Define truncating a number.

Truncating a number means chopping off the unwanted digits without looking at their value, unlike rounding, which takes account of them. So 2.549 truncated to two decimal places is 2.54, where rounding would give 2.55.

What decides the level of accuracy to use for a financial approximation?

The context decides it, because approximating is a balance between how quickly an answer is needed and how accurate it has to be. A personal monthly budget might sensibly be rounded to the nearest £10, while a global company estimating project costs might round to the nearest £1 million.

A measurement is recorded as 240, rounded to the nearest 10. How do you find its upper and lower bounds?

Halve the degree of accuracy, giving 5, then add it to the recorded value for the upper bound and subtract it for the lower bound. That gives a lower bound of 235 and an upper bound of 245.

A business is estimating its profit. Why might it round its costs up but its income down?

Rounding that way makes the estimated profit smaller than it is likely to be, which is a deliberately cautious estimate. That leaves a safety margin if the costs turn out higher, or the income lower, than expected.

A house that sold for £58 982 is said to be worth 4 times as much now. Why should the answer not be given as £235 928?

The multiplier "4 times" is stated to only one significant figure , so the answer cannot possibly be accurate to the nearest pound. An estimate of £200 000 matches the accuracy of the information actually available.

A mass is given as 14 kg, correct to 2 significant figures. What is the degree of accuracy?

The degree of accuracy is 1 kg , because the second significant figure of 14 sits in the units column. Significant figures do not fix the accuracy on their own: it depends on the size of the number as well.

Define multiplier in a percentage change.

A multiplier is the decimal number you multiply by in order to carry out a percentage change in a single step. It replaces the two-step method of working out the change and then adding it on or taking it off.

Factory A has 389 defects out of 12 098 products, and factory B has 3111 out of 79 781. Why compare these as percentages?

Turning each into a percentage puts both factories on the same scale , so their rates can be compared even though the totals are very different. Factory A's rate is 3.2% and factory B's is 3.9%, so factory A has the lower rate of defects.

A price of 10 p rises by 200%. Andrew says it is now 20 p. What has he done wrong?

Andrew has found 200% of 10 p, instead of adding 200% extra on to it. An increase of 200% makes the new price 300% of the old one, so the multiplier is 3 and the price is 30 p.

A calculation gives a multiplier of 0.75. What percentage change does that represent?

A multiplier of 0.75 is a decrease of 25% , because the new amount is 75% of the old one. Anything below 1 is a decrease and anything above 1 is an increase, so a multiplier of 1.24 would be an increase of 24%.

True or False? To undo an increase of 5%, you multiply by 0.95.

False. An increase of 5% is undone by dividing by 1.05, not by multiplying by 0.95. Decreasing £31 500 by 5% gives £29 925, whereas dividing it by 1.05 gives the £30 000 it actually started from.

Danny has saved £2040 towards a £6000 bathroom and £380 towards a £1000 holiday. Which is he further through?

Express each amount as a percentage of its own goal: £2040 is 34% of £6000 and £380 is 38% of £1000. Relative to the goals he is further through the holiday saving, even though the cash amount saved is much smaller.

Level 3MathsAQAMathematical Studies (Core Maths)Paper 1: Data, Finance, Estimation & ModellingFlashcardsPersonal FinancePersonal Finance Toolkit

Personal Finance Toolkit (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Flashcards

Exam code: 1350

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FrontFinancial Calculations
Complete the order of operations, working from the first step to the last.
Brackets first, then powers or $______$ next, then divisions or $______$ after that, and finally additions or subtractions.

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Cards in this collection (22)

Complete the order of operations, working from the first step to the last.
Brackets first, then powers or $______$ next, then divisions or $______$ after that, and finally additions or subtractions.
The completed order is:
Brackets first, then powers or indices next, then divisions or multiplications after that, and finally additions or subtractions.
Where two operations of the same rank appear together, work through them from left to right.
Why does $\frac{2 + 5}{7 - 2}$ have to be worked out as $(2 + 5) \div (7 - 2)$ ?
A fraction line means divide, and it acts as a pair of invisible brackets around the numerator and around the denominator.
The same thing happens under a root sign, so $\sqrt{9 + 16}$ means $\sqrt{(9 + 16)}$ .
Define truncating a number.
Truncating a number means chopping off the unwanted digits without looking at their value, unlike rounding, which takes account of them.
So 2.549 truncated to two decimal places is 2.54, where rounding would give 2.55.
In the calculation $(5 - 3) + 2 \times 7^{2}$ which operation is carried out last, and why?
The addition is carried out last, because additions and subtractions come at the very end of the order of operations.
The bracket gives 2, the power gives 49 and the multiplication gives 98, so only then is $2 + 98 = 100$ worked out.
A number $x$ has been rounded. Complete the error interval, where LB is the lower bound and UB is the upper bound.
$L B______x______U B$
The completed error interval is:
$L B \leq x < U B$
The lower bound is included in the interval but the upper bound is not, because a value equal to the upper bound would round up to the next number instead.
What decides the level of accuracy to use for a financial approximation?
The context decides it, because approximating is a balance between how quickly an answer is needed and how accurate it has to be.
A personal monthly budget might sensibly be rounded to the nearest £10, while a global company estimating project costs might round to the nearest £1 million.
True or False?
A value truncated to 2.95 lies in the interval $2.95 \leq a < 2.96$ .
True.
Truncating never rounds up, so the truncated value is the smallest value the original number could have been.
Unlike a rounded value, it therefore sits at the very bottom of its error interval rather than in the middle of it.
A measurement is recorded as 240, rounded to the nearest 10. How do you find its upper and lower bounds?
Halve the degree of accuracy, giving 5, then add it to the recorded value for the upper bound and subtract it for the lower bound.
That gives a lower bound of 235 and an upper bound of 245.
A business is estimating its profit. Why might it round its costs up but its income down?
Rounding that way makes the estimated profit smaller than it is likely to be, which is a deliberately cautious estimate.
That leaves a safety margin if the costs turn out higher, or the income lower, than expected.
A house that sold for £58 982 is said to be worth 4 times as much now. Why should the answer not be given as £235 928?
The multiplier "4 times" is stated to only one significant figure, so the answer cannot possibly be accurate to the nearest pound.
An estimate of £200 000 matches the accuracy of the information actually available.
A mass is given as 14 kg, correct to 2 significant figures. What is the degree of accuracy?
The degree of accuracy is 1 kg, because the second significant figure of 14 sits in the units column.
Significant figures do not fix the accuracy on their own: it depends on the size of the number as well.
Define multiplier in a percentage change.
A multiplier is the decimal number you multiply by in order to carry out a percentage change in a single step.
It replaces the two-step method of working out the change and then adding it on or taking it off.
How do you write a 4% increase and a 5% decrease as multipliers?
Turn the percentage into a decimal by dividing by 100, then add it to 1 for an increase and subtract it from 1 for a decrease.
So a 4% increase gives $1 + 0.04 = 1.04$ and a 5% decrease gives $1 - 0.05 = 0.95$ .
How do you express 7 as a percentage of 20?
Write one number as a fraction of the other, then turn that fraction into a decimal and finally into a percentage.
Here $\frac{7}{20} = 0.35$ , so 7 is 35% of 20.
True or False?
A percentage can never be greater than 100%.
False.
A percentage is simply a quantity written as a proportion of 100, so values above 100% are perfectly ordinary.
For example $\frac{24}{16} = 1.5$ , so 24 is 150% of 16.
Complete the formula for the multiplier $m$ of a percentage change, when the amounts before and after the change are both known.
$m = \frac{______}{______}$
The completed formula is:
$m = \frac{amount after}{amount before}$
The multiplier is what turns the amount before into the amount after, so the amount after always goes on top.
Factory A has 389 defects out of 12 098 products, and factory B has 3111 out of 79 781. Why compare these as percentages?
Turning each into a percentage puts both factories on the same scale, so their rates can be compared even though the totals are very different.
Factory A's rate is 3.2% and factory B's is 3.9%, so factory A has the lower rate of defects.
A price of 10 p rises by 200%. Andrew says it is now 20 p. What has he done wrong?
Andrew has found 200% of 10 p, instead of adding 200% extra on to it.
An increase of 200% makes the new price 300% of the old one, so the multiplier is 3 and the price is 30 p.
How do you find the original amount before a percentage change, when you know the amount afterwards?
Write down the multiplier $m$ for the change, then divide the amount afterwards by it.
$amount before = \frac{amount after}{m}$
The change happened to the amount before, not to the amount after, which is why dividing is what undoes it.
A calculation gives a multiplier of 0.75. What percentage change does that represent?
A multiplier of 0.75 is a decrease of 25%, because the new amount is 75% of the old one.
Anything below 1 is a decrease and anything above 1 is an increase, so a multiplier of 1.24 would be an increase of 24%.
True or False?
To undo an increase of 5%, you multiply by 0.95.
False.
An increase of 5% is undone by dividing by 1.05, not by multiplying by 0.95.
Decreasing £31 500 by 5% gives £29 925, whereas dividing it by 1.05 gives the £30 000 it actually started from.
Danny has saved £2040 towards a £6000 bathroom and £380 towards a £1000 holiday. Which is he further through?
Express each amount as a percentage of its own goal: £2040 is 34% of £6000 and £380 is 38% of £1000.
Relative to the goals he is further through the holiday saving, even though the cash amount saved is much smaller.

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