LET Secondary Major Mathematics Reviewer 2026 Philippines

By LisensyaPrep Team | Last Updated: April 2026 | 11-minute read

The LET Secondary Major in Mathematics is one of the more challenging specialization exams because it combines deep content knowledge across several branches of mathematics with the ability to teach those concepts effectively. You need to know not just how to solve problems but how to explain the thinking behind them.

This reviewer covers the major topic areas of the LET Mathematics major subject with worked examples for the most commonly tested problem types.

Number Theory and the Real Number System

Properties of Real Numbers

These properties appear in LET questions both directly and as the basis for explaining why certain algebraic steps are valid.

Commutative Property: a plus b equals b plus a. a times b equals b times a. Order does not matter for addition and multiplication.

Associative Property: (a plus b) plus c equals a plus (b plus c). Grouping does not matter for addition and multiplication.

Distributive Property: a times (b plus c) equals (a times b) plus (a times c). This property connects multiplication and addition.

Identity Property: Adding 0 does not change a value. Multiplying by 1 does not change a value.

Inverse Property: Every number has an additive inverse (its negative) and a multiplicative inverse (its reciprocal), except zero which has no multiplicative inverse.

Divisibility Rules

Divisibility rules are a reliable source of LET items because they test conceptual understanding rather than computation.

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Algebra

Linear Equations and Inequalities

A linear equation in one variable has the form ax plus b equals c. Solving involves isolating the variable by performing the same operation on both sides.

For inequalities, the same rules apply with one critical difference: when multiplying or dividing both sides by a negative number, the inequality sign reverses direction.

Quadratic Equations

A quadratic equation has the form ax squared plus bx plus c equals 0.

Factoring method: Express the quadratic as a product of two binomials and set each factor equal to zero.

Quadratic formula: x equals negative b plus or minus the square root of (b squared minus 4ac), all divided by 2a.

The discriminant is b squared minus 4ac.

Functions and Relations

A relation is any set of ordered pairs. A function is a relation where each input (x-value) corresponds to exactly one output (y-value).

The vertical line test determines if a graph represents a function. If any vertical line crosses the graph more than once, it is not a function.

Domain is the set of all valid input values. Range is the set of all output values.

Geometry

Angle Relationships

Complementary angles sum to 90 degrees. Supplementary angles sum to 180 degrees.

Vertical angles are formed by two intersecting lines and are always equal.

Corresponding angles formed when a transversal crosses parallel lines are equal.

Alternate interior angles formed when a transversal crosses parallel lines are equal.

Triangle Congruence and Similarity

Congruent triangles have exactly the same shape and size. Congruence postulates: SSS, SAS, ASA, AAS, and HL (for right triangles).

Similar triangles have the same shape but different sizes. Their corresponding angles are equal and corresponding sides are proportional.

Trigonometry

Basic Trigonometric Ratios

In a right triangle with angle theta, the hypotenuse, opposite side, and adjacent side:

SOH-CAH-TOA is the standard memory aid:

Special Angles

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Statistics and Probability

Measures of Central Tendency

Mean is the arithmetic average. Add all values and divide by the number of values.

Median is the middle value when data is arranged in ascending order. For an even number of values, take the average of the two middle values.

Mode is the most frequently occurring value. A data set can have no mode, one mode, or multiple modes.

Standard Deviation

Standard deviation measures how spread out values are from the mean. A small standard deviation means values are clustered close to the mean. A large standard deviation means values are spread far from the mean.

Probability

Simple probability: P(Event) = Number of favorable outcomes divided by total possible outcomes.

Complementary events: P(not A) = 1 minus P(A).

Independent events: P(A and B) = P(A) times P(B).

Mutually exclusive events: P(A or B) = P(A) plus P(B).

Teaching Mathematics: Methods and Approaches

Problem-Solving Approach (George Polya)

Polya's four-step problem solving framework is foundational for teaching mathematics and appears in LET questions:

Step 1: Understand the problem. What is given? What is being asked?

Step 2: Devise a plan. What strategy will you use? Draw a diagram, make a table, look for a pattern, work backward.

Step 3: Carry out the plan. Execute the strategy carefully.

Step 4: Look back. Does the answer make sense? Can you verify it? Is there another way?

Conceptual Understanding vs Procedural Fluency

The LET tests your understanding that effective math teaching requires both. Conceptual understanding means knowing why a procedure works. Procedural fluency means being able to carry out procedures accurately and efficiently. Strong math teachers develop both in their students.

Manipulatives and Concrete-Pictorial-Abstract Approach

The CPA approach moves from concrete objects (physical manipulatives) to pictorial representations (drawings and diagrams) to abstract symbols (numbers and equations). This sequence supports conceptual understanding before procedural practice.

Practice What You Just Learned

The LET Secondary Major Math exam includes both computation problems and pedagogical questions about how to teach mathematical concepts. Practice questions that combine both types are essential preparation.

Head to LisensyaPrep and practice now. No registration required.

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