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Algebra Toolkit (Cambridge (CIE) IGCSE Maths)

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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 (21)

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 $2 \times t \times t$ .
True or False?
The items in the following list are all examples of terms that you may come across in algebra: $y, a^{2}, 20, 7 x$ .
True.
$y, a^{2}, 20, 7 x$ are all examples of terms that you may come across in algebra.
A term is either:
- a letter (variable) on its own, e.g. $y$ ,
- a variable raised to a power, e.g. $a^{2}$ ,
- a number on its own, e.g. $20$ ,
- or a number multiplied by a letter, e.g. $7 x$ .
In algebra, what is a variable?
A variable is a letter that appears in a term.
E.g. In the expression $x^{2} - 2 y + 6$ , the $x$ and $y$ are both variables.
In algebra, what is a constant?
A constant is a term that is a number only.
There is no letter (variable) part.
E.g. In the expression $x^{2} + 3 x - 5$ , the $- 5$ is the only constant term.
In algebra, what is an expression?
An expression in algebra is a mathematical statement that does not have an equals sign.
It can include terms that are combined using operations like addition, subtraction, multiplication, and division.
E.g. $5 x^{2} + y$ is an algebraic expression.
True or False?
In the expression $4 x^{3} + x^{2} - 6$ , the coefficient of the $4 x^{3}$ term is $3$ .
False.
In the expression $4 x^{3} + x^{2} - 6$ , the coefficient of the $4 x^{3}$ term is not $3$ .
In an algebraic expression, the coefficient of a term is the number in front of the letter (variable).
E.g. In the expression $4 x^{3} + x^{2} - 6$ , the coefficient of the $4 x^{3}$ term is $4$ .
True or False?
$x^{2} + 8 x - 2$ is an equation.
False.
$x^{2} + 8 x - 2$ is not an equation.
An equation in algebra is a mathematical statement with an equals sign between a left-hand side and a right-hand side.
The equals sign indicates that both sides are equal in value.
Define the word formula in algebra.
A formula in algebra is a rule, definition, or relationship between different quantities, written in shorthand using letters.
E.g. $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ is the quadratic formula.
True or False?
A formula on its own can be solved.
False.
A formula on its own cannot be solved.
You need to substitute values into the formula to turn it into an equation that can be solved.
E.g. $a^{2} + b^{2} = c^{2}$ cannot be solved unless you know two of the variables.
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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