A market stall sells jam in 5 flavours (strawberry, raspberry, blackcurrant, apricot, plum) and jars in 2 sizes (small, large). A customer buys one jar of jam. List all the different flavour-and-size combinations that the customer could buy.
(Total for Question 1 is 2 marks)
2
Priya spins a fair spinner with three equal sections labelled A, B and C, and rolls a fair four-sided dice numbered 1 to 4. List all the possible outcomes.
(Total for Question 2 is 2 marks)
3
Using the digits 1, 4 and 7, list all the two-digit numbers greater than 40 that can be made. Each digit may be used only once in each number.
(Total for Question 3 is 2 marks)
4
Erin lists the possible starter-and-main combinations at a cafe, where a customer chooses 1 of 2 starters (soup, salad) and 1 of 3 mains (pasta, curry, fish), as: soup+pasta, soup+curry, salad+pasta, salad+fish. Give one reason why Erin's list is not a correct systematic list of all the possible combinations.
(Total for Question 4 is 1 mark)
5
A charity bake sale sells cupcakes in 2 flavours (vanilla, chocolate) and 2 icing colours (pink, white).
(a)List all the different flavour-and-icing combinations that could be made.(2)
(b)Write down the total number of different cupcakes possible.(1)
(Total for Question 5 is 3 marks)
6
Two fair spinners are spun together. Spinner P has three equal sections numbered 1, 2 and 3. Spinner Q has three equal sections numbered 2, 4 and 6. The two numbers shown are multiplied together to give a score.
(a)Complete the sample space diagram to show all 9 possible scores.(2)
(b)Use your diagram to find the probability that the score is greater than 10.(2)
(Total for Question 6 is 4 marks)
7
A padlock uses a 2-letter code chosen from the letters V, W, X, Y and Z. No letter is repeated in a code.
(a)List all the possible codes.(2)
(b)Write down the total number of different codes possible.(1)
(Total for Question 7 is 3 marks)
8
A phone case shop sells cases in 4 colours (black, white, red, blue) and 2 finishes (matte, glossy). A customer buys one case.
(a)List all the different colour-and-finish combinations possible.(2)
(b)Nadia says you do not need to list every combination to find the total number possible. Use multiplication to work out the total number of combinations.(2)
(Total for Question 8 is 4 marks)
9
A cafe sells jacket potatoes with a choice of 3 fillings (cheese, beans, tuna) and 2 sizes (regular, large). A table showing some of the possible combinations has been started below, but is not yet complete.
(a)Complete the table to show all 6 possible size-and-filling combinations.(2)
(b)Write down the total number of different jacket potatoes possible.(1)
(Total for Question 9 is 3 marks)
10
Four different books - a maths book (M), an atlas (A), a dictionary (D) and a thesaurus (T) - are placed in a row on a shelf. Show that there are 24 different possible orders in which the four books could be arranged.
(Total for Question 10 is 2 marks)
11
A furniture shop sells armchairs in 5 different fabrics and 3 different colours. A customer chooses one fabric and one colour. Without listing them, work out the total number of different armchairs possible.
(Total for Question 11 is 2 marks)
12
A birthday card shop lets a customer choose 1 of 5 card designs, 1 of 3 envelope colours and 1 of 2 ribbon styles. Work out the total number of different card packages possible.
(Total for Question 12 is 2 marks)
13
A voucher code uses 3 characters, each chosen from the letters A, B and C. A letter may be used more than once in a code. Work out the total number of different voucher codes possible.
(Total for Question 13 is 2 marks)
14
A garden centre sells plant pots in 4 sizes (small, medium, large, extra-large) and 3 colours (terracotta, grey, white).
(a)List all the different size-and-colour combinations possible.(2)
(b)A pot is chosen at random from all the possibilities in part (a). Find the probability that it is a large, grey pot.(2)
(Total for Question 14 is 4 marks)
15
A box contains 4 counters, numbered 1, 2, 3 and 4. Two counters are drawn from the box one after another, without replacement, and the two numbers are added together to give a total.
(a)List all the possible pairs of counters that could be drawn, showing which counter is drawn first each time.(2)
(b)Use your list to find the probability that the total of the two counters drawn is 5.(2)
(Total for Question 15 is 4 marks)
16
A sticker book lets a child choose 1 of 6 animal stickers and 1 of 4 sticker borders. Work out the total number of different animal-and-border stickers possible.
(Total for Question 16 is 2 marks)
17
Yusuf wants to make exactly 45p using only 20p, 10p and 5p coins. He may use more than one of each coin, or none of some of them. List all the different ways he could make exactly 45p, showing the number of each coin used each time.
(Total for Question 17 is 3 marks)
18
A gate code is 4 digits long, using 4 different digits chosen from 1, 2, 3, 4, 5 and 6. The order of the digits matters and no digit is repeated. Without listing them, work out the total number of different gate codes possible.
(Total for Question 18 is 2 marks)
19
Amelia has 3 different ornaments: a vase (V), a candle (C) and a photo frame (F). She chooses 2 of the ornaments and places them in order on a windowsill, so the order matters (for example, VC is different from CV). List all the different possible arrangements of 2 ornaments, and state the total number of arrangements.
(Total for Question 19 is 3 marks)
20
A garden design app lets a user choose 1 of 5 patio styles, 1 of 4 planting themes and 1 of 2 fence types. The pergola fence type cannot be chosen together with the wildflower planting theme. Work out the total number of different garden designs possible.
(Total for Question 20 is 3 marks)
Mark scheme · 2.3B Systematic Listing (Part 2)
Question 1
B1 systematic list or table shown, at least 6 correct combinations
B1 all 10 combinations listed with no repeats or omissions