Grade 11 Math Terminal Exam Study Guide Flashcards

Question and answer flashcards covering key concepts in logic, limits, derivatives, complex numbers, geometric series, and sequences for Grade 11 Mathematics.

What is a proposition in logic?

A statement that can be either true or false.

What are the logical connectives AND, OR, and NOT and their symbols in logic?

AND ($\land$), OR ($\lor$), and NOT ($\neg$).

How are logical implication and equivalence defined and denoted?

Implication is denoted by $p \Rightarrow q$ (If $p$ then $q$) and equivalence is denoted by $p \Leftrightarrow q$ ($p$ if and only if $q$).

What is the standard notation for the limit of a function $f(x)$ as $x$ approaches $a$?

$$\lim_{x \to a} f(x) = L$$

What key techniques are listed for evaluating limits?

Direct Substitution, Factorization, and L'Hôpital's Rule (for $\frac{0}{0}$ or $\frac{\infty}{\infty}$ forms).

What is the definition of a derivative?

A measure of how a function changes as its input changes.

What is the power rule formula for taking a derivative?

$$\frac{d}{dx}(x^n) = n x^{n-1}$$

What are the basic derivative rules for $\sin(x)$ and $\cos(x)$?

$\frac{d}{dx}(\sin(x)) = \cos(x)$ and $\frac{d}{dx}(\cos(x)) = -\sin(x)$

What is the Product Rule for differentiation?

$$(uv)' = u'v + uv'$$

What is the Quotient Rule for differentiation?

$$\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$$

What is the general form of a complex number $z$?

$z = a + bi$ where $a, b \in \mathbb{R}$

What is the formula for the addition of two complex numbers $z_1 = a_1 + b_1 i$ and $z_2 = a_2 + b_2 i$?

$$z_1 + z_2 = (a_1 + a_2) + (b_1 + b_2)i$$

What is the formula for the multiplication of two complex numbers $z_1 = a_1 + b_1 i$ and $z_2 = a_2 + b_2 i$?

$$z_1 \cdot z_2 = (a_1 a_2 - b_1 b_2) + (a_1 b_2 + a_2 b_1)i$$

What are the formulas for the conjugate and magnitude of a complex number $z = a + bi$?

The conjugate is $\overline{z} = a - bi$ and the magnitude is $|z| = \sqrt{a^2 + b^2}$.

What is the formula for the sum $S_n$ of a finite geometric series when $r \neq 1$?

$$S_n = a \frac{1 - r^n}{1 - r}$$

What is the formula for the sum $S$ of an infinite geometric series when $|r| < 1$?

$$S = \frac{a}{1 - r}$$

What is the formula for the $n$-th term $a_n$ of an arithmetic sequence?

$$a_n = a + (n-1)d$$

What is the formula for the sum $S_n$ of an arithmetic series given the first term $a$ and last term $l$?

$$S_n = \frac{n}{2}(a + l)$$

How is a recursive sequence defined?

It is defined by a formula relating later terms to earlier ones.