Question Bank › GCSE Number › Decimals
Decimals Topic Using a Calculator / BIDMAS (23) Standard Form (15) Surds (2) Properties of Numbers (44) Rounding (15) Upper & Lower Bounds (13) Compound Measures (20) Combinations (8) Fractions (54) Decimals (41) Percentages (48) Recurring Decimals (3) Ratio & Basic Proportion (52) Direct & Inverse Proportion (7) FDPR Mixed Context (17) Units & Time (33) Current PowerPoint version
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Foundation June 2025 Paper 1 Q15 15 Work out \(1.35 \times 48\) (3)
Mark scheme
Mark scheme Answer Mark Mark scheme 64.8(0) M1 for a complete method with relative place value correct including an intention to add all the appropriate elements of the calculation or for a complete method to find 35% of 48 or 0.48 and add this on eg \(48 \div 10\ (= 4.8)\) and \(\text{``}4.8\text{''} \div 2\ (= 2.4)\) and \(48 + 3 \times \text{``}4.8\text{''} + \text{``}2.4\text{''}\) A1 for digits 648 A1 ft (dep on M1) for correct placement of the decimal point into their final answer
Additional guidance 4000+800+1200+240+200+40
Incorrect answer scores maximum 2 marks.
Foundation June 2025 Paper 2 Q3 3 Write 0.7 as a percentage. (1)
Mark scheme
Mark scheme Answer Mark Mark scheme 70 B1 cao
Foundation June 2025 Paper 1 Q2 2 Write \(\dfrac{3}{4}\) as a decimal. (1)
Mark scheme
Mark scheme Answer Mark Mark scheme 0.75 B1 cao
Foundation June 2025 Paper 3 Q1 1 Write down the value of the 7 in the number 49.715 (1)
Mark scheme
Mark scheme Answer Mark Mark scheme tenths or \(\dfrac{7}{10}\) B1 for (7) tenths or \(\dfrac{7}{10}\) or 0.7
Additional guidance Condone incorrect spelling provided the intention is clear
Foundation November 2024 Paper 1 Q18 18 Work out \(818.4 \div 1.2\) (3)
Mark scheme
Mark scheme Answer Mark Mark scheme 682 M1 for a start to a method, eg \(8184 \div 12\) (or \(818.4 \div 1.2\)) that leads to 6 as the first digitor for a complete method with no more than one arithmetic error A1 for digits 682 A1 (ft) (dep M1) for correct placement of the decimal point into their final answer
Additional guidance A start to a repeated subtraction method or build-up method is acceptable if a correct first digit of 6 is found
Foundation November 2024 Paper 3 Q8 8 Nina orders some items from a DIY shop. Here is her bill.
Item Quantity Cost of each item Total Pack of screws 4 £29.99 £119.96 Tin of paint 2 £24.95 £ .......... Wooden plank .......... £7.75 £232.50 Delivery charge £14.95 Total cost £ ..........
(a) Complete all the missing information in the bill. (3)
At the beginning of January, Jeff had £892.48 in his bank account.
During January, Jeff had £4.47 interest added to his account paid £240 into his account spent £365.50 from his account.
(b) How much money did Jeff have in his account at the end of January? (3)
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Mark scheme 49.9(0) B1 for 49.9(0) 30 B1 for 30 417.31 B1 for 417.31, ft allow 367.41 + [their 49.9(0)] for this mark
Additional guidance To award B1ft, the total for tin of paint must not be blank or 0
Mark scheme (b) Answer Mark Mark scheme 771.45 M1 for a correct first step, eg \(892.48 + 4.47\ (= 896.95)\) or \(892.48 + 240\ (= 1132.48)\)or \(892.48 - 365.5(0)\ (= 526.98)\) or \(4.47 + 240\ (= 244.47)\) M1 for a complete method, eg \(892.48 + 4.47 + 240 - 365.5(0)\) A1 cao
Additional guidance May be seen embedded in other calculations eg \(4.47 + 240 - 365.5(0)\)
Foundation November 2024 Paper 2 Q3 3 Write these numbers in order of size. Start with the smallest number.
0.57 0.507 0.5 0.05 (1)
Mark scheme
Mark scheme Answer Mark Mark scheme 0.05, 0.5, 0.507, 0.57 B1 for 0.05, 0.5, 0.507, 0.57
Additional guidance Accept reverse order
Foundation November 2024 Paper 1 Q1 1 Write 25% as a decimal. (1)
Mark scheme
Mark scheme Answer Mark Mark scheme 0.25 B1 cao
Higher November 2024 Paper 1 Q1 1 Work out \(818.4 \div 1.2\) (3)
Mark scheme
Mark scheme Answer Mark Mark scheme 682 M1 for a start to a method, eg \(8184 \div 12\) (or \(818.4 \div 1.2\)) that leads to 6 as the first digitor for a complete method with no more than one arithmetic error A1 for digits 682 A1 ft (dep M1) for correct placement of the decimal point into their final answer
Additional guidance A start to a repeated subtraction method or build-up method is acceptable if a correct first digit of 6 is found
Foundation June 2025 Paper 3 Q9 9
(a) The square of a
whole number is a two-digit number.
Work out
the smallest number that could have been squared and the largest number that could have been squared. [3 marks]
(b) Which has the
larger value \(\quad 0.8^2 \quad\) or \(\quad 0.8^3\) ?
Tick a box.
Give a reason for your answer. [1 mark]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments 4 and 9 in correct positions B3 B2 9 in smallest position and 4 in largest position or only 4 in correct position or only 9 in correct position or \(4^2\) in smallest position and \(9^2\) in largest position or 16 or \(\sqrt{16}\) in smallest position and 81 or \(\sqrt{81}\) in largest position B1 \(4^2\) or 16 or \(\sqrt{16}\) or \(9^2\) or 81 or \(\sqrt{81}\)
Additional guidance \(4^2 = 16\) in smallest position and \(9^2 = 81\) in largest position B2 16, 4 in smallest position and 81, 9 in largest position B2 \(2^2 = 4\) in smallest position is not 4 in smallest position \(3^2 = 9\) in largest position is not 9 in largest position
Mark scheme (b) Answer Mark Comments \(0.8^2\) ticked with either 0.64 and 0.512 or \(\dfrac{64}{100}\) and \(\dfrac{64}{125}\) or \(0.8 \lt 1\) or suitable worded reason B1 oe in comparable form fractions must have same numerator or same denominator eg multiplying by decimals below 1 makes numbers smaller
Additional guidance Ignore further work after correct values in comparable form Condone 0.51 for 0.512 \(\dfrac{16}{25}\) and \(\dfrac{64}{125}\) (fractions do not have same numerator or denominator) B0 \(0.8^2\) ticked and squaring makes numbers bigger B0
Foundation June 2025 Paper 3 Q8 8 One burger costs £3.80
Two burgers and
three hotdogs cost £15.85
Work out the cost of one hot dog. [3 marks]
Mark scheme
Mark scheme Answer Mark Comments \(2 \times 3.8(0)\) or 7.6(0) M1 oe accept working in pounds or pence \(15.85 -\) their 7.6(0) or 8.25 M1dep oe accept working in pounds or pence 2.75 A1 SC2 275
Additional guidance Condone £2.75p \(7.60 - 15.85\) unless recovered M1M0dep
Foundation November 2024 Paper 1 Q19 19 Work out the value of \(1.5^2\) [2 marks]
Mark scheme
Mark scheme Answer Mark Comments \(1.5 \times 1.5\) or \(\left(\dfrac{3}{2}\right)^2\) M1 oe oe improper fraction squared 2.25 or \(\dfrac{9}{4}\) or \(2\dfrac{1}{4}\) A1 oe decimal, improper fraction or mixed number SC1 answer digits 225
Additional guidance Ignore attempt to simplify or convert if correct fraction seen Do not allow further work but condone adjusting place value eg \(1.5 \times 1.5 = 2.25\), \(2.25 \div 100 = 0.0225\) (adjusting place value) eg \(1.5 \times 1.5 = 2.25\), \(2.25 \times 1.5\) (cubing not squaring) M1A0 M0A0\(1.5 \times 1.5 = 3\) M1A0 \(2.25^2\) \(225^2\) M1A0 M0A0
Foundation November 2024 Paper 3 Q9 9 A loaf of bread has
14 slices each 12 mm thick and 2 crusts each 15 mm thick.
Not drawn accurately
Work out the total length of the loaf of bread.
Give your answer in centimetres . [3 marks]
Mark scheme
Mark scheme Answer Mark Comments \(14 \times 12\) or 168 or \(2 \times 15\) or 30 or \(12 \div 10\) or 1.2 or \(15 \div 10\) or 1.5 M1 oe \(14 \times 12 + 2 \times 15\) or \(168 + 30\) or 198 or \(14 \times 12 \div 10\) or 16.8 or \(2 \times 15 \div 10\) or 3 M1dep oe 19.8 A1 SC2 17.4
Additional guidance SC2 17.4 is from thinking 14 slices includes the 2 crusts Condone answer 20 with 19.8 seen M1M1A1 Answer 19 with 19.8 seen M1M1A0
Foundation November 2024 Paper 3 Q7 7 Tyler has £20
A notepad costs £1.30
Work out the greatest number of notepads he can buy. [2 marks]
Mark scheme
Mark scheme Answer Mark Comments \(20 \div 1.3(0)\) or [15.3, 15.4] or 19.5(0) M1 oe 15 with no incorrect working A1
Additional guidance \(15 \times 1.30 = 19.05\) with answer 15 (incorrect working) M1A0 \(15 \times 1.30\) without answer 15 M1A0 For build up method allow one error but must get above £18.70 eg1 13 14.30 15.60 17 18.30 19.60 and answer of 15 eg2 13 15.30 16.60 17.90 19.20 For build down method allow one error but must get below £1.30 eg3 20 18.70 17.40 16.10 14.60 \(\ldots\) 5.50 4.20 2.90 1.60 0.30 M1A0 M1A0 M1A0
Foundation November 2024 Paper 1 Q6 6 Sally buys two hats and three scarves.
The total cost is £28.50 Each hat costs £4.50
Work out the cost of each scarf. [4 marks]
Mark scheme
Mark scheme Answer Mark Comments \(2 \times 4.5\) or 9 M1 oe \(28.5 -\) their 9 or 19.5 M1dep oe their \(19.5 \div 3\) or 6.5 M1dep oe dep on M2 6.50 or 650p A1 SC2 7.50 condone £6.50p
Additional guidance Accept working in pence
SC2 is for using £4.50 as the cost of a scarf or interchanging the quantities
Foundation November 2024 Paper 3 Q4 4
(a) Write these numbers in order of size.
Start with the smallest number.
2 1.8 \(-1\) 0
[2 marks] (b) Write these numbers in order of size.
Start with the smallest number.
\(\dfrac{1}{2}\) \(3\dfrac{1}{10}\) \(\dfrac{1}{4}\) \(\dfrac{7}{8}\)
[2 marks] Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments \(-1\), 0, 1.8, 2 B2 B1 answer begins \(-1\) or ends 2 SC1 2, 1.8, 0, \(-1\)
Additional guidance Do not allow misreads for B2 Accept extra zeros and 1.8 written as a fraction eg \(-1\), 0, \(\dfrac{9}{5}\), 2.0 B2
Mark scheme (b) Answer Mark Comments \(\dfrac{1}{4}\), \(\dfrac{1}{2}\), \(\dfrac{7}{8}\), \(3\dfrac{1}{10}\) B2 B1 answer begins \(\dfrac{1}{4}\) or ends \(3\dfrac{1}{10}\) SC1 \(3\dfrac{1}{10}\), \(\dfrac{7}{8}\), \(\dfrac{1}{2}\), \(\dfrac{1}{4}\)
Additional guidance Do not allow misreads for B2 Accept correct conversions to equivalent fractions or decimals eg 0.25, \(\dfrac{4}{8}\), \(\dfrac{7}{8}\), \(3\dfrac{1}{10}\) B2Do not accept any incorrect working or incorrect conversions for B2 eg1 \(\dfrac{1}{4}\), \(\dfrac{1}{2}\), \(\dfrac{7}{8}\), \(3\dfrac{1}{10}\) with 3.01 seen in working eg2 \(\dfrac{1}{4}\), \(\dfrac{1}{2}\), \(\dfrac{7}{8}\), 3.01 B1 B1Condone any incorrect working or incorrect conversions for B1 eg \(\dfrac{1}{4}\), 0.3, \(\dfrac{1}{2}\), \(\dfrac{7}{8}\) B1Condone correct percentage value without percentage sign for B2 eg \(\dfrac{1}{2} = 50\) is condoned as not incorrect working
Foundation November 2024 Paper 3 Q3 3
(a) 3 apples cost 96p
Work out the cost, in pounds (£), of 12 of these apples. [2 marks]
(b) In total, the cost of 40 cartons of apple juice and 20 cartons of orange juice is £21.50
Work out the cost of
4 cartons of apple juice and 2 cartons of orange juice.
[2 marks] Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments \(12 \div 3\) or 4 or \(96 \div 3\) or 32 or \(96 \times 12\) or 1152 or \(96 \times 12 \div 3\) or 384 M1 oe accept working in pounds or pence 3.84 A1
Additional guidance Condone £3.84p
Mark scheme (b) Answer Mark Comments \(40 \div 4\) or \(20 \div 2\) or 10 or \(\dfrac{21.5(0)}{40 + 20}\) or 215 M1 oe accept working in pounds or pence 2.15 A1
Additional guidance Condone £2.15p Do not ignore further working eg 2.15 followed by \(2.15 \times 4 + 2.15 \times 2 = 12.90\) M1A010 can be implied by \(\dfrac{21.5}{40} \times 4\) or \(\dfrac{21.5}{20} \times 2\) M1
Foundation November 2024 Paper 2 Q2 2 Here is a price list.
Soap £2.00 Candle £4.55 Lip scrub £1.75 Body cream £3.80
(a) Work out the cost of three candles. [1 mark]
(b) Sal has £7.50
He wants to buy one soap and one body cream.
Does he have enough money to also buy one lip scrub?
Tick a box.
Show working to support your answer. [2 marks]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments 13.65 B1
Mark scheme (b) Answer Mark Comments Alternative method 1 \(2 + 3.8(0) + 1.75\) or 7.55 M1 oe 7.55 and No A1 Alternative method 2 \(7.5(0) - 2 - 3.8(0)\) or 1.7(0) M1 oe 1.7(0) and No A1 Alternative method 3 \(7.5(0) - 2 - 3.8(0) - 1.75\) or \(-0.05\) M1 oe \((-)0.05\) and No A1
Additional guidance No may be indicated by selecting the box or a statement in the working lines May work in pence In alts 1 and 2 ignore any attempt to evaluate differences once the correct value is seen Eg No ticked and 7.55 seen, followed by he is 0.5 short M1A1
Foundation June 2024 Paper 3 Q22 22 Kay hires a digger.
The cost per day is
£24.50 for the first 5 days reduced by 20% for day 6 the same as day 6 for day 7 onwards. The total cost is £259.70
For how many days did Kay hire the digger?
You must show your working. [5 marks]
Mark scheme
Mark scheme Answer Mark Comments \(5 \times 24.5\) or 122.5 M1 oe \(24.5 \times 0.2\) or 4.9 M1 oe \(24.5 -\) their 4.9 or 19.6 M1dep oe dep on 2nd M1 \(24.5 \times 0.8\) oe is 2nd M1 and 3rd M1 \((259.7 -\) their \(122.5) \div\) their 19.6 or \(137.2 \div\) their 19.6 M1dep oe dep on 3rd M1 eg1 \(7 \times 19.6 = 137.2\) eg2 \(122.5 + 19.6 + 19.6 + 19.6 + 19.6 + 19.6 + 19.6 + 19.6 = 259.7\) 12 with 19.6 seen or 12 with 122.5, 142.1, 161.7, 181.3, 200.9, 220.5, 240.1, 259.7 A1
Additional guidance Up to M3 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts Build up attempts must be fully correct or show method \(122.5 + 19.6\) M1M1M1 122.5, 142.1, 161.7, 181.3, 200.9, 220.5, 240.1, 259.7 without 12 M1M0M0M0
Foundation June 2024 Paper 3 Q16 16 Tins of beans are sold in shop A and shop B.
Shop A 1 tin 64p Buy 4 tins for the price of 3 tinsShop B 1 tin 62p Pack of 3 tins £1.70 10% reduction in price on all packs
At which shop is it cheaper to buy 20 tins?
State how much cheaper. [5 marks]
Shop \(\ldots\ldots\ldots\) Cheaper by \(\ldots\ldots\ldots\)
Mark scheme
Mark scheme Answer Mark Comments \(15 \times 0.64\) or 9.6 M1 oe eg1 \(20 \times 0.64 \times \dfrac{3}{4}\) eg2 \(20 \times 0.64 - (20 \div 4) \times 0.64\) \(1.7 \times 0.9\) or 1.53 or \(1.7 \times 6\) or 10.2 M1 oe eg \(1.7 - 0.1 \times 1.7\) \(1.7 \times 0.9 \times 6\) or 9.18 M1dep oe eg \(10.2 - 0.1 \times 10.2\) dep on 2nd M1 their \(9.18 + 2 \times 0.62\) or 10.42 M1 oe their 9.18 must be 6 times their pack price Shop A Cheaper by £0.82 A1 oe eg Shop A Cheaper by 82p
Additional guidance Accept working in pounds or pence Mixed units in the 4th M1 mark must be recovered with a correct value for their calculation 960 and \(9.18 + 2 \times 62\) 960 and \(9.18 + 2 \times 62\) and 10.42 M1M1M1M0 M1M1M1M1\(10.20 + 2 \times 0.62\) or 11.44 score the 2nd and 4th M1 mark
Foundation June 2024 Paper 1 Q14 14 Here is a multiplication table.
\(\times\) 61 63 65 67 61 3721 3843 3965 4087 63 3843 3969 4095 4221 65 3965 4095 4225 4355 67 4087 4221 4355 4489
Use the table to answer the following questions.
(a) Work out \(\quad 3843 \div 63\) [1 mark]
(b) Work out \(\quad 6.1 \times 6.7\) [1 mark]
(c) Work out \(\quad 63 \times 66\) [2 marks]
Mark scheme (a) Mark scheme (b) Mark scheme (c)
Mark scheme (a) Mark scheme (b) Answer Mark Comments 40.87 B1
Mark scheme (c) Answer Mark Comments \(4095 + 63\) or \(4221 - 63\) or \((4095 + 4221) \div 2\) or \(8316 \div 2\) or Valid attempt to multiply 63 by 66 with no conceptual error M1 oe from traditional method their \(378 +\) their 3780 or their \(198 +\) their 3960 with at least one correct and placeholder of zero correct or implied from grid method their \(3600 +\) their \(360 +\) their \(180 +\) their 18 (at least three correct) from Chinese / Napier’s bones method at least three values correct from 1/8, 1/8, 3/6 and 3/6 and total calculated for each diagonal with at least one carrying figure placed correctly 4158 A1
Foundation June 2024 Paper 2 Q10 10
(a) Leema buys 2 metres of linen at £8.50 per metre.
She also buys 5 metres of cotton.
The total cost is £38
What is the cost of one metre of cotton? [4 marks]
(b) Buttons cost 65p each.
The greatest number of buttons Leema can buy with £5 is 7
She says,
“The greatest number of buttons I can buy with £10 is 14 because £10 is double £5”
Is she correct?
Tick a box.
Show working to support your answer. [2 marks]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments \(2 \times 8.5(0)\) or 17(.00) M1 oe \(38 -\) their 17 or 21 M1dep their \(21 \div 5\) or 4.2 M1dep oe eg \(5 \times 4.2(0)\) 4.20 A1 correct money notation SC2 5.90 SC1 5.9
Additional guidance Special case is for using 1 metre of linen at £8.5(0) Allow 4.20(p) for the A mark \(4.20 \div 5 = 84\)p M1M1M1A0
Mark scheme (b) Answer Mark Comments \(14 \times 0.65\) or 9.1(0) or \(15 \times 0.65\) or 9.75 or \(10 \div 0.65\) or 15.3(…) or 15.4 or \((5 - 7 \times 0.65) \times 2\) or 0.9(0) M1 oe allow in pence No and 15 with M1 awarded or No and (£)9.75 A1 oe eg No and she can get 1 more with M1 awarded
Additional guidance Yes ticked max M1A0 No may be implied if neither box ticked \(0.65 \times 14 = 9.1\) she can buy another No ticked M1A1 \(10 \div 0.65 = 15.38\) No ticked M1A0 \(0.65 \times 14 = 9.1\) she can buy more No ticked M1A0 She can get 15 not 14 No ticked M0A0 The left over change would make up another 65p so enough for another button No ticked M0A0
Foundation June 2024 Paper 3 Q8 8
A pack of pegs costs 40p A bar of soap costs £2.20 A basket costs £7 Dan buys two packs of pegs, one bar of soap and one basket.
What fraction of the total cost is the cost of the basket? [3 marks]
Mark scheme
Mark scheme Answer Mark Comments 0.4 or 0.8 or 220 or 700 M1 oe \(2.2 + 2 \times 0.4 + 7\) or 10 or 1000 M1 oe allow mixed units 10 or 1000 implies M2 \(\dfrac{7}{10}\) or \(\dfrac{700}{1000}\) A1 oe fraction SC2 0.7(0) or 70%
Additional guidance Ignore simplification attempts after a correct fraction is seen \(\dfrac{7}{10}\) in working with 0.7 on answer line M1M1A0 Condone eg 0.80p for first M1 Do not allow eg £220 for first M1
Foundation June 2024 Paper 3 Q5 5 Complete each statement using one of these symbols. [3 marks]
\(\lt\) \(=\) \(\gt\)
2.54 \(\ldots\ldots\ldots\) 2.508 0.25 \(\ldots\ldots\ldots\) \(\dfrac{1}{4}\) 2 \(\ldots\ldots\ldots\) \(\dfrac{5}{2}\)
Mark scheme
Mark scheme Answer Mark Comments \(\gt\) B1 \(=\) B1 \(\lt\) B1
Additional guidance Must use the correct symbol, not word equivalents
Foundation June 2024 Paper 1 Q4 4
(a) Here is a list of four numbers.
6.92 7.27 7.18 7.14
Use one number from the list to complete each statement. [2 marks]
The number closest in value to 7 is \(\ldots\ldots\ldots\)
The number that rounds to 7.2 to 1 decimal place is \(\ldots\ldots\ldots\)
(b) Here is a list of six numbers.
\(-10\) \(-5\) \(-2\) 4 6 10
Use two numbers from the list to complete each statement. [2 marks]
Two numbers that add to make \(-1\) are \(\ldots\ldots\ldots\) and \(\ldots\ldots\ldots\)
Two numbers that multiply to make 20 are \(\ldots\ldots\ldots\) and \(\ldots\ldots\ldots\)
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments 6.92 B1 first answer 7.18 B1 second answer
Mark scheme (b) Answer Mark Comments \(-5\) and 4 B1 either order first answer \(-10\) and \(-2\) B1 either order second answer
Foundation June 2024 Paper 2 Q4 4
(a) One lettuce costs £1.29
How much do seven of these lettuces cost? [1 mark]
(b) Five cucumbers cost £6.40 in total.
How much do two of these cucumbers cost? [1 mark]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Additional guidance 9.03p B1 903p on the answer line B1 903 on the answer line with £ not crossed out B0
Mark scheme (b) Additional guidance 2.56p B1 256p on the answer line B1 256 on the answer line with £ not crossed out B0
Foundation June 2024 Paper 2 Q1 1
(a) Write 0.27 as a fraction. [1 mark]
(b) Write \(\dfrac{2}{5}\) as a decimal. [1 mark]
(c) Write 0.35 as a percentage. [1 mark]
Mark scheme (a) Mark scheme (b) Mark scheme (c)
Mark scheme (a) Answer Mark Comments \(\dfrac{27}{100}\) B1
Additional guidance Ignore attempt to simplify after correct answer seen
Mark scheme (b) Answer Mark Comments 0.4 B1 oe decimal eg 0.40
Mark scheme (c) Foundation November 2023 Paper 3 Q16 16 Which is closer in value to 2.5
\[\dfrac{3}{4} \quad \text{or} \quad 4\dfrac{1}{5}\ ?\]
You must show your working. [3 marks]
Mark scheme
Mark scheme Answer Mark Comments Alternative method 1 \(\left(\dfrac{3}{4} =\right)\ 0.75\) or \(\left(4\dfrac{1}{5} =\right)\ 4.2\) M1 \(2.5 - 0.75\) or 1.75 and \(4.2 - 2.5\) or 1.7 M1dep \(4\dfrac{1}{5}\) with 1.75 and 1.7 seen A1 Alternative method 2 \(\left(4\dfrac{1}{5} =\right)\ \dfrac{21}{5}\) or \((2.5 =)\ \dfrac{5}{2}\) M1 oe improper fraction \(\left(\dfrac{3}{4} =\right)\ \dfrac{15}{20}\) and \(\left(4\dfrac{1}{5} =\right)\ \dfrac{84}{20}\) and \((2.5 =)\ \dfrac{50}{20}\) M1dep oe with common denominators \(4\dfrac{1}{5}\) with 35 and 34 seen or \(4\dfrac{1}{5}\) with \(\dfrac{35}{20}\) and \(\dfrac{34}{20}\) seen A1 35 and 34 may be implied by the correct multiples of 35 and 34 dependent on the common denominator used oe with common denominators
Additional guidance Condone \(4\dfrac{1}{5}\) with \((2.5 - 0.75 =)\ 1.75\) and \((2.5 - 4.2 =)\ {-1.7}\) M1M1A1
Foundation November 2023 Paper 2 Q14 14 A golf club is organising a trip for 42 people.
The costs are shown in the table.
Minibus hire £450 per minibus Fuel £26 per minibus 1 game of golf £18.50 per person
Each minibus can hold 15 people.
Each person will play 2 games of golf.
The cost of the trip will be shared equally by the 42 people.
Work out the cost per person. [5 marks]
Mark scheme
Mark scheme Answer Mark Comments \(18.5(0) \times 2\) or 37 M1 implied by \(18.5(0) \times 84\) or 1554 \(42 \div 15\) or \(\dfrac{14}{5}\) or 2.8 or 3 M1 minibuses needed implied by \(3 \times 450\) or 1350 or \(3 \times 26\) or 78 \(450 \times\) their \(3 + 26 \times\) their 3 or \(1350 + 78\) or \(476 \times 3\) or 1428 M1dep oe dep on 2nd mark allow their 3 to be a decimal eg 2.8 1332.8 scores 2nd & 3rd marks 2982 or 2886.8 scores M3 their \(1428 \div 42 +\) their 37 or (their \(1428 + 42 \times\) their \(37) \div 42\) or \(2982 \div 42\) M1dep oe eg \((450 \times\) their \(3 + 26 \times\) their \(3 + 42 \times\) their \(37) \div 42\) dep on M3 71(.00) A1 SC4 52.50 SC3 52.5
Additional guidance Up to M4 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts Using 2.8 throughout gives an answer of 68.73(…) M4A0 Only 1 game of golf gives an answer of 52.50 SC4 \(1350 + 78\) may be seen embedded with an incorrect number of games of golf eg \((1350 + 78 + 37) \div 42\) M1M1M1M0
Foundation November 2023 Paper 3 Q14 14 Des delivers takeaways to houses A, B and C.
Scale : 1 cm represents 3 miles
Not drawn accurately
Des drives
from T to A and back
and
from T to B, then B to C, then C to T.
Des is paid
40p for each mile he drives
and
£1.35 for each house he delivers to.
How much is Des paid in total for this work? [4 marks]
Mark scheme
Mark scheme Answer Mark Comments Alternative method 1 \(0.6 + 0.6 + 1.3 + 0.8 + 1.7\) or 5 M1 oe condone one missing or incorrect distance their \(5 \times 3\) or 15 M1dep their \(15 \times 0.4(0) + 3 \times 1.35\) or \(6(.00) + 4.05\) M1dep oe working in pence their 15 can be a truncated or rounded up decimal 10.05 A1 SC2 6.05 Alternative method 2 \(0.6 \times 3\) or 1.8 or \(1.2 \times 3\) or 3.6 or \(1.3 \times 3\) or 3.9 or \(0.8 \times 3\) or 2.4 or \(1.7 \times 3\) or 5.1 M1 \(0.6 \times 3 + 0.6 \times 3 + 1.3 \times 3 + 0.8 \times 3 + 1.7 \times 3\) or \(1.8 + 1.8 + 3.9 + 2.4 + 5.1\) or 15 M1dep oe condone one missing or incorrect distance their \(15 \times 0.4(0) + 3 \times 1.35\) or \(6(.00) + 4.05\) M1dep oe working in pence their 15 can be a truncated or rounded up decimal 10.05 A1 SC2 6.05 Alternative method 3 \(0.6 \times 3\) or 1.8 or \(1.2 \times 3\) or 3.6 or \(1.3 \times 3\) or 3.9 or \(0.8 \times 3\) or 2.4 or \(1.7 \times 3\) or 5.1 M1 \(0.6 \times 3 \times 0.4\) or 0.72 or \(1.2 \times 3 \times 0.4\) or 1.44 or \(1.3 \times 3 \times 0.4\) or 1.56 or \(0.8 \times 3 \times 0.4\) or 0.96 or \(1.7 \times 3 \times 0.4\) or 2.04 M1dep oe working in pence \(0.6 \times 3 \times 0.4 \times 2 + 1.3 \times 3 \times 0.4 + 0.8 \times 3 \times 0.4 + 1.7 \times 3 \times 0.4 + 3 \times 1.35\) or \(0.72 \times 2 + 1.56 + 0.96 + 2.04 + 3 \times 1.35\) or \(6(.00) + 4.05\) M1dep oe working in pence condone one missing or incorrect distance 10.05 A1 SC2 6.05
Additional guidance Units must be consistent unless recovered All correct except for missing the return distance from A eg \(0.6 + 1.3 + 0.8 + 1.7\) or 4.4 \(4.4 \times 3 = 13.2\) \(13.2 \times 0.4 + 3 \times 1.35 = 9.33\) M1M1M1A0 Example using their 15 truncated or rounded up for each mile \(0.6 + 1.3 + 0.8 + 1.7\) or 4.4 \(4.4 \times 3 = 13.2\) \(13 \times 0.4 + 3 \times 1.35 = 9.25\) or \(14 \times 0.4 + 3 \times 1.35 = 9.65\) M1M1M1A0 \(3.6 + 3.9 + 5.1\) (BC missing) M1M1 \(3.9 + 2.4 + 5.1\) without further working (TA and AT missing) M1M0
Foundation November 2023 Paper 1 Q11 11 Last week, Erik worked for 10 hours.
He paid no tax and received £90
(a) This week, Erik works for 15 hours.
He assumes he will be paid at the same rate and pay no tax.
How much does he expect to receive this week? [3 marks]
(b) In fact,
this week , Erik
is paid an extra 50p per hour pays £8.90 tax.
What does this tell you about the amount he receives?
Tick one box.
It is less than he expected It is the same as he expected It is more than he expected Show working to support your answer. [2 marks]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments Alternative method 1 \(90 \div 10\) or 9 M1 oe their \(9 \times 15\) M1dep oe 135(.00) A1 Alternative method 2 \(15 \div 10\) or 1.5 or \(10 \div 15\) or \(\dfrac{2}{3}\) M1 oe \(90 \times\) their 1.5 or \(90 \div\) their \(\dfrac{2}{3}\) M1dep oe 135(.00) A1 Alternative method 3 \(90 \div (10 \div (15 - 10))\) or 45 M1 oe \(90 +\) their 45 or their \(45 \times 3\) M1dep oe 135(.00) A1
Additional guidance Allow one error in a build-up method
Mark scheme (b) Answer Mark Comments Alternative method 1: works out extra from hourly increase or totals (and compares to tax) \(15 \times (0.)50\) or \(15 \div 2\) or \(15 \times (\)their \(9 + 0.5) - 15 \times\) their 9 or \(142.5(0) -\) their 135 or 7.5(0) M1 oe may be working in pence or pounds It is less than he expected and 7.5(0) A1ft correct or ft their hourly rate and/or their answer in (a) Alternative method 2: works out actual amount (and compares to expected amount) \(15 \times (\)their \(9 + 0.5) - 8.9(0)\) or \(142.5(0) - 8.9(0)\) or 133.6(0) M1 oe may be working in pence or pounds Correct box ticked for comparison with their (a) and 133.6(0) A1ft correct or ft their hourly rate and/or their answer in (a)
Additional guidance It’s 1.40 less with 135 in (a) (with no box ticked) M1A1 Allow one error in a build-up method Ignore further work after correct answer seen
Foundation November 2023 Paper 3 Q10 10 Sanjit buys 1.75 kg of potatoes and 4 kg of leeks.
The total cost is £9.03
The potatoes cost 84p per kg
Work out the cost per kg of the leeks. [4 marks]
Mark scheme
Mark scheme Answer Mark Comments \(0.84 \times 1.75\) or 1.47 or \(84 \times 1.75\) or 147 M1 oe \(9.03 -\) their 1.47 or 7.56 or \(903 -\) their 147 or 756 M1 oe their \(1.47 \lt 9.03\) their \(147 \lt 903\) units must be consistent unless recovered their \(7.56 \div 4\) or their \(756 \div 4\) or 189 M1dep oe dep on 2nd M 1.89 A1
Additional guidance Up to M3 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts Accept 189 on answer line with £ crossed out and p(ence) added \(9.03 - 1.68 = 7.35\) M0M1 \(9.03 - 1.68\) and \(7.35 \div 4\) M0M1M1
Foundation November 2023 Paper 2 Q6 6 Complete the bank statement. [3 marks]
Date Description Credit (£) Debit (£) Balance (£) 01/11/2021 Starting balance 736.28 05/11/2021 Rent 450.00 14/11/2021 Refund 25.00 27/11/2021 Wages 1830.29
Mark scheme
Mark scheme Answer Mark Comments 286.28 B1 311.28 B1ft correct or ft their 286.28 + 25.00 2141.57 B1ft correct or ft their 311.28 + 1830.29
Additional guidance Mark the answer lines and ignore any numbers in the grey cells Ignore units 286.28 261.28 2091.57 B1 B0 B1ft 1186.28 1211.28 3041.57 B0 B1ft B1ft
Foundation November 2023 Paper 2 Q5 5 Work out \(\dfrac{9}{4}\) as a decimal. [1 mark]
Mark scheme
Mark scheme Foundation November 2023 Paper 1 Q4 4
(a) Here is a number line.
Which number is at A? [1 mark]
(b) Here is another number line.
Which number is at B? [1 mark]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments 1.25 B1 oe
Additional guidance Accept on number line but answer line takes precedence
Mark scheme (b) Answer Mark Comments \(-3400\) B1
Additional guidance Accept on number line but answer line takes precedence
Foundation November 2023 Paper 1 Q3 3 Write a number in the box to make the statement correct. [1 mark]
\(3.7 \;\lt\; \Box\)
Mark scheme
Mark scheme Answer Mark Comments any number greater than 3.7 B1
Foundation November 2023 Paper 1 Q1 1
(a) Write down the value of \(2^3\) [1 mark]
(b) Work out \(\quad 3.45 + 2.07 - 1.3\) [2 marks]
Mark scheme (a) Mark scheme (b)
Mark scheme (a) Answer Mark Comments 8 B1 accept \(2 \times 2 \times 2 = 8\)
Mark scheme (b) Answer Mark Comments \((3.45 + 2.07 =)\ 5.52\) or \((3.45 - 1.3 =)\ 2.15\) or \((2.07 - 1.3 =)\ 0.77\) B1 implied by correct answer 4.22 B1ft ft their \(5.52 - 1.3\) correctly evaluated or their \(2.15 + 2.07\) correctly evaluated or their \(0.77 + 3.45\) correctly evaluated SC1 6.82 or 0.08
Additional guidance SC1 arises from correctly adding all three values or from correctly subtracting the final two from the first
Foundation June 2017 Paper 1 Q9 9 Work out \(\quad 25.68 \div 12\) [2 marks]
Mark scheme
Mark scheme Answer Mark Comments Alternative method 1 2.14 B2 oe B1 answer of 2.1(……) except 2.14 B1 0.214 or 21.4 or 214 or 2140 Alternative method 2 Divides by 2, 2 and 3 in any order or divides by 3 and 4 in either order or divides by 2 and 6 in either order M1 oe Attempts at all divisions must be made using a valid method 2.14 A1 oe
Additional guidance \(25.68 \div 2 = 12.84\) \(25.68 \div 3 = 8.56\) \(25.68 \div 4 = 6.42\) \(25.68 \div 6 = 4.28\) Use of remainders is B0 eg \(\;25.68 \div 12 = 2\) remainder 1.68 B0B0 Do not accept rounding up to 26 or 30 or truncation to 25 eg \(\;26 \div 12 = 2.1666\ldots\) B0B0 \(2\dfrac{7}{50}\) (possibly from multiplying numerator and denominator by 1000 and cancelling the subsequent fraction) B2
Foundation June 2017 Paper 2 Q9 9 Complete the bank statement. [2 marks]
Date Description Credit (£) Debit (£) Balance (£) 13/12/2016 Starting balance 212.48 14/12/2016 Council tax 128.39 15/12/2016 Salary 856.21
Mark scheme
Mark scheme Answer Mark Comments Balance (£) 212.48 (£)84.09 (£)940.30
B2 Must be in correct boxes B1 (£)84.09 or (£)940.30 or (£)84.09p and (£)940.30p or B1ft for their 84.09 \(+\) 856.21
Additional guidance Date Description Credit (£) Debit (£) Balance (£) 13/12/2016 Starting balance 212.48 14/12/2016 Council tax 128.39 84.09 15/12/2016 Salary 856.21 940.30
B2 340.87 and 1197.08 B1ft 340.87 and 1197.08p B0ft 84.09 and 940.3 B1 Ignore any working in grey boxes 84.09p and 940.30p B1 £84.09p and £940.30p B1 84.09p and 940.3(p) B0
Foundation June 2017 Paper 2 Q3 3 What is \(\dfrac{3}{2}\) as a decimal?
Circle your answer. [1 mark]
Mark scheme
Mark scheme Foundation June 2017 Paper 1 Q2 2 Work out \(\quad \dfrac{1}{4} + 0.5\)
Circle your answer. [1 mark]
Mark scheme
Mark scheme No questions match these filters.