IB Number and Algebra

Natural Numbers (N)

The set of positive counting numbers, e.g., 1, 2, 3, 4, ...

Integers (Z)

The set of all whole numbers, including negatives and zero, e.g., -2, -1, 0, 1, 2, ...

Rational Numbers (Q)

The set of all numbers that can be expressed as fractions a/b, e.g., ½, 0.75, -3.1.

Irrational Numbers

The set of all numbers that are not expressible as fractions; their decimal expansions are non-terminating and non-repeating, e.g., sqrt(2), π, e.

Real Numbers (R)

The set of all rational and irrational numbers, representing every point on the number line.

Rounding Rule

Numbers greater than 4 are rounded up, while numbers less than or equal to 4 are rounded down.

Significant Figures (s.f.)

Non-zero digits are always significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros in a decimal are significant.

Addition Subtraction with s.f.

The result should have the same number of decimal places as the number with the fewest decimal places.

Percentage Error

Accuracy of an approximate value compared to the exact value, expressed as a percentage, calculated using the formula |(VA-VE)/VE| * 100%.

Arithmetic Sequences

A sequence with a constant difference (d) between consecutive terms, represented by the formula Un=U1+d(n-1).

Geometric Sequences

A sequence with a constant ratio (r) between consecutive terms, represented by the formula Un=U1*r(n-1).

Sigma Notation

A mathematical notation used to represent the sum of a sequence of terms, using the Greek letter Σ.

Exponent Rules

Rules governing the operation of exponents, including am * an = am+n and a0 = 1.

Natural Log

The logarithm with base e, where if ea = b, then ln(b) = a.

Binomial Theorem

Provides a formula to expand expressions of the form (a + b)ⁿ without direct multiplication.

Pascal's Triangle

A triangular array where each row contains the binomial coefficients for a given exponent n.

Compound Interest

Interest calculated on both the initial principal and the accumulated interest from previous periods, represented by A = P(1 + r/n)^(nt).

Depreciation

The reduction in the value of an asset over time, represented by A = P(1 - r)ⁿ.

Loan

Borrowing money to be paid back at regular intervals.

Savings Annuity

Saving money and making regular contributions.

Gift Annuity

Receiving a gift that is paid out at regular intervals.