The AEPA Middle Grades Mathematics Exam will test concepts needed to teach the subject in Arizona public schools, according to Arizona Academic Standards. The test contains five parts, each worth 20% of the total score. The first is Number Sense and Operations, which involves numeration systems and number theory, numerical operations, and properties of the real number system. The second part is Data Analysis, Probability, and Discrete Mathematics. In addition to the principles of probability, this test area deals with collecting, organizing, evaluating and analyzing data.

The Patterns, Algebra, and Function section includes recognizing patterns, manipulating basic algebraic functions, and using linear and nonlinear functions to solve problems. The fourth section is Geometry and Measurement, which requires an understanding of the principles of measurement, as well as Euclidean, coordinate, and transformational geometry. The last section-Mathematical Processes and Reasoning-calls for the ability to explain principles of problem solving and mathematical reasoning.

## AEPA Middle Grades Mathematics Exam Study Questions

**1. 4 ^{2} + 15^{3} x(3^{2})^{3} – 5^{4} / 2^{2} =**

A. 423,718.75

B. 617,853.5

C. 2,459,733.8

D. 2,460,234.8

**2. Identify the correct prime factorization of 72.**

A. 2^{3} x 3^{2}

B. 3^{2} x 2^{3}

C. 8 x 9

D. 12 x 6

**3. A rectangular wooden block is 48 in long, 30 in wide and 16 in high. If each cube of side 2 in is cut away from each of its corners, what is the volume of the wooden block left?**

A. 22,976 in^{3}

B. 23,008 in^{3}

C. 23,032 in^{3}

D. 23,040 in^{3}

**4. 5/12 of the visitors to a park were children, 1/3 were adults, and the rest were senior citizens. If there were 480 people altogether, how many were senior citizens?**

A. 90

B. 120

C. 200

D. 360

**5. The following table shows admission prices to a museum exhibit for members and non-members.**

Members | Non – Members | |

Adults | $8.50 | $10.50 |

Sr. Citizens | $6.50 | $8.50 |

Children | $5.50 | $7.50 |

A family, made up of 4 adults who are members, 2 senior citizens who are members, 1 senior citizen who is not a member, 3 children who are members and 3 children who are not members, visited the exhibit. Find the total amount they paid for admission.

A. $78.00

B. $86.50

C. $94.50

D. $102.50

**6. Ashley and Catherine departed to travel from town A to town B at constant speeds of 58 miles per hour and 63 miles per hour respectively, at the same time. How far apart were they after 3 ^{1}/_{2} hours?**

A. 9 miles

B. 15 miles

C. 17 miles

D. 17.5 miles

**7. Find the next two numbers in the following pattern:**

** 48,12,44,11,40,10,36,9,____,____**

A. 35,7

B. 32,8

C. 28,7

D. 8,32

**8. Identify which rule describes the sequence -20, -15, -10, -5, . . .**

A. Subtract +5

B. add -5

C. add +5

D. multiply by -5

**9. Which order of steps would you perform to solve for (a) in the equation 8a = 6a + 10?**

A. Subtract 6a from both sides of the equation, then divide by 2.

B. Divide by 8, and add 10 to both sides of the equation.

C. Add 10 to both sides of the equation, then subtract 8a.

D. Multiply by 6 and subtract 10 from both sides of the equation.

**10. Use the function y = 3x – 1 to determine the numbers that complete the function table.**

X | 2 | 4 | |

Y | 5 | 17 |

A. x = 1, y = 8

B. x = 3, y = 10

C. x = 5, y = 12

D. x = 6. y = 11