GCSEMathsAQAHigherFlashcards2. AlgebraForming & Solving Equations

Forming & Solving Equations (AQA GCSE Maths)

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FrontForming Equations from Words
Use algebra to represent double the amount of a quantity, given that $x$ is the initial quantity.

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Cards in this collection (10)

Use algebra to represent double the amount of a quantity, given that $x$ is the initial quantity.
Double the amount of a quantity $x$ can be written as $2 x$ .
Use algebra to represent half the amount of a quantity, given that $x$ is the initial quantity.
Half the amount of a quantity $x$ can be written as $\frac{1}{2} x$ or $\frac{x}{2}$ or $0.5 x$ .
Use algebra to represent five more than a quantity, given that $x$ is the initial quantity.
Five more than a quantity $x$ can be written as $x + 5$ .
This is not the same as $5 x$ .
Use algebra to represent ten lots of a quantity, given that $x$ is the initial quantity.
Ten lots of a quantity $x$ can be written as $10 x$ .
This is not the same as $x + 10$ .
True or False?
If my sister is 2 years younger than me, then $x$ is my age and $x - 2$ is her age.
True.
If my sister is 2 years younger than me, then $x$ is my age and $x - 2$ is her age.
It is also true to say that $y + 2$ is my age and $y$ is her age.
Three bags contain $x$ , $x + 5$ and $x + 10$ marbles each.
If there are 75 marbles in total, explain how to form an equation.
Three bags contain $x$ , $x + 5$ and $x + 10$ marbles each.
If there are 75 marbles in total, then an equation can be formed by adding all the quantities up and setting them equal to 75.
This gives $x + (x + 5) + (x + 10) = 75$ .
Examiners want to see this full equation (before simplifying or solving).
If the total perimeter of the regular pentagon below is $100$ cm, show how to form an equation.
The pentagon being regular means the side lengths are all equal.
If the total perimeter of a regular pentagon with side length $(x + 2)$ is $100$ cm, then:
1. Find the total perimeter in terms of $x$ by multiplying $(x + 2)$ by 5
2. Set this equal to 100
This forms the equation $5 (x + 2) = 100$ .
True or False?
If the interior angles of an $n$ -sided polygon are given algebraically in terms of $x$ , you can calculate the size of $x$ as the total sum of the angles will always be $180 (n - 2)$ .
True.
If the interior angles of an $n$ -sided polygon are given algebraically in terms of $x$ , you can calculate the size of $x$ as the total sum of the angles will always be $180 (n - 2)$ .
E.g. for any hexagon (regular or irregular), the sum of its interior angles will always be $180 (6 - 2) = 720 °$ .
So if the interior angles are in terms of $x$ , add them together and set equal to $720 °$ .
True or False?
You can use a 'show that' answer from part (a) to do part (b), even if you did not complete part (a) yourself.
True.
You can use a 'show that' answer from part (a) to do part (b), even if you did not complete part (a) yourself.
If part (a) says to show that certain information leads to the equation $x^{2} - x - 6 = 0$ , then you can use that equation in part (b) without having proved part (a)!
Explain the phrase answer the question in context.
Answer the question in context means that your final answer should
- be related to the real-life situation in the question
- be written in sentences
- use words and phrases from the question
- state the correct units
- be rounded appropriately
The answer should not be, for example:
- $x = 2$ (no explanation)
- "the length is bigger" (no context)

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