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Sample Topics

### Algebra

Algebra - is a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
Sample Questions:

1. Apply the product rule for exponents, if possible. 25) (-2×3)(9x10y6) 26) 5 5 -3 -3 0 4

2. A recipe calls for 1/2 cups of sugar. You find that you only have 1/18 cups of sugar left. What fraction of the recipe can you make? Your answer must be a fraction written in simplest terms. If your answer is a whole number, then give your answer as a fraction with 1 in the denominator. Cups of sugar

### Prealgebra

Prealgebra - the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.
Sample Questions:

1. Imagine a new pasture with grass growing on it. Every day after the seeds have germinated, the number of blades of grass in the pasture triples. After 18 days, the entire pasture is completely covered in grass. How many days did it take for the pasture to be one-third covered in grass?

2. Construct a Venn diagram illustrating the sets below U-(1,2,3,4,5,6,7,8,9) X (1,2, 4, 7) Y= {1, 6, 7, 8} Z-2,5, 6,7) 5 6 9

### Precalculus

Precalculus - A course of study taken as a prerequisite for the study of calculus, usually involving advanced algebra and trigonometric functions.
Sample Questions:

1. Write the following in terms of sin e and cos θ; then simplify if possible. (Leave your answer in terms of sin θ and/or cos θ.) csc θ tan θ Need Help?

2. Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if po log

### Geometry

Geometry - The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.
Sample Questions:

1. Congruent Inscribed Angles Proof.How would you prove that two angles in a circle that inscribe the same arc are congruent?Is it possible to prove it without using the “Congruent Inscribed Angles Theorem”

2.a. fx,y)-(e,cos(xy Let c(t) be a path with c(0) (0,0) and c'(0) 1,2). What is the tangent vector to f o clt) at t 0 b. fr,y)-esinx-y Let c(t) be a path with c(0) (0,0) and c'(0) (2,-3). What is the tangent vector to fo clt) at t0

### Trigonometry

Trigonometry - The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
Sample Questions:

1. Why is the magnitude of the sum of two vectors less than or equal to the sum of the magnitudes of each vector? Please be as detailed as possible.

2. 1)Explain why you will get an error for cos-1(-1.008). Specific.2) Solve algebraically, 2sin(3x)-1=0, give the first exact positive solutions.

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