Introduction to Algebra Flashcards

All 24 cards in this deck

What does $3y$ mean?

$3 \times y$, which is the same as $y + y + y$.

What does $a^2$ mean?

$a \times a$.

What are the steps to simplify a product of numbers and letters?

e.g. simplify $3 \times w \times 5 \times t$

1. Multiply the numbers together: $3 \times 5 = 15$
2. Write the letters after the number, usually alphabetically: $tw$
3. Write it with no $\times$ signs: $15tw$

True or false? $e + e + e + e$ simplifies to $e^4$.

False. It is $4e$; $e^4$ means $e \times e \times e \times e$.

What is an expression?

A collection of terms with no equals sign, e.g. $3x + 5y$.

What is an equation?

A statement with an equals sign that can be solved to find an unknown, e.g. $5x - 3 = 12$.

What is a formula?

A rule connecting two or more variables, written with an equals sign, e.g. $v = u + at$.

What is a term?

A single number, letter, or number and letters multiplied together, separated from others by $+$ or $-$.
e.g. $5y$ is a term in $3x + 5y$.

What is an identity?

A statement that is true for every value of the letters, written with $\equiv$, e.g. $2x + 3x \equiv 5x$.

True or false? $7y + 4$ is an equation.

False. It has no equals sign, so it is an expression.

What does it mean to substitute into a formula?

Replace each letter with its given numerical value and work out the answer.

What are the steps to substitute a value into a formula?

e.g. find $T$ when $m = 2$ in $T = 4m^2 - 11$

1. Replace the letter with its value: $4 \times 2^2 - 11$
2. Work out powers first: $4 \times 4 - 11$
3. Then multiply, then add/subtract: $T = 5$

When substituting a negative value into a squared term, what must you do?

e.g. $w = 40 - t^2$ with $t = -5$

Put the negative number in brackets before squaring: $40 - (-5)^2 = 40 - 25 = 15$.

True or false? If $m = -3$ then $m^2 = -9$.

False. $m^2 = (-3) \times (-3) = 9$, since a negative times a negative is positive.

In the formula $v = u + at$, what does $at$ tell you to do?

Multiply $a$ by $t$, then add the result to $u$.
e.g. $a = -3$, $t = \frac{1}{2}$ gives $at = -\frac{3}{2}$.

In $T = 4m^2 - 11$, which operation is done first when substituting?

The power: square $m$ first, then multiply by $4$, then subtract $11$.

What are like terms?

Terms with exactly the same letter or letters to the same power, e.g. $8h^3$ and $14h^3$.

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

e.g. simplify $3x + 5y + 2x - 4y$

1. Group the like terms, keeping the sign in front of each: $3x + 2x$ and $5y - 4y$
2. Add or subtract the number parts: $5x$ and $y$
3. Write the simplified terms together: $5x + y$

True or false? $3x + 5y$ simplifies to $8xy$.

False. $3x$ and $5y$ are unlike terms, so $3x + 5y$ cannot be simplified.

True or false? $8h^3 + 14h^3 = 22h^6$.

False. It is $22h^3$ — you add the number parts and the power stays the same.

What are the steps to write an expression from a worded context?

e.g. 3 boxes with $x$ sweets each and 2 packets with $y$ sweets each

1. Write each part as a product: $3x$ and $2y$
2. Combine them as the words say (total means add): $3x + 2y$
3. Collect any like terms: already simplest, so $3x + 2y$

How do you find a formula for the total length $L$ of several labelled rods?

e.g. rods of length $a - 1$, $a$ and $a + 4$ cm

Add all the lengths and collect like terms: $a - 1 + a + a + 4$, so $L = 3a + 3$.

True or false? $ab$ and $ba$ mean the same thing.

True. Multiplication can be done in any order, so $a \times b = b \times a$.

True or false? $\frac{x}{2}$ and $\frac{1}{2}x$ mean the same thing.

True. Both mean $x$ divided by $2$, i.e. half of $x$.