MMW1

January 20, 2026

By Patrick John Meneses

Mathematical Language and Symbols
Mathematics of Finance

Multiple Choice

Why is mathematics considered a language?

• It is spoken worldwide

• It uses only numbers

• It uses symbols, syntax, and conventions to communicate ideas clearly

• It replaces natural languages

Answer:

Mathematics is a language because it has:

• Symbols (like +, −, x) to represent ideas

• Syntax (rules on how symbols are arranged)

• Conventions (agreed meanings and rules)
  Together, these allow mathematicians to communicate clearly and consistently.

​It uses symbols, syntax, and conventions to communicate ideas clearly.

Rationale:

Multiple Choice

In mathematics, what is the main role of symbols?

• To decorate expressions

• To confuse learners

• To represent numbers, operations, and relationships

• To replace reasoning

Answer:

Mathematical symbols stand for specific meanings, such as:

• + for addition

• × for multiplication

• = for equality

  Without symbols, mathematical ideas would take much longer to express.

To represent numbers, operations, and relationships.

Rationale:

Multiple Choice

Which example best shows the precision of mathematical symbols?

• Symbols can change meaning anytime

• The symbol + always means addition

• Words explain math better than symbols

• Symbols depend on emotions

Answer:

• Math is precise because symbols have one exact meaning.

• For example, + always means add—never subtract or multiply.

The symbol + always means addition.

Rationale:

Multiple Choice

What does syntax mean in the language of mathematics?

• The values of numbers

• The symbols themselves

• The rules for arranging symbols correctly

• The answer to a problem

Answer:

• Syntax refers to how symbols and numbers must be arranged properly.
  

• For example, 8 + 2 is valid, but + 8 2 violates mathematical syntax.

The rules for arranging symbols correctly

Rationale:

Multiple Choice

Which mathematical statement shows correct syntax?

• = 5 + 3

• 5 + = 3

• 5 + 3 = 8

• + 5 3 =

Answer:

• Correct syntax follows proper order and structure, making the expression clear and meaningful.

5 + 3 = 8

Rationale:

Multiple Choice

Why is mathematics considered concise?

• It avoids symbols

• It uses long explanations

• It ignores grammar

• It expresses ideas briefly using symbols

Answer:

• Symbols shorten long statements.

• “Eight plus two equals ten” becomes 8 + 2 = 10, making communication faster and clearer.

It expresses ideas briefly using symbols.

Rationale:

Multiple Choice

What is a mathematical convention?

• A personal rule

• A generally agreed way of writing and interpreting math

• A rule based on feelings

• A natural law

Answer:

• Conventions are shared agreements, such as:

  • Evaluating multiplication before addition

  • Using = to show equality
    These ensure everyone interprets math the same way.

A generally agreed way of writing and interpreting math

Rationale:

Multiple Choice

Why is the order of operations considered a convention?

• It is based on nature

• It can change randomly

• It is optional

• It is an agreed rule to avoid confusion

Answer:

• There is nothing “natural” about PEMDAS/BODMAS—mathematicians agree on it so everyone gets the same answer.

It is an agreed rule to avoid confusion

Rationale:

Multiple Choice

Which statement best describes a mathematical sentence?

• It uses only numbers

• It can be judged as true or false

• It contains symbols but no meaning

• It avoids variables

Answer:

• An expression contains numbers and symbols but no comparison symbol, so it cannot be true or false.

It is an agreed rule to avoid confusion

Rationale:

Multiple Choice

Which of the following is a mathematical expression?

• 8x − 5

• x > 5

• 2 < 6

• 3 + 4 = 7

Answer:

• A mathematical sentence uses symbols like =, <, or > and makes a complete statement that can be evaluated.

It can be judged as true or false

Rationale:

Fill in the Blanks

Evaluate: 10 ÷ 2 + 12 + 2 × 3 =

Answer:

10

Rationale:

= 6 × 2 − 3 + 1
= 12 − 3 + 1
= 9 + 1
= 10

(11 − 5) × 2 − 3 + 1

​This follows the order of operations: parentheses, multiplication, subtraction, then addition.

Fill in the Blanks

Evaluate: (11 − 5) × 2 − 3 + 1 =

Answer:

23

Rationale:

10 ÷ 2 + 12 + 2 × 3
= 5 + 12 + 6
= 23

Division and multiplication are done first, then addition, according to convention.

Fill in the Blanks

Simplify: √2500=

Answer:

50

Rationale:

Rationale (with Solution):
√2500 = 50
because
50 × 50 = 2,500

The symbol √ means square root by mathematical convention.

Fill in the Blanks

Simplify: 16 − 3(8 − 3)² ÷ 5 =

Answer:

1

Rationale:

16 − 3(8 − 3)² ÷ 5

Parentheses are simplified first, then exponents, multiplication/division, and subtraction.

​= 16 − 3(5)² ÷ 5
= 16 − 3(25) ÷ 5
= 16 − 75 ÷ 5
= 16 − 15
= 1

Multiple Choice

What do we call the tax added to the price of goods and services in the Philippines?

• Discount

• Service Charge

• Value-Added Tax (VAT)

• Interest

Answer:

7

Rationale:

Division is performed before addition
based on mathematical convention.

4 + 6 ÷ 2
= 4 + 3
= 7

Multiple Choice

Which price is used when computing VAT?

• Final price

• Discounted price

• Original price

• Sale price

Answer:

VAT

Rationale:

VAT is computed based on the original price (or discounted price if a discount is applied first).

Multiple Choice

What is the correct order when both discount and VAT are applied?

• VAT then discount

• Discount then VAT

• Add both at the same time

• Ignore VAT

Answer:

Discount then VAT

Rationale:

In real transactions, discounts are applied first, then VAT is computed.

Multiple Choice

In simple interest, which values are needed in the formula?

• VAT then discount

• Principal, rate, time

• Income, expenses, savings

• Discount, tax, price

Answer:

Principal, rate, time

Rationale:

Simple interest uses
Principal (P), Rate (r), and Time (t).

Fill in the Blanks

A notebook costs ₱400. The VAT rate is 12%.

The VAT amount is ₱

.

Answer:

Rationale:

Simple interest uses
Principal (P), Rate (r), and Time (t).

Answer:

48

Rationale:

Computation:
VAT = Original Price × VAT Rate
VAT = 400 × 0.12
VAT = 48

Fill in the Blanks

A jacket costs ₱2,000 and is discounted by 20%.

The discount amount is ₱

.

Answer:

840

Rationale:

Computation:
VAT = 750 × 0.12 = 90
Final Price = 750 + 90
Final Price = 840

Fill in the Blanks

A bag costs ₱750 before VAT.

The final price after adding 12% VAT is ₱

.

Answer:

400

Rationale:

Discount = Original Price × Discount Rate
Discount = 2,000 × 0.20
Discount = 400

Fill in the Blanks

A pair of shoes costs ₱3,000 with a 10% discount.

The sale price is ₱

.

Answer:

2700

Rationale:

Discount = 3,000 × 0.10 = 300
Sale Price = 3,000 − 300
Sale Price = 2,700

Fill in the Blanks

A bag costs ₱5,000. It has a 10% discount and then 12% VAT.

The final price is ₱

.

Answer:

5040

Rationale:

Discount = 5,000 × 0.10 = 500
Discounted Price = 5,000 − 500 = 4,500

VAT = 4,500 × 0.12 = 540
Final Price = 4,500 + 540
Final Price = 5,040

Fill in the Blanks

You invest ₱8,000 at 5% simple interest for 4 years.

The interest earned is ₱

.

Answer:

1600

Rationale:

I = P × r × t
I = 8,000 × 0.05 × 4
I = 1,600

Fill in the Blanks

Your monthly income is ₱7,000 and expenses are ₱5,500.

Your monthly surplus is ₱

.

Answer:

1500

Rationale:

Surplus = Income − Expenses
Surplus = 7,000 − 5,500
Surplus = 1,500

Fill in the Blanks

You want to save ₱12,000 with a monthly surplus of ₱1,500.

You will reach your goal in

months.

Answer:

8

Rationale:

Time = Goal ÷ Monthly Surplus
Time = 12,000 ÷ 1,500
Time = 8 months