1. Arithmetic & Number Sense ➗

DLSUCET starts with fundamentals - don't underestimate these! Many students lose points on careless mistakes here.

Operations with Integers

Integer Rules

Adding same signs: Add values, keep sign. (+5) + (+3) = +8, (-5) + (-3) = -8
Adding different signs: Subtract, keep sign of larger. (+5) + (-3) = +2
Multiplying/Dividing: Same signs = positive, Different signs = negative

Fractions, Decimals, Percentages

Fraction	Decimal	Percent
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/3	0.333...	33.33%
2/3	0.666...	66.67%
1/8	0.125	12.5%

Percentage Problems

Find the Part

Part = % × Whole

What is 15% of 80?

= 0.15 × 80 = 12

Find the Percent

% = Part ÷ Whole

What % is 15 of 60?

= 15/60 = 0.25 = 25%

Find the Whole

Whole = Part ÷ %

30 is 20% of what?

= 30/0.20 = 150

2. Algebra Fundamentals 📐

Algebraic manipulation is key for DLSUCET. Master these core skills!

Solving Linear Equations

Step-by-Step Process

Remove parentheses (distribute)
Combine like terms on each side
Move variables to one side (add/subtract)
Move constants to other side
Divide by coefficient of variable
Check by substituting back

Systems of Equations

Substitution Method

Solve one equation for a variable
Substitute into the other equation
Solve for remaining variable
Back-substitute to find first variable

Elimination Method

Multiply equations to match coefficients
Add/subtract to eliminate one variable
Solve for remaining variable
Substitute to find the other

Inequalities

Important Rule!

When multiplying or dividing by a NEGATIVE NUMBER, FLIP the inequality sign!

-2x > 6 → x < -3 (sign flipped!)

3. Sequences & Series 🔢

Pattern recognition through number sequences - a DLSUCET favorite!

Arithmetic Sequences

Formula	Meaning	Example
a_n = a_1 + (n-1)d	nth term	2,5,8,11... → a_10 = 2+(9)(3) = 29
d = a_n - a_(n-1)	common difference	5-2 = 3
S_n = n(a_1 + a_n)/2	sum of n terms	Sum of first 10: 10(2+29)/2 = 155

Geometric Sequences

Formula	Meaning	Example
a_n = a_1 × r^(n-1)	nth term	3,6,12,24... → a_5 = 3×2^4 = 48
r = a_n / a_(n-1)	common ratio	6/3 = 2
S_n = a_1(1-r^n)/(1-r)	sum (r≠1)	Sum of 5 terms: 3(1-32)/(1-2) = 93

4. Probability & Statistics 📊

Basic probability concepts appear frequently in DLSUCET.

Probability Fundamentals

Basic Formula

P(event) = favorable outcomes / total outcomes

Probability is always between 0 and 1 (or 0% to 100%)

Complementary Events

P(not A) = 1 - P(A)

If P(rain) = 0.3, then P(no rain) = 0.7

Combined Events

AND (both): Multiply probabilities

OR (either): Add probabilities (subtract overlap)

Statistics Basics

Measure	Definition	Example (2,4,4,5,10)
Mean (Average)	Sum ÷ Count	(2+4+4+5+10)/5 = 5
Median	Middle value (sorted)	4 (middle of sorted list)
Mode	Most frequent	4 (appears twice)
Range	Max - Min	10 - 2 = 8

5. Geometry Essentials 📐

Basic geometry formulas you should memorize!

Angles

Angle Types

Acute: Less than 90°
Right: Exactly 90°
Obtuse: Between 90° and 180°
Straight: Exactly 180°

Angle Relationships

Complementary: Sum = 90°
Supplementary: Sum = 180°
Vertical: Opposite angles are equal

Triangle Properties

Sum of angles: Always 180°
Pythagorean Theorem: a² + b² = c² (for right triangles)
Common right triangles: 3-4-5, 5-12-13, 8-15-17, 7-24-25
Special triangles: 45-45-90 (sides 1:1:√2), 30-60-90 (sides 1:√3:2)

Circle Properties

Circumference: C = 2πr = πd
Area: A = πr²
Arc length: (θ/360°) × 2πr
Sector area: (θ/360°) × πr²

6. Word Problems 📝

DLSUCET includes practical math applications. Here's how to approach them!

Age Problems

Set up equations with variables.

"Maria is twice as old as Ana. In 5 years, their ages sum to 40."

Let Ana = x, Maria = 2x

(x+5) + (2x+5) = 40

Rate Problems

Distance = Rate × Time

"A jeepney travels 60km in 2 hours. What's the rate?"

Rate = 60/2 = 30 km/hr

Example: Mixture Problem

Problem: How many liters of 30% alcohol solution must be mixed with 60 liters of 80% alcohol to get 50% alcohol?

Solution:

Let x = liters of 30% solution

0.30x + 0.80(60) = 0.50(x + 60)

0.30x + 48 = 0.50x + 30

18 = 0.20x

x = 90 liters

7. DLSUCET Math Tips & Practice 🎯

Exam Strategies

Check Your Work: Careless errors cost points on easy questions
Use Estimation: Quickly eliminate obviously wrong answers
Plug In Values: When stuck, try substituting answer choices
Watch Units: Make sure your answer has the correct units
Manage Time: Don't spend too long on any single problem

Practice Questions

Q1: If 3x - 7 = 14, what is x?

3x = 14 + 7 = 21, so x = 21/3 = 7

Q2: What is 35% of 80?

0.35 × 80 = 28

Q3: In the sequence 5, 10, 20, 40, ?, what is the next term?

Geometric sequence with r=2. Next: 40 × 2 = 80

Q4: A bag has 3 red, 4 blue, and 5 green balls. What's the probability of picking a blue ball?

P(blue) = 4/(3+4+5) = 4/12 = 1/3 or 33.3%

Mathematics