Introduction to Algebra Flashcards

All 23 cards in this deck

What does $ab$ mean in algebra?

$a \times b$ — the multiplication sign is left out.

What does $a^2b$ mean written out as a product?

e.g. expand the notation

$a \times a \times b$ — only the $a$ is squared.

True or false? $3y$ means $3 + y$.

False. $3y$ means $3 \times y$.

True or false? In algebraic notation the number is written before the letter, so you write $5t$ and not $t5$.

True. The coefficient goes first, e.g. $5t$.

What is an expression?

A collection of terms with no equals sign, e.g. $3x + 2$.

What is a formula?

A rule linking two or more variables, written with an equals sign, e.g. $A = lw$.

What is an identity, and which symbol is used for one?

A statement true for all values of the variable, written with $\equiv$, e.g. $2(x+3) \equiv 2x + 6$.

True or false? $2x + 1 \le 7$ is an equation.

False. It is an inequality; an equation has an equals sign.

What are the terms in the expression $4x^2 - 7x + 3$?

$4x^2$, $-7x$ and $3$ — the parts separated by $+$ or $-$.

What is meant by the coefficient of a term?

e.g. the term $-7x$

The number multiplying the letter(s), including its sign: $-7$.

What are the steps to substitute a value into an expression?

e.g. find $3x + 4$ when $x = 5$

1. Replace the letter with the number in brackets: $3 \times (5) + 4$
2. Apply BIDMAS: $15 + 4$
3. Answer: $19$

When substituting a negative value, how should you write it in the expression?

e.g. $m = -3$ in $4m^2$

In brackets: $4 \times (-3)^2$, so the whole of $-3$ is squared.

True or false? $(-3)^2 = -9$.

False. $(-3)^2 = -3 \times -3 = 9$.

In what order are operations carried out once you have substituted the numbers in?

BIDMAS: brackets, indices, division and multiplication, then addition and subtraction.

True or false? When $x = 4$, $x^3 = 12$.

False. $x^3 = 4 \times 4 \times 4 = 64$; the power means repeated multiplication, not multiply by $3$.

What must you check about the values before substituting into a scientific or real-life formula?

That the units match the ones the formula needs, e.g. convert minutes to hours for a speed in km/h.

In the formula speed $= \dfrac{\text{distance}}{\text{time}}$, what unit does the answer have if distance is in km and time is in hours?

km/h — the distance unit divided by the time unit.

What are like terms?

Terms with exactly the same letters raised to the same powers, e.g. $3x^2y$ and $-5x^2y$.

What are the steps to simplify an expression by collecting like terms?

e.g. $5a + 3b - 2a + b$

1. Group the like terms: $5a - 2a$ and $3b + b$
2. Add/subtract the coefficients: $3a$ and $4b$
3. Write the simplified expression: $3a + 4b$

When collecting like terms, what happens to the $+$ or $-$ sign in front of a term?

It belongs to that term and moves with it, e.g. in $7y - 3y$ the term is $-3y$.

True or false? $3x + 4y$ simplifies to $7xy$.

False. They are unlike terms, so $3x + 4y$ cannot be simplified.

True or false? $x^2$ and $x$ are like terms.

False. The powers are different, so they cannot be collected.

True or false? $4ab$ and $7ba$ are like terms.

True. They contain the same letters, so they collect to $11ab$.