Number Operations and Applications — Free IB MYP3 Mathematics Questions

1QuestionSolving with Units and ConversionsConcept Practice

5 marks~8 minCriterion C

A student claims: "A 3.5 km race is shorter than running a 4000 m race twice."

a

Calculate the distance of the 3.5 km race in metres. [1]

b

Calculate the total distance of running the 4000 m race twice, then compare this with your answer to part (a). [2]

c

Justify whether the student's claim is correct. [2]

Solutions

2QuestionChoosing the Correct OperationConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of 5 cm and a width of 3 cm.

(a) Calculate the perimeter of the rectangle. [2]

Solutions

3QuestionMath in Cooking and RecipesConcept Practice

2 marks~3 minCriterion B

A basic cookie recipe uses 2 cups of flour to make 12 cookies.

Number of cookies	12	24	36	48
Cups of flour	2	4	6	8

a

Describe the relationship between the number of cookies and the cups of flour. [1]

b

Calculate the number of cups of flour needed to make 60 cookies. [1]

Solutions

4QuestionEstimating in Daily Life SituationsConcept Practice

2 marks~3 minCriterion A

A pencil is placed along a ruler. The left end of the pencil lines up with the 2 cm mark and the right end lines up with the 16.8 cm mark.

a

Calculate the length of the pencil in centimetres. [1]

b

Round your answer to the nearest whole number of centimetres. [1]

Solutions

5QuestionAdding and Subtracting Mixed NumbersConcept Practice

2 marks~3 minCriterion A

The diagram shows two rectangles of equal size.

Rectangle A is divided into 5 equal parts, with 3 parts shaded.
Rectangle B is divided into 3 equal parts, with 2 parts shaded.

Calculate the total shaded area from both rectangles, expressing your answer as a mixed number. [2]

Solutions

6QuestionModeling Problems with DiagramsAssessment Practice

5 marks~8 minCriterion B

Square tables are arranged in a row with chairs placed around the outside, as shown in the diagram.

Number of tables	1	2	3
Number of chairs	4	6	8

a

Describe the pattern in the number of chairs as each table is added. [1]

b

Write a formula for

C

, the total number of chairs needed for

n

tables arranged in a row. [2]

c

A school hall can fit a maximum of 25 chairs around a single row of tables. Calculate the greatest number of tables that can be arranged in one row. [2]

Solutions

7QuestionChoosing the Correct OperationAssessment Practice

5 marks~8 minCriterion D

A student plans a school bake sale. They calculate the total cost of ingredients as

\text{Total cost} = 15 \times 2.50

budgeting for 15 batches of cookies at 2.50 dollars per batch. They forget to include a fixed table-rental fee of 10 dollars.

a

Calculate the correct total cost, showing all steps. [2]

b

Explain why omitting the table-rental fee makes this model unreliable for budgeting. [2]

c

Analyse how the student could improve the model if the number of batches changes each time. [1]

Solutions

8QuestionBanking Savings and TransactionsAssessment Practice

2 marks~3 minCriterion D

A student deposits 200 dollars in a bank account that earns simple interest at 3% per year, modelled by

I = P \times r \times t

where

I

is the interest earned,

P

is the principal,

r

is the annual rate as a decimal, and

t

is the time in years.

Explain one limitation of using simple interest to model the growth of this student's savings over 10 years. [2]

Solutions

9QuestionMath in Shopping and DiscountsAssessment Practice

8 marks~12 minCriterion C

A jacket costs 150 dollars. Store A applies a 30% discount, then a further 20% off the reduced price. Store B applies a single 50% discount to the same jacket.

a

Calculate the final price of the jacket at Store A after both discounts are applied in sequence. [2]

b

Calculate the difference in final price between the two stores. [2]

c

A customer claims that shopping at Store A gives the same saving as Store B because

30\% + 20\% = 50\%

. Analyse this claim. In your answer, show the effective percentage discount at Store A and explain why sequential discounts do not add in the way the customer expects. [4]

Solutions

10QuestionAdding and Subtracting Mixed NumbersAssessment Practice

8 marks~12 minCriterion B

When two mixed numbers are added, their fractional parts sometimes sum to exactly 1.

1\tfrac{1}{3} + 2\tfrac{2}{3} \qquad 2\tfrac{1}{4} + 1\tfrac{3}{4} \qquad 3\tfrac{1}{5} + 2\tfrac{4}{5} \qquad 1\tfrac{1}{6} + 2\tfrac{5}{6} \qquad 4\tfrac{3}{8} + 3\tfrac{5}{8}

a

Calculate the first four sums. Express each result as a whole number. [4]

b

Describe the rule that determines when the sum of the fractional parts of two mixed numbers equals exactly 1. [2]

c

A student claims the fifth sum equals 8 without working out the fractions separately. Justify whether the student is correct. [2]

Solutions

11QuestionAdding and Subtracting Mixed NumbersAssessment Practice

6 marks~9 minCriterion D

A baker has

3\frac{1}{3}

cups of flour, adds

2\frac{3}{4}

cups for a large batch, then removes

1\frac{1}{5}

cups to make a smaller batch. Each measurement has a possible error of

\pm\frac{1}{8}

cup.

a

Calculate the final amount of flour as a simplified mixed number. [2]

b

Explain how the measurement error affects the reliability of your answer in part (a). [2]

c

A recipe requires exactly

4\frac{3}{4}

cups of flour. Analyse whether the baker's final amount is sufficient, taking into account the maximum possible measurement error. [2]

Solutions

12QuestionApplications in Geometry and MeasurementAssessment Practice

6 marks~9 minCriterion C

A room has a rectangular section measuring

4\dfrac{1}{2}

m by

3\dfrac{1}{3}

m, and a semi-circular bay window of radius

1\dfrac{1}{4}

m. A student claims the total floor area is

18\dfrac{1}{8}

m

^2

.

a

Calculate the correct total floor area of the room. Show all working. [3]

b

Explain one reason why the rectangular section area alone may not be exact in a real room. [1]

c

The student's answer differs from the correct value by approximately

0.67

m

^2

. Interpret what this difference suggests about the reliability of the student's method. [2]

Solutions

Number Operations and Applications — Free MYP3 Mathematics Practice Questions