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Introduction to Algebra (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontAlgebraic Notation
True or False?
The expression $4 (a + b)$ means $4 \times (a + b)$ .

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Cards in this collection (22)

True or False?
The expression $4 (a + b)$ means $4 \times (a + b)$ .
True.
The expression $4 (a + b)$ means $4 \times (a + b)$ .
True or False?
The expression $3 a b$ means $3 + a + b$ .
False.
The expression $3 a b$ means $3 \times a \times b$ .
True or False?
The expression $\frac{f}{2} - x y$ means $f \div 2 - x \times y$ .
True.
The expression $\frac{f}{2} - x y$ means $f \div 2 - x \times y$ .
True or False?
The expression $2 t^{2}$ means $2 \times t \times 2$ .
False.
The expression $2 t^{2}$ means $2 \times t^{2}$ , which is the same as $2 \times t \times t$ .
Define a term in algebra.
A term is a single part of an expression: a letter on its own, a letter raised to a power, a number on its own, or a number multiplied by one or more letters.
Examples are $x$ , $4 x^{2}$ , $20$ and $6 x y$ .
In the term $- 5 y$ , what is the coefficient of $y$ ?
The coefficient of $y$ is $- 5$ , not $5$ .
The coefficient is the number in front of a letter, and it takes the sign that sits in front of it.
Complete the pair of sentences by filling in the missing words:
In algebra, a letter whose value can change is called a $______$ .
A number whose value cannot change is called a $______$ .
The completed sentences are:
In algebra, a letter whose value can change is called a variable.
A number whose value cannot change is called a constant.
Write down all four factors of the term $3 x$ .
The factors of $3 x$ are $1$ , $3$ , $x$ and $3 x$ .
A factor is anything that divides the term exactly, leaving no remainder, so a letter can be a factor just as a number can.
Define an algebraic expression.
An expression is an algebraic statement made by combining terms with $+$ , $-$ , $\times$ or $\div$ , and it has no equals sign.
There is therefore nothing to solve, though an expression can often be simplified: $x + x + x$ simplifies to $3 x$ .
True or False?
A single term such as $7 x$ is an expression on its own.
True.
A single term such as $7 x$ is an expression, and so is a number on its own such as $20$ .
An expression does not have to contain more than one term.
Define an equation.
An equation is an algebraic statement with an equals sign, where the left-hand side and the right-hand side have the same value.
An equation can be solved: the value of the letter that makes both sides equal is called the solution, so $2 x = 10$ has the solution $x = 5$ .
Define a formula.
A formula is a rule or relationship between different quantities, written in shorthand using letters.
For example, weight $w$ is mass $m$ multiplied by gravitational acceleration $g$ , which is written as the formula $w = m g$ .
What extra information turns the formula $w = m g$ into an equation that can be solved?
You need the numerical values of all but one of the letters.
If $w = 50$ and $m = 5$ , the formula $w = m g$ becomes the equation $50 = 5 g$ , which can then be solved to find $g$ .
What does substitution mean in algebra?
Substitution in algebra is the process of replacing letters in a formula with their corresponding numerical values (inputs) in order to calculate an output of the formula.
E.g. If $v = 3$ and $a = - 5$ , substituting them into the formula $a^{2} + 2 v = t$ would give $(- 5) + 2 \times 3 = t$ .
True or False?
When substituting in the number $g = - 3$ you should replace $g$ with $(- 3)$ , not $- 3$ .
True.
It is important to put brackets around any negative numbers that you substitute into an algebraic expression.
E.g. Substitute $g = - 3$ into the expression $4 g^{2}$ .
If you use brackets it will give you the correct answer $4 \times {(- 3)}^{2} = 4 \times 9 = 36$ .
If you don't use brackets it will give an incorrect answer $4 \times - 3^{2} = 4 \times - 9 = - 36$ .
True or False?
You can rearrange a formula first before substituting numbers in.
True.
You can rearrange a formula first, before substituting numbers in.
E.g. $A = l \times w$ can be rearranged as $l = \frac{A}{w}$ if you know the values of $A$ and $w$ , and want to substitute to find the value of $l$ .
True or False?
It is a good idea to simplify an expression before substituting in values.
E.g. simplifying the expression $2 a + 7 t - 2 (5 a + t)$ to $5 t - 8 a$ before substitution.
True.
It is a good idea to simplify an expression before substituting in values.
Doing this reduces the number of substitutions you need to do (and the number of errors you could make).
True or False?
Substituting $y = 2$ into $- 3 y^{2}$ will give ${(- 6)}^{2}$ which is $36$ .
False.
You do not multiply $- 3$ by $y$ first. You need to do the power $y^{2}$ first (from BIDMAS).
This gives $- 3 \times 2^{2}$ which simplifies to $- 3 \times 4$ which is $- 12$ .
True or False?
The term $x y$ is the same as the term $y x$ .
True.
The term $x y$ is the same as the term $y x$ , as they both represent $x$ multiplied by $y$ .
Multiplication can be done in either order.
True or False?
When collecting like terms, $2 x + 3 y$ is the same as $5 x y$ .
False.
The terms $2 x$ and $5 y$ are not like terms because their letters (variables) are different.
They cannot be combined, so the expression must be left as $2 x + 5 y$ .
True or False?
There are no like terms in the expression $2 x^{2} - 2 x + 2$ .
True.
There are no like terms in the expression $2 x^{2} - 2 x + 2$ .
This expression cannot be simplified any further.
True or False?
$4 q^{3}$ and $- 8 q (q^{2})$ are like terms.
True.
$4 q^{3}$ and $- 8 q (q^{2})$ are like terms as $- 8 q (q^{2})$ simplifies to $- 8 q^{3}$ .

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