In you opinion, what are the hardest math SAT questions you've seen?

I'm studying for the SAT, and I'd like some advice on tackling the most difficult math questions. What question types or concepts have you found particularly tough, and do you have any tips for mastering those problems?

I can understand why you'd want to focus on the more challenging SAT math questions. Here are some commonly difficult question types and concepts, along with tips to tackle them:

1. Complex Word Problems: These problems often involve multiple steps, such as solving for a variable and then using it to answer the main question. To approach these questions, carefully read the problem, underline key information, and consider drawing a diagram if relevant. Break the problem into smaller pieces, and use logic and intuition to guide your steps.

2. Systems of Equations: To master systems of equations, make sure you're familiar with different solving methods, such as substitution, elimination, and matrices. Depending on the system, one of these methods may end up being more efficient.

3. Quadratic Equations and Functions: Quadratics can appear in various forms, so understand how to manipulate equations into standard form, vertex form, or factored form. Practice using the Quadratic Formula, completing the square, and factoring quadratics to solve equations.

4. Advanced Geometry: Challenging geometry problems on the SAT may include circles inscribed within or around other shapes, parallelograms, or three-dimensional shapes. Familiarize yourself with relevant theorems and properties for these concepts (e.g., properties of parallelograms) and practice applying them to various problems.

5. Trigonometry: Trigonometry questions are less common but can be quite tricky. Make sure you know the basic trigonometric ratios, SOHCAHTOA, the Pythagorean trigonometric identity, and how to use these concepts to solve problems involving right triangles.

6. Functions: These questions often involve function notation, composition, inverses, and transformations. To prepare, review these concepts, and practice combining and manipulating different functions.

7. Probability and Statistics: Understand permutations, combinations, and probability rules (e.g., the addition and multiplication rules). Analyze data in tables and graphs, and calculate the mean, median, mode, and standard deviation.