About Patterns & Functions — Class 7 IB

Identify functional relationships from tables and graphs; introduce input-output models. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 10). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Patterns & Functions

• Uncovering the Magic of Patterns
• Input-Output Machines: The Heart of Functions
• Finding the $n^{th}$ Term: Predicting the Future
• Visualizing Functions: Tables and Graphs
• Linear Patterns: Straight Lines and Constant Change

Interactive lesson · about 15 minutes · checkpoint question after every unit

Patterns & Functions — solved examples for Class 7 IB

Practice questions on Patterns & Functions

1. Q1.easy

   A student, Clara, claims that the rule for the sequence 2, 5, 8, 11, ... is 'multiply the term number by 3, then subtract 1'. Which statement about Clara's rule is true?

   1. A)Clara's rule is correct for all terms.
   2. B)Clara's rule is incorrect because it doesn't work for the first term.
   3. C)Clara's rule is incorrect because it doesn't work for the second term.
   4. D)Clara's rule is incorrect because it doesn't work for the third term.
   Show answer

   Answer: Clara's rule is correct for all terms.

   Hint: Test Clara's rule with the first few terms of the sequence to see if it holds true for each one.

2. Q2.easy

   A linear pattern starts with 6 and increases by 4 each time. What is the 5th term in this pattern?

   1. A)18
   2. B)22
   3. C)26
   4. D)30
   Show answer

   Answer: 22

   Hint: Write out the first few terms of the sequence by repeatedly adding the common difference.

3. Q3.easy

   A small café in Paris charges for coffee based on the number of sugar packets requested. The table below shows the cost (C) in Euros (€) for different numbers of sugar packets (S). If the pattern continues, what is the cost for 4 sugar packets?

   1. A)€2.60
   2. B)€2.70
   3. C)€2.80
   4. D)€2.90
   Show answer

   Answer: €2.80

   Hint: Look for a consistent change in cost as the number of sugar packets increases. This will help you find the rule.

4. Q4.medium

   Consider the sequence of numbers: 6, 11, 16, 21, ... Which expression represents the nth term of this sequence?

   1. A)n + 5
   2. B)5n + 1
   3. C)5n - 1
   4. D)n + 1
   Show answer

   Answer: 5n + 1

   Hint: Determine the common difference first. This will help you find the 'n' term. Then adjust for the first term.

5. Q5.medium

   An input-output machine follows the rule: 'Multiply the input by 3, then subtract 2'. If the input is 9, what is the output?

   1. A)25
   2. B)27
   3. C)29
   4. D)31
   Show answer

   Answer: 25

   Hint: Follow the operations in the rule exactly, step by step, applying them to the given input value.

6. Q6.medium

   A scientist is tracking the growth of a special type of crystal. She records its height (h) in mm over several hours (t). The relationship is linear. Complete the table below for t = 4 hours and determine the rule relating h to t.
   
   | t (hours) | h (mm) |
   |-----------|--------|
   | 0 | 5 |
   | 1 | 8 |
   | 2 | 11 |
   | 3 | 14 |
   | 4 | ? |
   
   Which option correctly provides the missing height and the rule?

   1. A)h = 3t + 5; height at 4 hours = 17 mm
   2. B)h = 3t + 5; height at 4 hours = 19 mm
   3. C)h = t + 5; height at 4 hours = 9 mm
   4. D)h = 5t + 3; height at 4 hours = 23 mm
   Show answer

   Answer: h = 3t + 5; height at 4 hours = 17 mm

   Hint: First, find the common difference in the height values for each hour. This will help you find the 't' part of the rule and the next term.

7. Q7.hard

   A historical clock tower in Prague chimes once at 1:00 PM, three times at 2:00 PM, five times at 3:00 PM, and so on. If this pattern continues, how many times will the clock chime at 9:00 PM?

   1. A)15
   2. B)17
   3. C)19
   4. D)21
   Show answer

   Answer: 17

   Hint: Identify the sequence of chimes for each hour and find a general rule (nth term) that relates the hour (n) to the number of chimes.

8. Q8.hard

   A scientist records the growth of a special plant in a laboratory. The table shows the plant's height (H, in cm) at different times (T, in days).
   
   | Time (T) | Height (H) |
   | :------: | :--------: |
   | 0 | 3 |
   | 2 | 4 |
   | 4 | 5 |
   | 6 | 6 |
   
   Which rule describes the relationship between H and T?

   1. A)H = T + 3
   2. B)H = 2T + 3
   3. C)H = 0.5T + 3
   4. D)H = T + 2
   Show answer

   Answer: H = 0.5T + 3

   Hint: Calculate the rate of change in height for each unit increase in time. The height at T=0 is the starting value for the linear relationship.

9. Q9.hard

   An input-output machine takes an input number, performs two operations, and gives an output. When the input is 5, the output is 23. When the input is 8, the output is 35. The first operation is 'multiply by 4'. What is the second operation?

   1. A)Add 3
   2. B)Subtract 3
   3. C)Add 5
   4. D)Subtract 5
   Show answer

   Answer: Add 3

   Hint: Apply the first known operation ('multiply by 4') to both given inputs. Then, determine what operation is needed to get from the result of the first step to the final output for each case.

These are 9 of the 59 questions available for Patterns & Functions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.