OCR GCSE Maths
Topic questions Number Systematic listing and the product rule for counting
26 questions · 107 marks · about 1.5 hours
Also involves Factors, multiples and primes
Sasha creates a four-digit passcode.
They use four digits from 0 to 9. They do not use any digit more than once.
Work out how many of the possible four-digit passcodes are even.
Also involves Fractions
An app’s passcode consists of three digits. Each of the digits is a number from 0 to 9. A digit can be used more than once.
Find the fraction of the possible passcodes that contain at least one 5.
Also involves Fractions
A play group offers four activities to their children.
Baking (B) Drawing (D) Exercise (E) Reading (R)
Complete the list below to show all the possible combinations of two different activities. You may not need all the answer lines.
Write down the fraction of the combinations that include Reading (R).
Kai has these four number cards.
Kai takes two of the cards at random without replacement and finds the positive difference between the two numbers.
Complete the table to show all of the possible differences.
Find the probability that Kai takes two cards with a difference that is an even number or a factor of 10.
Kai has these four number cards.
Kai takes two of the cards at random without replacement and finds the positive difference between the two numbers.
Complete the table to show all of the possible differences.
Find the probability that Kai takes two cards with a difference that is an even number or a factor of 10.
A restaurant menu has 4 main courses and 3 side dishes. For their meal, each customer chooses 1 main course and 1 side dish.
Work out the percentage of possible meals that cost less than £8.
A restaurant menu has 4 main courses and 3 side dishes. For their meal, each customer chooses 1 main course and 1 side dish.
Work out the percentage of possible meals that cost less than £8.
Sasha is trying to remember a 4-digit pin number. Sasha knows it has the following digits and that the first digit is 9.
Write down all of the possible orders for Sasha’s 4-digit pin number.
Sasha tries one of these orders at random.
Write down the probability that the last digit of the pin number that Sasha tries is 2.
Also involves Fractions
A college offers 41 different subjects including 9 different languages. Students are asked to choose one subject from Option A, one subject from Option B and one subject from Option C.
Each of the 41 different subjects appears only once, either in Option A, or in Option B or in Option C.
Option A: 14 subjects including 2 languages Option B: 12 subjects including 3 languages Option C: 15 subjects including 4 languages
Work out the proportion of all the possible subject combinations that include at least one language. You must show your working.
Also involves Fractions
A meal deal consists of a burger, a side dish and a drink chosen from these lists.
Burgers
Side dish
Drink Hamburger (H) Baked beans (B) Cola (C) Veggie burger (V) Fries (F)
Lemonade (L) Sweetcorn (S)
Some of the possible meal deals are shown in this table.
Complete the table to show all the possible meal deals. You may not need all the rows.
Write down the fraction of the meal deals that include baked beans (B).
Mrs Sweet has 8 different milk chocolates and 9 different plain chocolates.
Her daughter chooses one of the milk chocolates. Her son then chooses one of the plain chocolates. Mrs Sweet then chooses one of the remaining chocolates.
Work out how many different combinations of three chocolates they can choose.
Also involves Fractions
Here is a restaurant’s menu.
A 3-course meal consists of one starter, one main and one dessert.
Work out how many different 3-course meals can be chosen from the menu.
Find the fraction of the 3-course meals which are completely vegetarian (V).
Also involves Powers and roots · Using a calculator
A car registration plate has two letters, a number from 10–99 and three letters. For example:
The letters I and O are not used, leaving 24 possible letters.
Show that there are approximately 720 million possible car registration plates of this form.
Ali (A), Blake (B), Rowan (R) and Sam (S) are in a relay team. Sam always runs fourth in the team. The order for the other three is chosen at random.
Complete this table to show all the possible orders for the team. The first row has been completed for you. You may not need to use all the rows.
Find the probability that Ali will run first.
Nada is planning the colour scheme for her bedroom.
The colour of her carpet can be blue (B), grey (G) or red (R). The walls can be painted yellow (Y), white (W) or pink (P).
Complete the table to show all of the possible colour combinations she can make. You may not need all the rows.
Explain why it would not be mathematically correct to find the probability that Nada decides on a grey carpet and pink walls using this formula.
the total number of colour combinations
Also involves Converting between units
A transport lorry consists of a cab and a trailer. The trailer has a volume of 90 m3. Alfie makes a model of this lorry using a scale of 1: 72.
Work out the volume of the trailer in Alfie’s model, giving your answer in cm3.
Alfie paints his model lorry. He has eight colours available.
He decides to paint the cab in one colour and the trailer in a different colour.
He then wants to paint his name on the trailer. The name must be in a different colour to the trailer.
In how many different ways can Alfie paint his model lorry?
Also involves Percentages
The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English.
| Mathematics | English |
| Alice | Alice |
| Ben | Claire |
| Emma | Gabi |
| Paddy | Simon |
The winner of each subject prize is picked at random. It is possible for Alice to win both prizes.
In what percentage of the combinations of prize winners does Alice win at least one prize?
Lev (L), Maria (M) and Nicholas (N) sit in a row of three seats.
Use the table to list all the different orders in which they could sit. One possible order is already shown in the table. You may not need to use all the rows in the table.
All possible orders in which they could sit are equally likely.
What is the probability that Lev (L) sits next to Maria (M)?
Also involves The four operations
Megan’s Cafe sells ice cream. Customers choose to have a tub or a cone, and a wafer or no wafer. They can choose vanilla, lemon or chocolate ice cream.
This frequency tree shows the number of people making some of the choices.
Anaya buys an ice cream.
One choice she can make is
a cone, no wafer and vanilla.
How many different choices can she make?
Complete the frequency tree.
Which flavour of ice cream was most popular? Show how you decide.
Also involves Fractions
Danisha is going to visit two of these places.
London Eye (LE) Buckingham Palace (BP) Tower of London (TL) British Museum (BM)
List all the combinations of these places that she can visit. One combination is already shown in the table. You may not need all the rows.
What fraction of the combinations include the London Eye (LE)?
Frances has three cards: Ace (A), King (K) and Queen (Q). She shuffles these cards and deals them one at a time.
List all the different orders in which she can deal the cards. One possible order is already shown in the table. You may not need to use all the rows.
Find the probability that, in the three cards Frances deals, the King (K) is dealt immediately after the Queen (Q).
A counter has 3 on one side and 5 on the other. Lena flips the counter. She then picks one of these three cards at random.
Lena puts the card next to the counter and works out the answer.
For example 5 × 2 gives the answer 10.
Find the probability that Lena gets an answer less than 8. You must show your working.
A menu has
• 6 starters
• 10 main dishes
• 7 desserts.
A three-course meal consists of a starter, a main dish and a dessert.
How many different three-course meals are possible?
A two-course meal consists either of a starter with a main dish, a starter with a dessert or a main dish with a dessert.
Show that there are 172 possible different two-course meals.
Diners choose one starter and one main from the options given in the table below. Vegetarian dishes are indicated with a (v).
| Starter | Main |
| Cheese salad (v) | Steak and chips |
| Prawn cocktail | Fish and chips |
| Mozzarella sticks (v) | Tomato pizza (v) |
| Pork chops | |
| Nut cutlet (v) |
Work out the fraction of all the meal combinations which have at least one vegetarian option.
Diners also choose one of 6 dessert options.
How many different three-course meal combinations are available?
Also involves Forming and solving equations
There are 20 coins in a pot. The coins are 1p, 2p, 5p and 10p.
A coin is taken at random from the pot.
• The probability that it is a 1p coin is 
• The probability that it is a 2p coin is 
The total value of the coins in the pot is 57 pence.
Work out how many of each type of coin there are in the pot.
1p........, 2p........, 5p........, 10p........
Students at a school must choose one subject from Option 1 and one from Option 2. The school offers two languages, French and Spanish.
The subjects are given in this table.
| Option 1 | Option 2 |
| French | Spanish |
| Art | Geography |
| Music | History |
| Economics |
Work out the percentage of all the subject combinations which have exactly one language.
John has
• 8 different shirts
• 6 different hats
• 4 different scarves.
On Monday, he picks a shirt, a hat and a scarf.
Show that there are 192 different combinations he can pick.
John thinks that if he picks just two of the three items of clothing there will be more than 192 combinations.
Is he correct? Show your reasoning.
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
Mum 💖
did you do your maths homework sweetie?? 🥰
yes I solved for x
proud of you!!!
📱 Screen time this week · TikTok6h 7m
Maths starter pack