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Calculator 1 mark
Use your calculator to work out the value of the reciprocal of \(0.0128\)
Show answer
78.125 (or \(\frac{625}{8}\), as a calculator may show it)The reciprocal of a number is 1 divided by that number.
\(1 \div 0.0128 = 78.125\)
On a calculator this is the reciprocal key \(x^{-1}\) pressed after typing 0.0128. It is not the negative, \(-78.125\).
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Calculator 2 marks
Ben uses a calculator to work out \(46 + 17 \times 3\)
He types \(46 + 17\), presses equals, then types \(\times 3\) and presses equals again.
The display shows \(189\), which is not the right answer.
(a)Calculate the correct value of \(46 + 17 \times 3\)
(b)Explain what Ben did wrong.
Show answer
(a) \(97\)
(b) He pressed equals after 46 + 17, so the calculator added first and then multiplied the whole of 63 by 3. The calculation should be typed in one go, without pressing equals in the middle.A calculator does multiplication before addition, so the multiplication comes first.
\(17 \times 3 = 51\)
\(46 + 51 = 97\)
Pressing equals part-way through finishes that calculation off, so Ben really worked out \((46 + 17) \times 3 = 189\)
Typed in one go, the calculator does \(17 \times 3\) first by itself and gives 97.
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Calculator 3 marks
Leila wants to use a calculator to work out
\(\frac{ 77.7 + 54.8 }{ 61 - 8 }\)
(a)Write down the calculation Leila should type into the calculator.
Use brackets in your answer.
(b)Calculate the value of the calculation.
Show answer
(a) \((77.7 + 54.8) \div (61 - 8)\)
(b) \(2.5\)Everything on the top is added before the dividing happens, and everything on the bottom is subtracted before it happens, so both need brackets.
\((77.7 + 54.8) \div (61 - 8)\)
Top: \(77.7 + 54.8 = 132.5\)
Bottom: \(61 - 8 = 53\)
\(132.5 \div 53 = 2.5\)
- (b) M1top \(132.5\) and bottom \(53\) worked out
- (b) A1\(2.5\)
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Calculator 4 marks
A group of nine friends share the cost of a meal equally.
The total cost is £48.41.
(a)Use a calculator to work out how much each friend pays.
Give your answer correct to the nearest penny.
(b)Each friend pays the amount from part (a).
Calculate how much the 9 friends pay altogether.
Show answer
(a) \(\text{£}5.38\)
(b) \(\text{£}48.42\)\(£48.41 \div 9\) gives a display of \(5.378889\ldots\)
Money is written to two decimal places, so round to the nearest penny.
Each friend pays £5.38.
\(9 \times £5.38 = £48.42\)
That is 1p more than the £48.41 bill, because every share was rounded to the nearest penny.
- (a) M1divides the total by \(9\), display \(5.378889\ldots\)
- (a) A1rounds to the nearest penny, \(£5.38\)
- (b) M1multiplies the share by \(9\)
- (b) A1total paid \(£48.42\)
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Calculator 3 marks
A rectangular plot is being priced by area.
\(x = \frac{ 63 \times 45 }{ 4 }\)
(a)Use a calculator to work out \(x\).
Write down all the figures on your calculator display.
(b)Write down your answer to part (a) correct to 2 significant figures.
Show answer
(a) \(708.75\)
(b) \(710\)The line across a fraction acts like a bracket, so work out the whole of the top first.
\(63 \times 45 = 2835\)
\(2835 \div 4 = 708.75\)
The first two significant figures are the first two digits that are not leading zeros, and the next digit decides whether the second one goes up.
\(708.75\) to 2 significant figures is \(710\).
- (a) M1top of the fraction \(63 \times 45 = 2835\)
- (a) A1\(2835 \div 4 = 708.75\)
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Calculator 2 marks
Use your calculator to work out
\(\frac{ 6.72^2 }{ 4.375 } + \sqrt{ 5.7 }\)
Give your answer as a decimal. Write down your full calculator display.
Show answer
\(12.70938728\)The line in the fraction divides the whole of the top by the bottom, and the root is a separate term.
\(6.72^2 = 45.1584\)
\(45.1584 \div 4.375 = 10.32192\)
\(\sqrt{ 5.7 } = 2.3874672773\ldots\)
Add the root: \(10.32192 + \sqrt{ 5.7 } \approx 12.70938728\)
- M1\(6.72^2 \div 4.375 = 10.32192\) and \(\sqrt{ 5.7 } = 2.3874672773\ldots\)
- A1\(12.70938728\)
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Calculator 2 marks
Calculate \(\dfrac{ 3.24 \times 10^{ 7 } }{ 3.6 \times 10^{ 7 } }\)
Give your answer in standard form.
Show answer
\(9 \times 10^{ -1 }\)Put both the top and the bottom in brackets, using the \(\times 10^x\) key for each power of ten.
\(( 3.24 \times 10^{ 7 } ) \div ( 3.6 \times 10^{ 7 } )\)
The calculator shows \(0.9\).
Rewrite this with one non-zero digit in front of the decimal point, and count the places the point moves to get the power of ten.
\(0.9 = 9 \times 10^{ -1 }\)
- M1dividing the two numbers on the calculator: \(0.9\)
- A1standard form \(9 \times 10^{ -1 }\)
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Calculator 2 marks
Use a calculator to work out
\(\frac{ 11.35 + 5.81 }{ 6 }\)
Show answer
\(2.86\)The line in a fraction means that the whole of the top is divided by the bottom, so work the top out first.
Top: \(11.35 + 5.81 = 17.16\)
Then divide: \(17.16 \div 6 = 2.86\)
On a calculator, put brackets round the top: \((11.35 + 5.81) \div 6\)
Typing \(11.35 + 5.81 \div 6\) with no brackets divides only 5.81 by 6, and gives about \(12.3\)
- M1top worked out first, \(11.35 + 5.81 = 17.16\)
- A1\(17.16 \div 6 = 2.86\)
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Calculator 3 marks(a)
State the value a calculator gives for \((-41)^2\).
(b)State the value a calculator gives for \(-41^2\).
(c)Explain why the two answers are different.
Show answer
(a) \(1681\)
(b) \(-1681\)
(c) The brackets decide what is squared: in \((-41)^2\) the minus sign is inside, and in \(-41^2\) it is outside, so it is applied after the squaring.The brackets mean the whole of \(-41\) is squared.
\((-41) \times (-41) = 1681\)
Without brackets the calculator squares the 41 first and then makes it negative.
\(41^2 = 1681\), so \(-41^2 = -1681\)
A calculator follows the order of operations, and an index comes before a minus sign that is not inside brackets.
\((-41)^2\) squares the whole of \(-41\); \(-41^2\) squares only the 41 and then takes the negative.
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Calculator 3 marks
Here are two calculations.
\(3^4\) and \(4^3\)
They use the same two numbers, swapped round.
(a)Use a calculator to work out both.
(b)State which of the two is larger.
Show answer
(a) \(3^4 = 81\) and \(4^3 = 64\)
(b) \(3^4\)The power key does each one in a single step.
\(3^4 = 81\)
\(4^3 = 64\)
\(81\) is larger than \(64\), so \(3^4\) is the larger.
Swapping the base and the power does not usually give the same answer.
- (a) B1\(3^4 = 81\)
- (a) B1\(4^3 = 64\)