Patterns, Sequences & Algebraic Thinking — Free IB MYP1 Mathematics Questions

1QuestionCalculating Common RatiosConcept Practice

5 marks~8 minCriterion C

Look at this number sequence:

3, \ 6, \ 12, \ 24

a

Identify the common ratio of this sequence. [1]

b

Calculate the ratio between each pair of consecutive terms. Show all three divisions. [2]

c

A student says the common ratio is

8

because

24 \div 3 = 8

. Describe what this student did wrong and explain how the common ratio should be found. [2]

Solutions

2QuestionCalculating Common RatiosConcept Practice

2 marks~3 minCriterion A

Three squares are shown with side lengths of 2 cm, 4 cm, and 8 cm.

a

Identify the common ratio of this sequence of side lengths. [1]

b

Calculate the side length of the next square in the sequence. [1]

Solutions

3QuestionComparing Arithmetic and Geometric SequencesConcept Practice

2 marks~3 minCriterion B

Squares have side lengths of 1 cm, 2 cm, 3 cm, and 4 cm. The perimeter of each square is found using

P = 4 \times \text{side length}

.

Side length (cm)	1	2	3	4
Perimeter (cm)	4	8	12	16

a

State the next perimeter in the sequence. [1]

b

Identify whether the sequence of perimeters is arithmetic or geometric. Give one reason for your answer. [1]

Solutions

4QuestionIntroduction to Arithmetic SequencesConcept Practice

2 marks~3 minCriterion D

Mia saves 2 dollars every week. She starts with 5 dollars in her piggy bank. The amounts each week form a sequence:

Week 1: 7 dollars, Week 2: 9 dollars, Week 3: 11 dollars, Week 4: 13 dollars

a

State how much money Mia will have after Week 6. [1]

b

Describe one reason why this sequence might not match Mia's real savings over time. [1]

Solutions

5QuestionFinding nth Term Formula for Arithmetic SequencesConcept Practice

2 marks~3 minCriterion B

A shop sells candles in boxes. The table shows the total number of candles for different numbers of boxes.

Number of boxes $n$	1	2	3	4
Total candles	5	8	11	14

a

State the common difference of this sequence. [1]

b

Write the formula for the

n

th term in the form

an + b

. [1]

Solutions

6QuestionEvaluating Terms Using nth Term RuleConcept Practice

2 marks~3 minCriterion C

A sequence starts: 3, 5, 7, 9, …

The

n

th term rule for this sequence is

2n + 1

.

a

State what the letter

n

stands for in an

n

th term rule. [1]

b

Describe how you would use the rule

2n + 1

to find the 10th term of this sequence. [1]

Solutions

7QuestionEvaluating Terms Using nth Term RuleConcept Practice

2 marks~3 minCriterion A

A pattern of squares grows as shown in the diagram.

Term 1: 1 square — Term 2: 4 squares — Term 3: 9 squares

The

n

th term is given by

n^2

.

Calculate the number of squares in the 5th term. [2]

Solutions

8QuestionAnalyzing and Explaining Real-World PatternsConcept Practice

2 marks~3 minCriterion A

The diagram shows triangle

ABC

with side

BC

extended to point

D

.

a

Name angle

ACD

. [1]

b

Describe where angle

ACD

is in relation to the triangle. [1]

Solutions

9QuestionPatterns in Nature and ArchitectureConcept Practice

2 marks~3 minCriterion D

Daisies often have 13 or 21 petals, sunflowers often have 55, and pinecones often have 8 spirals. All of these numbers appear in the Fibonacci sequence, where each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …

a

Identify one example of the Fibonacci pattern found in a plant. [1]

b

Describe one way this pattern helps the plant to survive or grow. [1]

Solutions

10QuestionAnalyzing and Explaining Real-World PatternsConcept Practice

3 marks~5 minCriterion B

Each pattern in a sequence is made of dots arranged in a square.

Pattern 1:

1 \times 1

(1 dot). Pattern 2:

2 \times 2

(4 dots). Pattern 3:

3 \times 3

(9 dots).

a

Identify the number of dots in Pattern 4. [1]

b

State the number of dots in Pattern 10. [1]

c

Describe how you can find the number of dots in any pattern in this sequence. [1]

Solutions

11QuestionCreating Expressions from PatternsConcept Practice

2 marks~3 minCriterion B

The table shows the number of small squares in square grids of different sizes.

Side length	1	2	3
Number of small squares	1	4	9

a

Identify the pattern shown in the table. [1]

b

Write an expression for the number of small squares in an

n \times n

grid. [1]

Solutions

12QuestionEvaluating Expressions Derived from PatternsConcept Practice

2 marks~3 minCriterion A

The number of matchsticks needed to build

n

squares in a row is given by

3n + 1

.

Calculate the number of matchsticks needed to build 5 squares. [2]

Solutions

13QuestionIdentifying Patterns in Number SeriesConcept Practice

4 marks~6 minCriterion C

A number sequence starts at 2. Each term is made by adding 3 to the term before it.

a

List the first three terms of the sequence. [1]

b

Describe the pattern in one sentence. [1]

c

A classmate says the 5th term is 16. Calculate the 5th term and explain whether your classmate is correct. [2]

Solutions

14QuestionCreating Patterns Using RulesConcept Practice

2 marks~3 minCriterion A

A number pattern starts at

3

and goes up by

4

each time.

a

State the rule for this pattern in words. [1]

b

List the first three terms of the pattern. [1]

Solutions

15QuestionDescribing Patterns Using Words and SymbolsConcept Practice

4 marks~6 minCriterion B

Matchsticks are arranged to make a row of triangles.

Shape 1: 3 matchsticks. Shape 2: 5 matchsticks. Shape 3: 7 matchsticks.

a

List the number of matchsticks for shapes 1, 2, and 3. [1]

b

Describe in one sentence how the number of matchsticks changes each time a new triangle is added. [1]

c

Shape 3 uses 7 matchsticks. Describe how this compares to shape 8, and calculate how many matchsticks shape 8 needs. [2]

Solutions

16QuestionIdentifying Pattern Rules in DiagramsConcept Practice

2 marks~3 minCriterion B

The diagram shows squares made from matchsticks in a row.

1 square uses 4 matchsticks. 2 squares share a side and use 7 matchsticks. 3 squares share sides and use 10 matchsticks.

a

Identify the number of extra matchsticks needed each time one more square is added. [1]

b

Calculate the number of matchsticks needed for 4 squares in a row. [1]

Solutions

17QuestionIdentifying Pattern Rules in DiagramsConcept Practice

5 marks~8 minCriterion C

Each step in a dot pattern is shown below.

Step 1: 1 dot — Step 2: 5 dots — Step 3: 9 dots — Step 4: 13 dots

A student says the rule for the number of dots in Step

n

is

4n - 3

.

a

List the number of dots that the rule

4n - 3

gives for Steps 1, 2, 3, and 4. [2]

b

Describe in one sentence how the number of dots changes from one step to the next. [1]

c

State whether the student's rule is correct or incorrect, and give one reason using your results from part (a). [2]

Solutions

18QuestionFractal Patterns and RepetitionConcept Practice

2 marks~3 minCriterion B

A fractal tree grows by splitting. At Stage 1 there is 1 branch. At Stage 2 there are 2 branches. At Stage 3 there are 4 branches.

a

Identify the number of branches at Stage 4. [1]

b

Describe the rule that connects the number of branches at one stage to the next. [1]

Solutions

19QuestionFractal Patterns and RepetitionConcept Practice

2 marks~3 minCriterion A

The diagram shows a Sierpinski triangle at stage 1. A large triangle with area

8 \text{ cm}^2

is split into 4 equal smaller triangles by joining the midpoints of its sides. The middle triangle is then removed.

a

State the number of small triangles that remain. [1]

b

Calculate the remaining area as a fraction of the original triangle's area. Give your answer in its simplest form. [1]

Solutions

20QuestionUnderstanding nth Term ConceptAssessment Practice

2 marks~3 minCriterion D

A student saves money each week. In week 1 she saves 1 dollar, in week 2 she saves 3 dollars, in week 3 she saves 5 dollars, and in week 4 she saves 7 dollars. The formula for week

n

is

2n - 1

dollars.

Describe one reason why this formula may not correctly predict her savings in week 10. [2]

Solutions

21QuestionCultural Patterns in Art and DesignAssessment Practice

6 marks~9 minCriterion C

An Islamic tile pattern has a row of repeated shapes. The table shows how far each shape is from the centre of the pattern.

Shape number	1	2	3	4
Distance from centre (cm)	3	5	7	9

a

Identify the number that the distance goes up by each time. [1]

b

Describe how you can use the pattern in the table to find the distance of the 5th shape from the centre. [2]

c

The artist says: "Shape 10 is exactly 20 cm from the centre." State whether you agree or disagree, and give the correct distance. [3]

Solutions

22QuestionUsing Letters to Represent NumbersAssessment Practice

6 marks~9 minCriterion D

A student is selling cakes and brownies at a school bake sale. One cake costs

c

dollars and one brownie costs

b

dollars.

a

State the total cost, in dollars, of buying 3 cakes and 2 brownies. [1]

b

Calculate the total cost when

c = 5

and

b = 3

. Show your working. [2]

c

Describe two ways the expression

3c + 2b

might not give the real total cost at an actual bake sale. [3]

Solutions

23QuestionEvaluating Expressions Derived from PatternsAssessment Practice

5 marks~8 minCriterion C

A student is designing a square patio. For a patio with a side length of

n

tiles, she uses the expression

4n

to count the edge tiles. The patio measures

6 \times 6

tiles.

a

Calculate the number of edge tiles using

4n

when

n = 6

. [1]

b

Identify one problem with using

4n

to count edge tiles on a square patio. [1]

c

Describe how the problem you identified changes the total tile count for this patio. [3]

Solutions

24QuestionGenerating Terms from Position-to-Term RuleAssessment Practice

2 marks~3 minCriterion D

A party planner uses this rule to work out the cost of a party:

\text{cost} = 5 \times \text{number of guests} + 20 \text{ dollars}

a

Give an example of a party where this rule would work well. [1]

b

Describe one reason why this rule might not work for a very large party. [1]

Solutions

Patterns, Sequences & Algebraic Thinking — Free MYP1 Mathematics Practice Questions