## AFOQT Mathematical Concepts to Master:

### I. Arithmetic

**Properties/Types of Integers:**- Divisibility
- Factorization
- Prime Numbers
- Remainders
- Odd & Even Integers
- Arithmetic Operations
- Exponents & Roots

**Concepts You Should Be Familiar With:**- Estimation
- Percent
- Ratio
- Rate
- Absolute Value
- The Number Line
- Decimal Representation
- Number Sequences

### II. Algebra

- Operations with Exponents
- Factoring & Simplifying Algebraic Expressions
- Relations
- Functions
- Equations & Inequalities (Solving Simultaneous Equations & Inequalities)
- Setting Up Equations to Solve Word Problems

### III. Geometry

- Parallel & Perpendicular Lines
- Circles (Find Area: (3.14)(r^2))
- Triangles (Area & Perimeter)
- Isósceles, Equilateral
- Pythagorean Theorem
- Rectangles, Squares (Area & Perimeter)
- Cylinders (Area, Volume)

(Answers provided at the bottom of the page)

## Practice Questions

57.2%

### Answers:

- C (3451/7562=.4563)
- D (V=LxWxH)
- E ($4.20/4 = $1.05; $4.20-$1.05=$3.15)
- E (3925/4906)
- A (-1×1.8+32=30.2)
- B (10×3) = 30 ; 12+18 = 30
- A (angles of a triangle add up to 180 deg)
- E
- D
- A
- A (-9x, -6x, -3x, x, 5x; Since we know x is positive, the terms can be placed in order from smallest to largest. By definition the median is the middle term in this list)
- C (There are a total of 28 cards – 7 orange; 21 blue. Therefore the probability of selecting an orange card is: 7/28 = 1/4)
- C (The goal here is to isolate the variable to one side with the constants on the other. By subtracting 5x from both sides, you can rewrite the equation as: -5 = x + 8. This simplifies to x = -13 when 8 is subtracted from both sides)
- A (After distributing the 2, the equation is equivalent to 6a -1 = 2a + 2. Simplifying, 4a = 3, so a = 3/4)
- D (The diagonal forms a right triangle with the width and the length acting as legs. Using the Pythagorean theorem, the length of the triangle will be √25^2 – 15^2 = √400 = 20, and the area will be 20 x 15 = 300)
- A
- C
- D (If the number of sophomores in the room is x, then the number of freshman is 7x. The total number of people in the room is 7x + x = 8x. The number of people in the room (8x) must be a multiple of 8.)
- D
- B (The sum of the exterior angles of any polygon is 360°, so the exterior angle at vertex Z is 360°-130°-110° = 120°. However, this is not the value of the question asked. Since the sum of the interior angle of a polygon and its exterior angle is 180°, the interior angle at vertex Z is 180°-120° = 60°)