Understanding the intricacies of actuarial science requires familiarity with a comprehensive set of formulas. These formulas play a pivotal role in evaluating the financial implications of future events, such as mortality rates, interest rates, and insurance premiums. Actuarial professionals rely heavily on these formulas to calculate premiums, design insurance policies, and assess financial risks associated with various life events. As such, it is essential for aspiring actuaries to master these formulas to succeed in their field.
The Best Structure for Formulas to Know for ACT
Many students struggle with the math section of the ACT, but knowing the right formulas can make a big difference. Here’s a breakdown of the most important formulas you should know for the ACT, organized by topic:
Algebra
- Solving linear equations: ax + b = c; x = (c – b)/a
- Solving quadratic equations: ax^2 + bx + c = 0; x = (-b ± √(b^2 – 4ac)) / 2a
- Factoring polynomials: (a + b)(a – b) = a^2 – b^2; (a + b)^2 = a^2 + 2ab + b^2
- Simplifying radical expressions: √(ab) = √a √b; √(a/b) = √a / √b
Geometry
- Area of a triangle: A = (1/2)bh
- Area of a circle: A = πr^2
- Area of a rectangle: A = lw
- Volume of a cube: V = s^3
- Volume of a cylinder: V = πr^2h
- Volume of a cone: V = (1/3)πr^2h
Trigonometry
- Sine, cosine, and tangent: sin θ = opposite / hypotenuse; cos θ = adjacent / hypotenuse; tan θ = opposite / adjacent
- Pythagorean theorem: a^2 + b^2 = c^2
- Law of sines: a / sin A = b / sin B = c / sin C
- Law of cosines: c^2 = a^2 + b^2 – 2ab cos C
Other
- Percent: % = (part / whole) * 100
- Slope-intercept form of a line: y = mx + b
Question 1: What formulas are essential for success in ACT?
Answer:
– Future Value (FV) Formula: FV = PV * (1 + r)^n
– Present Value (PV) Formula: PV = FV / (1 + r)^n
– Compound Interest Formula: A = P(1 + r/n)^(nt)
– Geometric Sequence Formula: an = a1 * r^(n-1)
– Arithmetic Sequence Formula: an = a1 + (n-1)d
Question 2: How are these formulas used in ACT?
Answer:
– FV and PV formulas: Solve problems involving future or present value of investments, loans, and annuities.
– Compound Interest formula: Calculate the accumulated value of an investment over time with compound interest.
– Geometric and Arithmetic Sequence formulas: Determine the nth term or sum of terms in a geometric or arithmetic sequence, often used in probability and counting problems.
Question 3: What are some strategies for using these formulas in ACT?
Answer:
– Memorize the formulas: Avoid wasting time looking for them during the test.
– Understand the underlying concepts: Comprehend how each formula relates to the principles of interest, annuities, and sequences.
– Practice applying the formulas: Solve numerous practice problems to build fluency and accuracy.
– Estimate and check: Make reasonable estimates to verify the plausibility of your answers and avoid calculation errors.
Thanks for sticking with me through this ACT math formulas crash course. I know it’s not the most exciting topic, but it’s essential for acing the test. If you’ve got any more ACT-related questions, feel free to drop me a line. And be sure to check back for more study tips and tricks. Until next time, keep calm and conquer the ACT!