1. Speed Math & Algebra Mastery ⚡

ACET Math is notorious for being time-pressured. Hindi sapat na alam mo lang ang concept - you need to solve FAST and ACCURATELY.

Time Pressure Reality Check

ACET Math: ~50-60 items in limited time = less than 1 minute per item!

Essential Algebra Shortcuts

Expression	Shortcut Formula	Example
(a+b)^2	a^2 + 2ab + b^2	(x+3)^2 = x^2 + 6x + 9
(a-b)^2	a^2 - 2ab + b^2	(x-4)^2 = x^2 - 8x + 16
a^2 - b^2	(a+b)(a-b)	x^2 - 25 = (x+5)(x-5)
(a+b)^3	a^3 + 3a^2b + 3ab^2 + b^3	Expand carefully!
a^3 + b^3	(a+b)(a^2 - ab + b^2)	Sum of cubes
a^3 - b^3	(a-b)(a^2 + ab + b^2)	Difference of cubes

Fast Factoring Techniques

GCF First: Always look for Greatest Common Factor FIRST before anything else
Quadratic Factoring: For ax^2 + bx + c, find factors of (a)(c) that add up to b
AC Method: Multiply a and c, find factor pair that sums to b, split middle term
Reverse FOIL: (x + p)(x + q) where p + q = b and pq = c

2. Quantitative Comparison Questions 🧠

Unique to ACET! These questions test your analytical skills - comparing two quantities without necessarily solving for exact values.

Quantitative Comparison Format

Column A: [Quantity A] vs Column B: [Quantity B]

Choices:

A) Column A is greater
B) Column B is greater
C) Both are equal
D) Cannot be determined

Pro Strategies for Quantitative Comparison

Don't Solve Fully: Compare relationships, not exact answers
Plug In Values: Try x = 0, 1, -1, 2, 1/2 to test relationships
Simplify Both Sides: Add/subtract same value from both columns
Check Edge Cases: Negative numbers, fractions, zero
D is Tricky: Only choose "Cannot be determined" if relationship changes with different valid values

Example: Quantitative Comparison

Column A: x^2 when x > 0

Column B: x when x > 0

Analysis:

If x = 2: A = 4, B = 2 (A > B)
If x = 1/2: A = 1/4, B = 1/2 (B > A)

Answer: D - Cannot be determined

3. Number Theory & Properties 🔢

ACET loves testing number properties. Master these concepts cold!

Divisibility Rules

By 2: Last digit is even
By 3: Sum of digits divisible by 3
By 4: Last 2 digits divisible by 4
By 5: Ends in 0 or 5
By 6: Divisible by both 2 and 3
By 9: Sum of digits divisible by 9
By 11: Alternating sum of digits = 0 or 11

Number Properties

Even x Even = Even
Odd x Odd = Odd
Even x Odd = Even
Negative x Negative = Positive
(-1)^even = 1
(-1)^odd = -1

Prime Numbers to Memorize

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Note: 1 is NOT prime, 2 is the ONLY even prime number

4. Functions & Graphs 📊

Understanding function behavior is crucial for ACET math success.

Function Transformations

Transformation	Effect on Graph
f(x) + k	Shifts UP by k units
f(x) - k	Shifts DOWN by k units
f(x + h)	Shifts LEFT by h units
f(x - h)	Shifts RIGHT by h units
-f(x)	Reflects over x-axis
f(-x)	Reflects over y-axis
af(x) where a > 1	Vertical stretch
af(x) where 0 < a < 1	Vertical compression

Key Function Types

Linear: f(x) = mx + b (straight line, constant slope)
Quadratic: f(x) = ax^2 + bx + c (parabola, vertex at x = -b/2a)
Absolute Value: f(x) = |x| (V-shape, vertex at origin)
Exponential: f(x) = a^x (rapid growth/decay)
Logarithmic: f(x) = log_a(x) (inverse of exponential)

5. Word Problems & Data Analysis 📝

ACET word problems require quick translation from English to Math. Here's how to approach them systematically.

Word Problem Translation Guide

Addition Words:

sum, total, increased by, more than, plus, combined

Subtraction Words:

difference, decreased by, less than, minus, remaining

Multiplication Words:

product, times, of, twice, triple

Division Words:

quotient, per, ratio, divided by, out of

Common Word Problem Types

Age Problems: Set up equations using current age and age at different times
Distance/Rate/Time: D = RT (Distance = Rate x Time)
Work Problems: Combined rate = 1/A + 1/B, time = 1/(combined rate)
Mixture Problems: Amount1 x Concentration1 + Amount2 x Concentration2 = Total
Percentage Problems: Part = Percent x Whole

Example: Work Problem

Problem: Worker A can finish a job in 6 hours. Worker B can finish the same job in 4 hours. How long will it take both working together?

Solution:

Rate A = 1/6 job per hour
Rate B = 1/4 job per hour
Combined = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 job per hour
Time = 1 / (5/12) = 12/5 = 2.4 hours or 2 hours 24 minutes

6. Geometry Essentials 📐

Geometry appears in ACET - know your formulas and properties!

Shape	Area Formula	Perimeter/Circumference
Rectangle	A = lw	P = 2l + 2w
Triangle	A = (1/2)bh	P = a + b + c
Circle	A = pi*r^2	C = 2pir
Trapezoid	A = (1/2)(b1+b2)h	P = sum of sides
Parallelogram	A = bh	P = 2(a+b)

Triangle Properties

Pythagorean Theorem: a^2 + b^2 = c^2 (right triangles only)
Special Right Triangles: 30-60-90 (1 : sqrt(3) : 2) and 45-45-90 (1 : 1 : sqrt(2))
Triangle Inequality: Sum of any 2 sides > third side
Interior Angles: Always sum to 180 degrees

7. ACET Math Tips & Strategies 🎯

Time Management is EVERYTHING

Skip and Return: If stuck for more than 30 seconds, mark and move on
Easy First: Answer all easy questions first to secure points
No Blank Answers: No negative marking, so guess if needed
Use Process of Elimination: Cross out obviously wrong answers
Plug Answer Choices: Sometimes faster than solving from scratch

Calculator Alternative Strategies

ACET is non-calculator! Master mental math:

Round numbers for estimation
Break complex calculations into simpler parts
Memorize perfect squares (1-25) and cubes (1-10)
Use fraction equivalents: 1/4 = 0.25, 1/3 = 0.33, 1/5 = 0.20

8. Practice Questions 📋

Q1: If x^2 - 9 = 0, what is |x|?

x^2 = 9, so x = 3 or x = -3. Therefore |x| = 3

Q2: Compare: Column A (3^10) vs Column B (9^5)

9^5 = (3^2)^5 = 3^10. Answer: C - Equal

Q3: What is the sum of interior angles of a hexagon?

Formula: (n-2) x 180 = (6-2) x 180 = 4 x 180 = 720 degrees

Mathematics