Systematic Listing: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

14 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 5)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

GCSE · Counting

2.3DB Systematic Listing: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A cafe lunch deal lets you choose one sandwich from 4 types (cheese, ham, tuna, egg) and one drink from 3 types (water, juice, tea). Work out how many different lunch deals are possible.

(Total for Question 1 is 1 mark)

A boutique sells jackets in two colours (Blue, Red) and hats in three styles (Cap, Beanie, Bobble). Two of the six possible jacket-and-hat combinations are already known: Blue Cap and Red Bobble. Using a table with jacket colour as rows and hat style as columns, complete the table to show the remaining four combinations, then state the total number of different outfits possible.

(Total for Question 2 is 2 marks)

Four charity bake-sale items, a flapjack, a brownie, a cookie and a muffin, are to be arranged in a row on a shelf. Work out how many different arrangements are possible.

(Total for Question 3 is 2 marks)

Two fair four-sided spinners are each numbered 1 to 4. Both spinners are spun once. List all the possible ordered outcomes (first spinner, second spinner) for which the difference between the two numbers is exactly 2.

(Total for Question 4 is 3 marks)

A school ID badge shows one shape chosen from circle, square, triangle and star, together with one colour chosen from red, green and blue. Work out how many different badges can be made in which the shape is not a star.

(Total for Question 5 is 2 marks)

A drama club has 9 members. Two of the members are to be chosen to perform a duet at the end-of-term show. The order in which they are chosen does not matter. Work out how many different pairs of performers could be chosen.

(Total for Question 6 is 2 marks)

A sandwich shop lets customers choose 2 fillings for a sandwich from cheese, ham, tuna and egg. The same filling may be chosen twice (a double portion), and the order in which the fillings are chosen does not matter. Work out how many different sandwiches are possible.

(Total for Question 7 is 2 marks)

A padlock code is made from 3 digits, each chosen from 0 to 9. Digits may be repeated. Work out how many different codes are possible.

(Total for Question 8 is 2 marks)

In a school choir competition, gold, silver and bronze medals are awarded in order to 3 of the 8 semi-finalists. Work out how many different ways the three medals could be awarded.

(Total for Question 9 is 2 marks)

Using the digits 3, 4, 5 and 7, each digit used at most once within a number, list all the two-digit numbers greater than 40 that can be formed, then state how many there are.

(Total for Question 10 is 2 marks)

Zara was asked to list all the ways to choose 2 different toppings for a pizza from mushroom (M), pepper (P), onion (O) and olives (L), where the order the toppings are chosen in does not matter. Her working is shown below:

MP, MO, ML, PM, PO, PL, OM, OL, OM, LM

She has concluded there are 10 different pizzas. Explain what is wrong with Zara's list, and work out the correct number of different pizzas.

(Total for Question 11 is 2 marks)

A vending machine sells a hot drink: first you choose Tea or Coffee, then you choose Whole milk, Semi-skimmed milk or None. Part of the tree diagram is shown: the Tea branch splits into three further branches (Whole, Semi-skimmed, None), but the branches after Coffee are missing.

Figure (to be drawn): A two-stage tree diagram. Stage 1 has two branches from a single starting point, labelled 'Tea' and 'Coffee'. From the end of the 'Tea' branch, three further branches are drawn and labelled 'Whole', 'Semi-skimmed' and 'None'. From the end of the 'Coffee' branch, no further branches are drawn; this is the part the student must complete.

(a)Copy and complete the tree diagram by adding the three missing branches after Coffee, labelled correctly.(1)

(b)Use the completed tree diagram to work out the total number of different drink orders possible.(1)

(Total for Question 12 is 2 marks)

A cafe lunch deal lets a customer choose one main course from soup, sandwich, salad and jacket potato, and one drink from juice, tea, coffee, water and hot chocolate.

(a)Work out the total number of different lunch deals possible.(1)

(b)Kwame will not choose soup, and will not choose hot chocolate. Work out how many different lunch deals Kwame could choose.(2)

(c)The cafe advertises 'over 15 different lunch deals available'. Using your answer to part (a), determine whether this claim is correct. Give a reason.(1)

(Total for Question 13 is 4 marks)

A quiz team of 4 people is to be chosen from a group of 5 women and 3 men, so that the team contains exactly 2 women and 2 men. Work out how many different teams are possible.

(Total for Question 14 is 4 marks)

Mark scheme · 2.3DB Systematic Listing: Fluency and Exam Drill (Part 2)

Question 1

B1 12 cao
Answer: 12

Question 2

M1 all four missing combinations correctly identified: Blue Beanie, Blue Bobble, Red Cap, Red Beanie oe
A1 6 cao
Answer: Blue Beanie, Blue Bobble, Red Cap, Red Beanie; total 6

Question 3

M1 recognise 4 choices for the first position, 3 for the second, 2 for the third and 1 for the last, 4*3*2*1 oe
A1 24 cao
Answer: 24

Question 4

M1 at least two correct ordered pairs identified systematically, e.g. (1,3),(2,4)
M1 remaining correct ordered pairs identified systematically, e.g. (3,1),(4,2)
A1 all four ordered pairs listed: (1,3),(3,1),(2,4),(4,2) cao, no extras
Answer: (1,3), (3,1), (2,4), (4,2)

Question 5

M1 identify 3 allowed shapes (excluding star) and multiply by 3 colours, 3*3 oe
A1 9 cao
Answer: 9

Question 6

M1 use combinations, C(9,2) = 9*8 / 2*1 oe
A1 36 cao
Answer: 36

Question 7

M1 use combinations with repetition, C(4+2-1,2) or (4*5)/2 oe
A1 10 cao
Answer: 10

Question 8

M1 recognise 10 choices for each of 3 positions and set up 10³ oe
A1 1000 cao
Answer: 1000

Question 9

M1 recognise 8 choices for gold, 7 for silver, 6 for bronze and multiply, 8*7*6 oe
A1 336 cao
Answer: 336

Question 10

M1 systematic listing by tens digit (4_, 5_, 7_) showing at least 5 correct numbers oe
A1 all nine numbers listed: 43, 45, 47, 53, 54, 57, 73, 74, 75 cao, 9 stated
Answer: 43, 45, 47, 53, 54, 57, 73, 74, 75 (9 numbers)

Question 11

C1 identify that order does not matter, so a pair and its reverse (e.g. MP and PM, or MO and OM) represent the same pizza and should not both be counted, oe; and/or identify that OM has been written twice (an exact repeat)
B1 6 cao
Answer: 6 different pizzas (Zara double-counted each pair in reverse order and also repeated OM)

Question 12

(a) B1 three branches added after Coffee, correctly labelled Whole, Semi-skimmed and None oe
(a) Answer: Coffee branches to Whole, Semi-skimmed, None
(b) B1 6 cao
(b) Answer: 6

Question 13

(a) B1 20 cao
(a) Answer: 20
(b) M1 3 remaining mains x 4 remaining drinks, 3*4 oe
(b) A1 12 cao
(b) Answer: 12
(c) C1 correct conclusion with reason, e.g. 'True, since 20 is greater than 15' ft from (a)
(c) Answer: True: 20 > 15

Question 14

M1 use combinations to choose 2 women from 5, C(5,2) = 5*4 / 2*1 oe
A1 10 seen
M1 use combinations to choose 2 men from 3, C(3,2) = 3*2 / 2*1 oe, and multiply the two results together
A1 30 cao
Answer: 30

Mark my answers

Systematic Listing: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

More on this topic

Next in this strand

2.3DB Systematic Listing: Fluency and Exam Drill (Part 2)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Mark your answers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14