1. Arithmetic & Number Sense โ
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 = % ร Whole
What is 15% of 80?
= 0.15 ร 80 = 12
Find the Percent
% = Part รท Whole
What % is 15 of 60?
= 15/60 = 0.25 = 25%
Find the Whole
Whole = Part รท %
30 is 20% of what?
= 30/0.20 = 150
2. Algebra Fundamentals ๐
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 โ x < -3 (sign flipped!)
3. Sequences & Series ๐ข
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... โ 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 ร r^(n-1) | nth term | 3,6,12,24... โ a_5 = 3ร2^4 = 48 |
| r = a_n / a_(n-1) | common ratio | 6/3 = 2 |
| S_n = a_1(1-r^n)/(1-r) | sum (rโ 1) | Sum of 5 terms: 3(1-32)/(1-2) = 93 |
4. Probability & Statistics ๐
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 รท 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 ๐
Basic geometry formulas you should memorize!
Angles
Angle Types
- Acute: Less than 90ยฐ
- Right: Exactly 90ยฐ
- Obtuse: Between 90ยฐ and 180ยฐ
- Straight: Exactly 180ยฐ
Angle Relationships
- Complementary: Sum = 90ยฐ
- Supplementary: Sum = 180ยฐ
- Vertical: Opposite angles are equal
Triangle Properties
- Sum of angles: Always 180ยฐ
- Pythagorean Theorem: aยฒ + bยฒ = cยฒ (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:โ2), 30-60-90 (sides 1:โ3:2)
Circle Properties
- Circumference: C = 2ฯr = ฯd
- Area: A = ฯrยฒ
- Arc length: (ฮธ/360ยฐ) ร 2ฯr
- Sector area: (ฮธ/360ยฐ) ร ฯrยฒ
6. Word Problems ๐
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 ร 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 ๐ฏ
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 ร 80 = 28
Q3: In the sequence 5, 10, 20, 40, ?, what is the next term?
Geometric sequence with r=2. Next: 40 ร 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%