Mathematics C – Fundamental Concepts

These flashcards review core principles from Mathematics C: order of operations, sign rules, algebraic manipulation, fraction arithmetic, exponent laws, equation solving, and coordinate-geometry basics.

What is the main learning goal emphasized when moving from school arithmetic to Mathematics C?

To progress from "knowing how" to "knowing why"—being able to justify each calculation with the relevant rule.

List the four fundamental arithmetic operations and their symbols.

Addition (+), subtraction (−), multiplication (·), and division (: or fraction bar).

State the standard order of operations (hierarchy) including parentheses and powers.

1) Parentheses, roots, and powers 2) Multiplication and division 3) Addition and subtraction.

What is the resulting sign when you multiply or divide two numbers with the SAME sign?

The result is positive.

What sign results from multiplying a positive number by a negative number?

The result is negative.

In the expression 5 + 2·3, which part is calculated first and why?

2·3 is calculated first because multiplication precedes addition in the hierarchy.

Define the terms "term" and "factor" in an algebraic expression.

Terms are separated by + or −; factors are the numbers or letters multiplied within a term.

How do you remove a plus-parenthesis, e.g., a + (2b − a)?

Drop the parentheses unchanged: a + 2b − a.

What happens when you multiply a constant into a parenthesis, e.g., 2(a − b)?

Multiply the constant by every term: 2a − 2b.

State the distributive rule for multiplying two parentheses (a + b)(c + d).

ac + ad + bc + bd.

Expand (a + b)².

a² + 2ab + b².

Expand (a − b)².

a² − 2ab + b².

Expand (a + b)(a − b).

a² − b².

In a fraction a⁄b, what are a and b called?

a is the numerator, b is the denominator.

How do you multiply a whole number by a fraction?

Multiply the numerator by the number; keep the denominator the same.

What is the rule for multiplying two fractions?

Multiply numerators together and denominators together.

How do you divide a fraction by a whole number?

Multiply the denominator by the number.

How do you divide by a fraction?

Multiply by the reciprocal of the fraction.

What must you do before adding or subtracting fractions?

Find a common (shared) denominator.

What is the value of a⁰ for a ≠ 0?

1.

Rewrite a⁻ⁿ using positive exponents.

a⁻ⁿ = 1⁄aⁿ.

State the exponent rule for aᵐ · aⁿ.

aᵐ·aⁿ = aᵐ⁺ⁿ.

State the exponent rule for aᵐ ⁄ aⁿ.

aᵐ⁄aⁿ = aᵐ⁻ⁿ.

State the exponent rule for (aⁿ)ᵐ.

(aⁿ)ᵐ = aⁿ·ᵐ.

State the exponent rule for (ab)ⁿ.

(ab)ⁿ = aⁿ·bⁿ.

When solving equations, what two operations can you perform on both sides without changing the solution set?

Add/subtract the same number or multiply/divide by the same non-zero number.

What is the primary objective when solving a linear equation in one variable?

Isolate the variable (usually x) to find its value.

Explain the scale (balance) analogy for equation solving.

Whatever you do to one side of the equation, you must do to the other to keep the "scale" balanced.

What are the names of the two perpendicular axes in a Cartesian coordinate system?

The horizontal x-axis and the vertical y-axis.

How is a point written in coordinate form?

(x, y) using parentheses.

In the line equation y = ax + b, what does the parameter a represent?

The slope (gradient) of the line.

In the line equation y = ax + b, what does the parameter b represent?

The y-intercept—the point where the line crosses the y-axis.

How can you find the intersection point of two lines algebraically?

Solve their equations simultaneously as a system to get the (x, y) coordinates.