True or False? On an irregular shape you may assume that sides which look equal are equal.

False. With an irregular shape, assume every angle and every length is different unless you are told otherwise. Only marked equal sides, marked equal angles, or a stated property such as a line of symmetry let you treat two of them as the same.

How do you handle a shape that is not one of the standard ones?

Split it into common shapes, then add or subtract their areas or perimeters to build the expression you need. If no diagram is given, sketch one first and mark on it every length and angle the question states.

How do you find the volume of a prism whose cross-section is a trapezium?

Work out the area of the cross-section using the trapezium formula, then multiply that area by the length of the prism. A prism has a constant cross-section, which is what makes a single multiplication enough.

IGCSEMathsEdexcelMaths BFlashcardsAlgebraForming & Solving Equations

Forming & Solving Equations (Edexcel IGCSE Maths B): Flashcards

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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 (15)

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).
What turns a shape with algebraic side lengths into an equation?
A property of the shape combined with a value the question gives you, such as a stated perimeter, area or angle.
Write the property as an expression in $x$ , then set that expression equal to the value given.
A rectangle has length $3 x + 1$ and width $2 x - 5$ , and its perimeter is 22. Fill in the missing part of the equation.
$2 (3 x + 1) +______= 22$
The completed equation is:
$2 (3 x + 1) + 2 (2 x - 5) = 22$
A rectangle has two lengths and two widths, so each expression is doubled before the two are added together.
Why should you put brackets round an algebraic side length before substituting it?
Because the shape's property usually multiplies the whole side length, and without brackets only the first term gets multiplied.
A width of $2 x - 5$ contributes $2 (2 x - 5) = 4 x - 10$ to a perimeter, not $4 x - 5$ .
True or False?
On an irregular shape you may assume that sides which look equal are equal.
False.
With an irregular shape, assume every angle and every length is different unless you are told otherwise.
Only marked equal sides, marked equal angles, or a stated property such as a line of symmetry let you treat two of them as the same.
How do you handle a shape that is not one of the standard ones?
Split it into common shapes, then add or subtract their areas or perimeters to build the expression you need.
If no diagram is given, sketch one first and mark on it every length and angle the question states.
How do you find the volume of a prism whose cross-section is a trapezium?
Work out the area of the cross-section using the trapezium formula, then multiply that area by the length of the prism.
A prism has a constant cross-section, which is what makes a single multiplication enough.
A prism has cross-sectional area $7 x^{2}$ and length $x + 3$ , and its volume is 784. How do you reach $x^{3} + 3 x^{2} - 112 = 0$ ?
Multiply out the volume, $7 x^{2} (x + 3) = 7 x^{3} + 21 x^{2}$ , and set the result equal to 784.
Dividing every term by 7 gives $x^{3} + 3 x^{2} = 112$ , and subtracting 112 from both sides puts it in the form asked for.
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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