Systematic Listing
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Either paper Higher3 marks
Dev is choosing one filling and one type of bread at a sandwich shop.
The filling can be chicken, cheese or falafel.
The type of bread can be white or brown.
(a)List all the possible combinations he could choose.
(b)Dev decides to add a sauce as well. There are 6 different sauces to choose from.
How many different combinations are possible now?
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Either paper 2 marks
A sandwich has three different fillings. The fillings are chosen from
- egg (e) - tuna (t) - cheese (c) - ham (h)
List all the possible options for the three fillings.
One option has been done for you: \(e c h\)
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Either paper Higher3 marksHere are three cards. Each card has one digit written on it.
5 6 7 (a)Each card is used once to make a three-digit number.
Write down all the three-digit numbers that can be made, starting with the smallest.
(b)A different set of 3 cards is used, each showing a different digit. This time a card may be used more than once, so a digit can be repeated.
How many different three-digit numbers can be made from that set?
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Either paper Higher4 marks
Isla, Jack, Kaya and Liam are in a group.
(a)Two of them are chosen to hand out the prizes.
List all the possible pairs that could be chosen.
(b)A larger group of 7 people is asked instead. One of them is chosen to be head student and a different one is chosen to be deputy head student.
Work out how many different ways this can be done.
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Either paper 4 marks
Here are four cards. Each card shows a digit.
\(3,\ 6,\ 5,\ 9\)
Grace chooses two of the cards and puts them side by side to make a two-digit number.
(a)Calculate how many different two-digit numbers she can make.
(b)List all the even two-digit numbers she can make.
(c)State the largest two-digit number she can make.
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Either paper 3 marksHere are the subjects available in Year 12 at a school.
Students choose three subjects. They cannot choose more than one subject from a block. Omar decides to study Art. Omar decides not to study any of these subjects:Block 1 Block 2 Block 3 Block 4 Maths English History French Geography Physics Biology Drama Music Spanish Art Chemistry - Maths
- Geography
- French
- Drama
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Either paper 3 marks
Use each of the whole numbers 2 to 13 once, writing one in each box, so that the four calculations are correct.
\(\square + \square + \square = 36\)
\(\square + \square + \square = 26\)
\(\square + \square + \square = 10\)
\(\square + \square + \square = 18\)
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Either paper 3 marksThe numbers 1 to 12 are put in a grid. Six of the numbers are shown. The letters A to F stand for the six numbers that are missing.
Each of the four sides of the grid must add up to 27. Complete the grid using the numbers 1, 3, 4, 6, 11, 12. Use each of them once, and give the number that each letter stands for.2 A 10 B 8 C D 9 E F 7 5 -
Either paper 6 marks
A shop sells ice creams. Each ice cream has two scoops.
The flavours are chocolate (c), strawberry (s), banana (b) and pistachio (p).
The two scoops can be the same flavour or different flavours.
(a)List all the possible options for the two scoops. The order of the scoops does not matter.
One option, sb, has been written in for you.
(b) In one day the shop sells 576 scoops of ice cream. The table shows the number of scoops of each flavour.
A pie chart is to be drawn to show the data. Work out the angle, in degrees, that stands for one scoop.Flavour Number of scoops Chocolate 80 Strawberry 112 Banana 160 Pistachio 224 (c)The sector for chocolate has been drawn. The marks round the circle are \(10^\circ\) apart.
Complete the pie chart to show the data in the table in part (b).
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Either paper 2 marks
Anya has six coins.
The value of each coin is 2p, 5p or 10p.
She can make 22p using three of the coins.
She can make 30p using four of the coins.
She cannot make 9p using any three of the coins.
She cannot make 32p using any four of the coins.
List the values of the six coins.
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(a) chicken and white, chicken and brown, cheese and white, cheese and brown, falafel and white, falafel and brown
(b) \(36\) - \(t c h\), \(e c h\), \(e t h\), \(e t c\), in any order
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(a) \(567,\ 576,\ 657,\ 675,\ 756,\ 765\)
(b) \(27\) -
(a) Isla and Jack, Isla and Kaya, Isla and Liam, Jack and Kaya, Jack and Liam, Kaya and Liam
(b) \(42\) -
(a) \(12\)
(b) \(36,\ 56,\ 96\)
(c) \(96\) -
Subject 1 Subject 2 Subject 3 Art Music English Art Music Physics Art Music Spanish Art Music Chemistry Art English Chemistry Art Physics Chemistry Art Spanish Chemistry - \(11 + 12 + 13 = 36\); \(7 + 9 + 10 = 26\); \(2 + 3 + 5 = 10\); \(4 + 6 + 8 = 18\) (the three numbers in each calculation may be in any order)
- A = 3, B = 12, C = 1, D = 6, E = 11, F = 4
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(a) all 10 options, in any order and either way round: cc, cs, cb, cp, ss, sb, sp, bb, bp, pp
(b) \(0.625\)
(c) Sectors of \(70^\circ\) for strawberry, \(100^\circ\) for banana and \(140^\circ\) for pistachio, in any order round the chart(c) - 2p, 5p, 5p, 5p, 10p, 10p (in any order)
Takes a couple of seconds the first time a sheet is made.