What does the symbol ≈ mean?

The symbol ≈ means approximately equal to .

True or False? The equals sign (=) is used to show that two expressions are identical .

False. The equals sign (=) is used to show that two expressions are equal , while the identical sign (≡) is used to show that two expressions are identical .

What is an inequality ?

An inequality is a statement that compares two quantities in terms of their size using symbols such as >, <, ≥, or ≤.

True or False? The symbol ± is used to represent two distinct answers .

True. The symbol ± is used to represent two distinct (different) answers, often in quadratic equations.

What do the letters of BIDMAS/BODMAS represent?

The letters in BIDMAS/BODMAS represent: Brackets, Indices, Division, Multiplication, Addition, Subtraction. BIDMAS/BODMAS is an acronym that stands for the order of operations in mathematics.

True or False? Multiplying two negative numbers results in a negative value.

False. When multiplying two negative numbers, the result is a positive value .

When multiplying a positive and a negative , is the resultant value positive or negative ?

When multiplying a positive and a negative, the result is a negative value .

True or False? Subtracting a negative number is the same as adding a positive number.

True. Subtracting a negative number is the same as adding a positive number.

True or False? When finding the square of a negative number , the result is positive .

True. When finding a square of a negative number, the result is positive . This is because you are multiplying a negative by a negative , which results in a positive.

When finding the cube of a negative number, is the result positive or negative ?

When finding the cube of a negative number, you are multiplying a negative by a negative, by a negative so the final result is a negative .

Define the term currency .

A currency is a system of money in general use in a particular country or region.

True or False? Final answers in calculations with money should always be rounded to the nearest integer .

False. You should usually round answers involving money to two decimal places . However, you may sometimes be asked to round answers to the nearest integer .

True or False? Large monetary amounts , such as the cost of a car, are usually rounded to the nearest whole number , e.g. nearest dollar.

True. Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number.

True or False? Monetary values given in more than two decimal places within a question should be rounded to two decimal places before doing any calculations .

False. Monetary values given in more than two decimal places should be used in the working . They should only be rounded for the final answer .

What mathematical operation does the word sum imply?

The word sum implies that you need to add numbers together.

If you are asked to find the difference of two numbers, which operation should you use?

Subtraction is the mathematical operation of finding the difference between two numbers by taking one number away from another.

True or False? The word share implies that you need to divide numbers.

True. The word share implies that you need to divide numbers.

What mathematical operation is implied by a question asking you to find the product of two or more numbers?

The word product is often used to imply that you need to multiply two numbers together.

True or False? Writing a list systematically means there is some sort of order to the list.

True. Writing a list systematically means there is some sort of order to the list. It is not the same as trying to write out a list randomly.

True or False? Writing a list systematically means it is impossible to miss out an option.

True. Writing a list systematically means it is impossible to miss out an option. Systematic means the list was created in an organised way.

ZYX is a possible arrangement of the letters XYZ. Create a systematic way to list all the arrangements of the letters XYZ.

For example, make the first letter an X and swap the other two: XYZ, XZY. Then make the first letter a Y and swap the other two: YXZ, YZX. Finally, make the first letter a Z and swap the other two: ZXY, ZYX. All the arrangements are: XYZ, XZY, YXZ,YZX, ZXY, ZYX. (There are other acceptable ways to create an organised list like this).

True or False? A bag contains ten green (G) marbles and ten red (R) marbles. Two marbles are selected at random. The possibilities are GR or RG.

False. There are ten green (G) marbles and ten red (R) marbles. Two marbles selected at random might both be green, or both be red. The possibilities are actually GR, RG, GG or RR.

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Number Operations (AQA GCSE Maths)

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Cards in this collection (43)

What is an exponent?
An exponent is a power or order used in mathematical expressions to represent repeated multiplication of a base number.
E.g. In the expression $4^{5}$ , the 5 is the exponent.
What does the symbol ≈ mean?
The symbol ≈ means approximately equal to.
True or False?
The equals sign (=) is used to show that two expressions are identical.
False.
The equals sign (=) is used to show that two expressions are equal, while the identical sign (≡) is used to show that two expressions are identical.
What is an inequality?
An inequality is a statement that compares two quantities in terms of their size using symbols such as >, <, ≥, or ≤.
True or False?
The symbol ± is used to represent two distinct answers.
True.
The symbol ± is used to represent two distinct (different) answers, often in quadratic equations.
What does this symbol $\sqrt{}$ represent?
$\sqrt{}$ is the positive square root.
It represents the positive result when you find perform the opposite (inverse) operation of squaring a number.
$- \sqrt{}$ is the negative square root.
What do the letters of BIDMAS/BODMAS represent?
The letters in BIDMAS/BODMAS represent: Brackets, Indices, Division, Multiplication, Addition, Subtraction.
BIDMAS/BODMAS is an acronym that stands for the order of operations in mathematics.
True or False?
When using BIDMAS/BODMAS on a calculation that only involves addition and subtraction, the calculation should be performed from left to right.
E.g. $\begin{array}{rcl} 2 - 5 + 7 - 3 - 2 \end{array}$
True.
When using BIDMAS/BODMAS on a calculation that only involves addition and subtraction, the calculation should be performed from left to right.
E.g. $\begin{array}{rcl} 2 - 5 + 7 - 3 - 2 \end{array}$
$\begin{array}{rcl} = & - 3 + 7 - 3 - 2 \\ = & 4 - 3 - 2 \\ = & 1 - 2 \\ = & - 1 \end{array}$
True or False?
When using BIDMAS/BODMAS on a calculation that only involves multiplication and division, the divisions should always be performed first.
E.g. $3 \times 8 \div 2 \times 9$
False.
When using BIDMAS/BODMAS on a calculation that only involves multiplication and division, the calculation should be performed from left to right.
E.g. $3 \times 8 \div 2 \times 9$
$= 24 \div 2 \times 9 = 12 \times 9 = 108$
What is a rational number?
A rational number is a number that can be written as a fraction, $\frac{a}{b}$ , where both $a$ and $b$ are integer (whole number) values.
True or False?
$\sqrt{5}$ is a rational number.
False.
$\sqrt{5}$ is not a rational number, it is irrational.
It cannot be written as a fraction where both the numerator and denominator are integer (whole number) values.
True or False?
2.456456456... is an irrational number
False.
2.456456456... is a recurring decimal so is not an irrational number.
It can be written as the fraction $\frac{818}{333}$ .
True or False?
Multiplying two negative numbers results in a negative value.
False.
When multiplying two negative numbers, the result is a positive value.
When multiplying a positive and a negative, is the resultant value positive or negative?
When multiplying a positive and a negative, the result is a negative value.
True or False?
Subtracting a negative number is the same as adding a positive number.
True.
Subtracting a negative number is the same as adding a positive number.
True or False?
When finding the square of a negative number, the result is positive.
True.
When finding a square of a negative number, the result is positive.
This is because you are multiplying a negative by a negative, which results in a positive.
When finding the cube of a negative number, is the result positive or negative?
When finding the cube of a negative number, you are multiplying a negative by a negative, by a negative so the final result is a negative.
True or False?
Subtracting a negative from a number will always result in a positive answer.
False.
Although subtracting a negative number is equivalent to adding a positive number, the final result will only be positive if the number you are adding it to is large enough.
For example, the calculation $- 3 - - 5 = 2$ but the calculation $- 7 - - 5 = - 2$ .
True or False?
${(- 3)}^{2} = - 3^{2}$
False.
${(- 3)}^{2} = - 3 \times - 3 = 9$ but $- 3^{2} = - (3 \times 3) = - 9$ .
It is always important to put brackets around negative values when you are substituting them into calculations!
Define the term currency.
A currency is a system of money in general use in a particular country or region.
True or False?
Final answers in calculations with money should always be rounded to the nearest integer.
False.
You should usually round answers involving money to two decimal places.
However, you may sometimes be asked to round answers to the nearest integer.
True or False?
Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number, e.g. nearest dollar.
True.
Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number.
True or False?
Monetary values given in more than two decimal places within a question should be rounded to two decimal places before doing any calculations.
False.
Monetary values given in more than two decimal places should be used in the working.
They should only be rounded for the final answer.
What mathematical operation does the word sum imply?
The word sum implies that you need to add numbers together.
If you are asked to find the difference of two numbers, which operation should you use?
Subtraction is the mathematical operation of finding the difference between two numbers by taking one number away from another.
True or False?
The word share implies that you need to divide numbers.
True.
The word share implies that you need to divide numbers.
What mathematical operation is implied by a question asking you to find the product of two or more numbers?
The word product is often used to imply that you need to multiply two numbers together.
How can you perform a division by cancelling common factors in a fraction?
E.g. $1008 \div 28$
A division can be treated like a fraction where common factors from both the numerator and denominator can be found and cancelled.
E.g. $1008 \div 28$ can be written as $\frac{1008}{28}$
You can then cancel it to its simplest form by finding common factors, $\frac{1008}{28} = \frac{504}{14} = \frac{252}{7} = 36$
True or false?
$a \times b$ is the same as $b \times a$ .
True.
$a \times b$ is the same as $b \times a$ .
For example, $5 \times 0.05$ is the same as $0.05 \times 5$ .
It is okay to swap them round.
True or false?
$a - b$ is the same as $b - a$ .
False.
$a - b$ is not the same as $b - a$ .
For example, $10 - 2$ is not the same as $2 - 10$ .
The first gives $8$ but the second gives $- 8$ .
True or false?
If $6 \times 17 = 102$ then $17 = \frac{6}{102}$ .
False.
The correct answer is: if $6 \times 17 = 102$ then $17 = \frac{102}{6}$ .
That is because $a \times b = c$ means $b = \frac{c}{a}$ (the $c$ stays on the top of the fraction).
How would you use the fact that $9 \times 15 = 135$ to work out $900 \times 150 ?$
You could write $900 \times 150$ as $9 \times 10 \times 10 \times 15 \times 10$ .
Then bring the 9 and 15 together, giving $9 \times 15 \times 10 \times 10 \times 10$ .
You know that $9 \times 15 = 135$ so the number above becomes $135 \times 10 \times 10 \times 10$ .
Multiplying by ten each time adds an extra zero, so the answer is $135 000$ .
True or false?
If $3 \times 2 = 6$ then $0.3 \times 0.2 = 0.6$ .
False.
$0.3 \times 0.2$ is the same as $(3 \div 10) \times (2 \div 10)$ .
This is also the same as $(3 \times 2) \div (10 \times 10)$ .
Alternatively, you can use fractions to see this: $\frac{3}{10} \times \frac{2}{10} = \frac{6}{100}$ .
The correct answer is $0.3 \times 0.2 = 0.06$ .
What is the first line of working when simplifying $\frac{126}{1.4}$ ?
$\frac{126}{1.4} = \frac{1260}{14}$ .
You multiply the top and bottom of the fraction by 10 to remove the decimal.
These two fractions are identical, so you can continue working on the second one.
True or False?
Writing a list systematically means there is some sort of order to the list.
True.
Writing a list systematically means there is some sort of order to the list.
It is not the same as trying to write out a list randomly.
True or False?
Writing a list systematically means it is impossible to miss out an option.
True.
Writing a list systematically means it is impossible to miss out an option.
Systematic means the list was created in an organised way.
ZYX is a possible arrangement of the letters XYZ.
Create a systematic way to list all the arrangements of the letters XYZ.
For example, make the first letter an X and swap the other two: XYZ, XZY.
Then make the first letter a Y and swap the other two: YXZ, YZX.
Finally, make the first letter a Z and swap the other two: ZXY, ZYX.
All the arrangements are: XYZ, XZY, YXZ,YZX, ZXY, ZYX.
(There are other acceptable ways to create an organised list like this).
True or False?
A bag contains ten green (G) marbles and ten red (R) marbles.
Two marbles are selected at random.
The possibilities are GR or RG.
False.
There are ten green (G) marbles and ten red (R) marbles.
Two marbles selected at random might both be green, or both be red.
The possibilities are actually GR, RG, GG or RR.
For a long journey, I download one audio book and one film.
There are 10 audio books to choose from and 12 films to choose from.
How many different options are there for my journey?
There are $10 \times 12 = 120$ different options.
This uses the product rule for counting.
For each of the 10 books I choose, there are 12 films I could choose.
True or False?
If a menu has 5 main courses and 3 desserts, there are 8 possible ways to choose a main with a dessert.
False.
If a menu has 5 main courses and 3 desserts, there are 15 possible ways to choose a main with a dessert.
This is because $5 \times 3 = 15$ (using the product rule for counting).
For each of the 5 main courses I choose, there are 3 desserts I could choose.
In a school, a pupil must learn one out of 6 different languages and one out of 7 different musical instruments.
What is the quickest way to calculate the number of possible combinations being offered to a pupil by this school?
The quickest way to calculate the number of possible combinations being offered to a pupil by this school is to use the product rule for counting.
This means there are $6 \times 7 = 42$ possible combinations.
This is much faster than listing out all the possible combinations and counting them.
There are $m$ ways to do a task.
For each of these, there are $n$ ways to do another task.
What is the total number of ways in which the two tasks can be done?
The total number of ways is $m \times n$ .
This is the same as $m n$ .
This is how the product rule for counting works.
True or False?
If a rescue centre has 8 cats and 4 dogs and a visitor wants to adopt one animal, the visitor has $8 \times 4 = 32$ possibilities to choose from.
False.
The visitor wants to adopt one animal only (not one cat and one dog).
That means they will choose either a cat, or a dog, so 1 out of all 12 animals.
There are 12 possibilities to choose from.

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2. Algebra

3. Ratio, Proportion & Rates of Change

4. Geometry & Measures

5. Probability

6. Statistics