1. Advanced Algebra 📐

Algebra forms the foundation of higher mathematics. Mastering these concepts is crucial for the DOST-SEI exam and your future STEM studies.

Topic	Key Concepts	Common DOST Questions
Polynomials	Addition, subtraction, multiplication, division, factoring	Find roots, factor completely
Quadratic Equations	ax² + bx + c = 0, Quadratic formula, discriminant	Solve for x, nature of roots
Systems of Equations	Substitution, elimination, Cramer's rule	Solve 2 or 3 variable systems
Functions	Domain, range, composition, inverse	Find f(g(x)), f⁻¹(x)
Sequences & Series	Arithmetic, geometric progressions	Find nth term, sum of series

Essential Formulas:

Quadratic Formula:

x = (-b ± √(b²-4ac)) / 2a

Discriminant (b² - 4ac):

> 0: Two real roots
= 0: One real root (repeated)
< 0: No real roots

💡 DOST Tip:

The exam loves word problems that translate to systems of equations. Practice converting verbal problems to mathematical expressions!

2. Geometry & Trigonometry 📏

Geometry tests your spatial reasoning while trigonometry is essential for engineering and physics applications.

Plane Geometry:

Triangle: Area = ½bh, angles sum = 180°
Circle: Area = πr², Circumference = 2πr
Parallelogram: Area = bh
Trapezoid: Area = ½(b₁+b₂)h

Solid Geometry:

Cube: V = s³, SA = 6s²
Cylinder: V = πr²h
Sphere: V = (4/3)πr³
Cone: V = (1/3)πr²h

Angle θ	0°	30°	45°	60°	90°
Sin θ	0	1/2	√2/2	√3/2	1
Cos θ	1	√3/2	√2/2	1/2	0
Tan θ	0	√3/3	1	√3	∞

🔥 Memorize SOH-CAH-TOA:

SOH: Sin = Opposite / Hypotenuse
CAH: Cos = Adjacent / Hypotenuse
TOA: Tan = Opposite / Adjacent

3. Statistics & Probability 📊

Data analysis and probability are increasingly important in the DOST exam, reflecting their relevance in modern STEM fields.

Measure	Formula	When to Use
Mean (Average)	Σx / n	Symmetric data, no outliers
Median	Middle value when sorted	Skewed data, with outliers
Mode	Most frequent value	Categorical data
Range	Max - Min	Quick spread measure
Variance	Σ(x-x̄)² / n	Measure of spread
Standard Deviation	√Variance	Same unit as data

Probability Rules:

Basic: P(E) = Favorable outcomes / Total outcomes
Complement: P(not E) = 1 - P(E)
Addition (OR): P(A or B) = P(A) + P(B) - P(A and B)
Multiplication (AND): P(A and B) = P(A) × P(B) for independent events

4. Practice Questions 📝

Question 1: Quadratic Equation

Find the roots of 2x² - 5x - 3 = 0

Solution: Using quadratic formula: x = (5 ± √(25+24)) / 4 = (5 ± 7) / 4

Answer: x = 3 or x = -1/2

Question 2: Trigonometry

In a right triangle, if sin θ = 3/5, what is cos θ?

Solution: Using Pythagorean identity: sin²θ + cos²θ = 1

cos²θ = 1 - (3/5)² = 1 - 9/25 = 16/25

Answer: cos θ = 4/5

Question 3: Probability

A bag contains 5 red and 3 blue balls. If two balls are drawn without replacement, what is the probability both are red?

Solution: P(both red) = P(1st red) × P(2nd red | 1st red) = (5/8) × (4/7) = 20/56 = 5/14

Answer: 5/14 or approximately 0.357

Question 4: Statistics

Find the mean and median of: 3, 7, 7, 2, 9, 5, 8

Solution:

Mean = (3+7+7+2+9+5+8) / 7 = 41/7 ≈ 5.86

Sorted: 2, 3, 5, 7, 7, 8, 9 → Median = 7 (middle value)

Answer: Mean ≈ 5.86, Median = 7

Mathematics