Overview of the Math Content

The math section of the THEA Study exam includes various topics, which can be broadly categorized as follows:

1. Number Operations and Quantitative Reasoning
2. Algebraic Reasoning
3. Geometric Reasoning
4. Data Analysis and Probability

1. Number Operations and Quantitative Reasoning

This section tests your understanding of basic arithmetic operations, as well as your ability to apply these operations in real-world scenarios. Key concepts include:

• Whole numbers and decimals
• Fractions
• Ratios and proportions
• Percentages

Example Problem:

If a shirt originally costs $40 and is on sale for 25% off, what is the sale price?

Solution:

1. Calculate the discount: $0.25\times 40=10$
2. Subtract the discount from the original price: $40-10=30$

The sale price is $30.

2. Algebraic Reasoning

Algebraic reasoning involves understanding variables, expressions, equations, and functions. Important topics include:

• Simplifying expressions
• Solving equations and inequalities
• Understanding functions and graphs

Example Problem:

Solve for $x$: $2x+5=15$

Solution:

1. Subtract 5 from both sides: $2x=10$
2. Divide by 2: $x=5$

3. Geometric Reasoning

Geometric THEA Study reasoning tests your understanding of shapes, sizes, and the properties of space. Topics include:

• Area and perimeter
• Volume and surface area
• Angles and lines

Example Problem:

What is the area of a rectangle with a length of 8 units and a width of 5 units?

Solution:

Area = Length × Width = $8\times 5=40$ square units.

4. Data Analysis and Probability

This section assesses your ability to interpret and analyze data. Key concepts include:

• Mean, median, and mode
• Interpreting graphs and charts
• Basic probability

Example Problem:

Find the mean of the following set of numbers: 3, 7, 5, 10.

Solution:

Mean = 3+7+5+104=254=6.25\frac{3 + 7 + 5 + 10}{4} = \frac{25}{4} = 6.2543+7+5+10​=425​=6.25.

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