is equal to f(1.76), which is easily solved. f(1.76) = = 1.21. The correct answer is (B).

This is a complex number, because it has both real and imaginary components. To find its absolute value, visualize the term 6 - 3i on the complex plane, where one axis represents real values and the other represents imaginary values.

This is a great question for Plugging In. Plug In a couple of simple values, like x = 3 and y = 5, and solve. |3 - 5| + |5 - 3| = |- 2| + |2| = 2 + 2 = 4 The correct answer must also equal 4. Using x = 3 and y = 5, you'll find that only (D) gives you the correct value.

An arithmetic series is one that increases by a constant added amount. From 4 to 15 is a total increase of 11, which happens from the second term in the arithmetic series to the tenth, taking 8 steps. This means that each step is worth one-eighth of 11, , or 1.375. That's the constant amount added to each term in the series to get the next term. To find the first term in the series, just take one step backward from the second term, that is, subtract 1.375 from 4. You get 2.625.

A The simple, grinding way to do this one is to use the distance formula on the answer choices. Any answer choice that produces a distance other than 25 or 26 can be discarded immediately. Only (A) produces distances of 25 and 26 from the two points given.

The statements f(a, b) = 15, f(b, c) = 20, and f(a, c) = 10 can be rewritten as equations by inserting the definition of the function f(x, y).

(A) Subtract |x| from both sides of the equation. Since |y| cannot be negative, graph the piecewise function

This is a little tricky; you've got to pay attention to that underlined word, "increased." The values in the equation g(x) = A[sin (Bx + C)] + D that determine amplitude and period are A and B, respectively. Quantities C and D do not have to change to alter the amplitude or period, so (C) and (E) are out. The trick is that while you increase the amplitude by increasing A, you increase the period by decreasing B. If the amplitude and period of the curve both increase, that means that A increases and B decreases.

(D) Length =

(D) Substitute 3 for x set equal to zero and solve for K.

(A) Graph y = sin x and y = cos in radian mode using the Xmin = 0 and Xmax = . Observe that the first graph is beneath the second on [0,0.79].

Set up a proportion: = . Simplify: 4a = 350, and a = 87.5. You can also approximate. When b goes up, a goes up. So you can eliminate (A) and (B).

is a radius of the circle, and

Isolate y:

B Use three average pies:

Let P = the number of employees at the beginning of 2003. By the end of 2003, the number of employees increases by 18% of P or 0.18P, so the number becomes P + 0.18P = 1.18P.

(D) The probability that a student is a girl at this high school is 0.6. The probability that a student who plays a sport is a girl is 0.65. Therefore, the probability that a girl student plays a sport is (0.6)(0.65) = 0.39. [4.2]

(D) Add the components to get The magnitude is

If 25% of a number is 36, then that number is 36 times 4, or 144. Forty percent of that is (0.40)(144) = 57.6.

The first couple must compete against 5 couples. The second couple has already faced the first couple, so they have to compete against only four new couples. The third couple has to compete against three new couples, and so on. This means that to make sure everyone competes in a dance-off with everyone else, there have to be 5 + 4 + 3 + 2 + 1 = 15 dance-offs. Multiply 15 by the 3 times this must happen, and you get 45.

You'll want to use Process of Elimination here to knock out some answer choices. The best numbers to plug into the function are the ones in the answer choices: 10 and -10. Start by finding out whether the statement f(x) = f(-x) is true when x = 10. f(10) = |10| + 10 = 20. f(-10) = |-10| +10 = 10 + 10 = 20. Since f(10) and f(-10) are equal, f(x) = f(-x) is true when x = 10, and every answer choice that does not include 10 can be eliminated. That gets rid of (A), (D), and (E). To choose between the remaining answers (B) and (C), Plug In a number included in (C) but not in (B). A simple number like zero works best. f(0) = |0| + 10 = 10. f(-0) = |-0| + 10 = 0 + 10 = 10. You can see that f(0) = f(-0), so zero must be part of the correct answer. (B) does not include zero, so you can eliminate it. (C) is correct.

This is a fancy simultaneous-equations question. It's impossible to solve for the value of x, y, or z, but you can find the value of their sum. It's done by adding the equations, like

(D)a2 = 5, a3 = 8, a4 = 12, a5 = 17. Therefore, S5 = 45

This is a great PITA question. When you receive an inheritance in Titheland, you get the first 1,000 florins free and clear. After that, you get only 35% of the remaining amount; the government keeps the other 65%. To find the right answer, take the numbers from the answer choices and see which one would give you 2,500 florins after taxes.

Mary spends 40% of her earnings on rent.

Sketch a diagram. First the ball drops 10 meters and rebounds of that, or 8 meters:

Solving x2 + 2x - 3 = 0 is just a matter of factoring.

Draw a rough sketch:

(A) Since f(2) implies that x = 2, g(f(2)) = 2. Therefore, g(f(2)) = 3(f(2)) + 2 = 2. Therefore, f(2) = 0.

D With few exceptions, logic questions on the Math Level 1 test you on the contrapositive. The idea is that, given a statement like "If A, then B," the only thing you automatically know is the contrapositive: "If not B, then not A." Here, you're told that no doctoral candidates graduate. In Cookie Monster language, that would read "If doctoral student, then no graduate." The contrapositive would be "If graduate, then not doctoral student." That's almost exactly what (D) says (since there are only engineers and doctoral candidates at this school, not being a doctoral candidate is the same as being an engineer). The other answer choices all talk about subjects you don't know anything about, like the number of students or the quality of their scholarly skills. You can eliminate those answer choices.

A PITA. Plug In values from the answer choices, and see which one makes the equation true. Only (A) does it. When solving this question algebraically, the trick is to isolate x one step at a time. The correct order is below.

In a composition of functions, first evaluate the innermost function, in this case g(2): 4 × 2 + 3 = 8 + 3 = 11. Now use this result in the outermost function f: f(11) = 112 - 10 = 121 - 10 = 111.

(D) Press 5 ENTER into your graphing calculator. Then enter and press ENTER twice more to get a3.

Use the Group Problem Formula, Total = Group 1 + Group 2 + Neither - Both. Here, you've got 850 = 250 + 450 + 350 - Both. So Both = 200. Pick (C). You need to memorize this formula!

Translate the words into algebra. Six less than a number n is n - 6. The equation is thus (n - 6)5 = 32. Take the fifth root of each side to get n - 6 = 2. Add 6 to both sides of the equation, and n = 8.

Use the definition of a logarithm to rewrite the equation logy 2 = 8 in exponential form, y8 = 2. To find the value of y, take the eighth root of both sides. This can be done on your calculator by raising 2 to the power of one-eighth, or 0.125. You'll find that y = 1.09. The correct answer is (C). You can also PITA, starting with (C), which works.

(B) Since one particular man must be on the committee, the problem becomes: "Form a committee of 3 from 8 men." Calculate 8nCr3 = 56. [3.1]

(A) Calculate the common ratio as . The first term is so the nth term is . Use the sum and sequence features of your calculator to evaluate the sum of the first 10 terms in the generated sequence:

Divide this polynomial using long division: