Number Operations and Applications — Free IB MYP2 Mathematics Questions

1QuestionApplying Rules with Fractions and DecimalsConcept Practice

2 marks~3 minCriterion B

A unit fraction has 1 as its numerator. Study the pattern below.

\frac{1}{2} + \frac{1}{4} = \frac{3}{4} \qquad \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \qquad \frac{1}{4} + \frac{1}{8} = \frac{3}{8}

a

Identify the relationship between the two denominators in each sum. [1]

b

Calculate

\dfrac{1}{5} + \dfrac{1}{10}

, showing your working. [1]

Solutions

2QuestionApplying Rules to Whole NumbersConcept Practice

2 marks~3 minCriterion A

The diagram shows a right angle divided into two parts. A right angle measures

90°

.

One part measures

35°

.

a

Identify the type of angle formed by the two parts together. [1]

b

Calculate the measure of the missing angle. [1]

Solutions

3QuestionApplications of Remainders in ContextConcept Practice

2 marks~3 minCriterion A

A baker arranges 23 identical rolls into trays. Each tray holds exactly 5 rolls.

a

State the number of complete trays that can be filled. [1]

b

Calculate the number of rolls left over after filling the complete trays. [1]

Solutions

4QuestionAddition and Subtraction of Whole NumbersConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

5

cm and

3

cm.

a

State the number of sides a rectangle has. [1]

b

Calculate the perimeter of the rectangle. [1]

Solutions

5QuestionProperties of OperationsConcept Practice

3 marks~5 minCriterion B

The bar chart shows the results of four calculations:

5 + 3

,

3 + 5

,

5 - 3

, and

3 - 5

.

a

Identify which operation gives the same result when the order of the numbers is swapped. [1]

b

Explain why that operation is described as commutative (meaning the order of the numbers does not change the result). [1]

c

Compare the results of

5 - 3

and

3 - 5

, and explain what this tells you about whether subtraction is commutative. [1]

Solutions

6QuestionModeling Problems with DiagramsConcept Practice

3 marks~5 minCriterion C

The distance–time graph below shows a car's distance from home during a 3-hour trip.

a

Identify what the car is doing during the section from

(0, 0)

to

(1, 60)

. [1]

b

Describe what is happening to the car during the section from

(1, 60)

to

(2, 60)

, and explain how the graph shows this. [1]

c

Compare the car's journey during the section from

(2, 60)

to

(3, 0)

with its journey in part (a). [1]

Solutions

7QuestionChoosing the Correct OperationConcept Practice

2 marks~3 minCriterion A

The diagram shows a rectangle with sides labelled

8 \, \text{cm}

and

5 \, \text{cm}

.

a

Identify the type of quadrilateral shown in the diagram. [1]

b

A rectangle has a perimeter of

26 \, \text{cm}

and one side measures

8 \, \text{cm}

. Calculate the length of the shorter side. [1]

Solutions

8QuestionModeling Problems with DiagramsConcept Practice

6 marks~9 minCriterion B

L-shaped staircases are built from square tiles. Each step adds an L-shaped border around the previous shape.

Step number: 1, 2, 3, 4
Number of tiles: 3, 5, 7, 9

a

State the number of tiles needed for Step 5. [1]

b

Calculate the number of tiles for Steps 5 and 6, then write the complete sequence for Steps 1–6. Show your working. [2]

c

Identify a general rule for the number of tiles

T

at Step

n

, and use it to find the number of tiles at Step 10. [3]

Solutions

9QuestionAdding and Subtracting DecimalsConcept Practice

5 marks~8 minCriterion C

A student claims: "The sum of

0.5

and

0.23

is

0.28

, because

5 + 3 = 8

and

0 + 2 = 2

."

a

State the place value of the digit

5

in

0.50

and the digit

3

in

0.23

. [1]

b

Calculate the correct sum of

0.5

and

0.23

, showing your working by aligning the decimal points. [2]

c

Explain why the student's method is incorrect, referring to place value in your answer. [2]

Solutions

10QuestionAdding and Subtracting DecimalsConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

3.25

cm and

4.5

cm. The side opposite the

4.5

cm side is labelled

?

cm.

a

State the length of the side labelled

?

cm. [1]

b

A second rectangle has a perimeter of

15.5

cm and one side of

3.25

cm. Calculate the length of the other side. [1]

Solutions

11QuestionMath in Cooking and RecipesConcept Practice

2 marks~3 minCriterion B

A cookie recipe uses 2 cups of flour for every 1 cup of sugar.

a

State the ratio of flour to sugar in colon notation. [1]

b

The recipe is doubled. Describe what happens to the ratio of flour to sugar, and explain why. [1]

Solutions

12QuestionEstimating in Daily Life SituationsConcept Practice

2 marks~3 minCriterion A

A rectangular garden has a length of 8.3 m and a width of 4.6 m.

a

State the formula for the area of a rectangle. [1]

b

Estimate the area of the garden by first rounding each dimension to the nearest whole number, then calculating. Show your working. [1]

Solutions

13QuestionAdding and Subtracting FractionsConcept Practice

3 marks~5 minCriterion A

Two bar models are shown. The first bar is divided into 3 equal parts with 2 parts shaded, representing

\dfrac{2}{3}

. The second bar is divided into 5 equal parts with 1 part shaded, representing

\dfrac{1}{5}

.

a

Identify the least common multiple (LCM) of 3 and 5. [1]

b

Calculate the total shaded fraction. Show your working. [1]

c

Explain why

\dfrac{13}{15}

cannot be simplified further. [1]

Solutions

14QuestionEquivalent FractionsConcept Practice

4 marks~6 minCriterion B

Each square below is divided into equal parts. The shaded region shows a fraction of the whole square.

Diagram 1	2 equal parts	1 shaded.
Diagram 2	4 equal parts	2 shaded.
Diagram 3	6 equal parts	3 shaded.
Diagram 4	8 equal parts	4 shaded.

a

Identify the fraction of each square that is shaded. [2]

b

Explain why all four fractions represent the same value, and state the general rule that connects them. [2]

Solutions

15QuestionAdding and Subtracting Mixed NumbersConcept Practice

2 marks~3 minCriterion B

Look at these three subtraction equations:

2\tfrac{1}{3} - 1\tfrac{1}{3} = 1 \qquad 3\tfrac{1}{2} - 2\tfrac{1}{2} = 1 \qquad 4\tfrac{1}{5} - 3\tfrac{1}{5} = 1

a

Identify one pattern you notice in these equations. [1]

b

Using your pattern, write two new subtraction equations in the form

a\dfrac{b}{c} - d\dfrac{e}{f} = 1

. [1]

Solutions

16QuestionAdding and Subtracting Mixed NumbersConcept Practice

2 marks~3 minCriterion A

A recipe needs

1\dfrac{1}{2}

cups of flour for the dough and

2\dfrac{1}{3}

cups for the topping.

a

Calculate the total amount of flour needed. Show your working. [1]

b

Explain whether a measuring cup marked only in whole cups can measure this amount exactly. [1]

Solutions

17QuestionApplying Rules to Whole NumbersAssessment Practice

6 marks~9 minCriterion D

A class runs a bake sale. They sell 12 items at 5 dollars each. Costs are: ingredients at 4 dollars per batch for 3 batches, plus 9 dollars for packaging. The profit can be modelled by the expression

(12 \times 5) - (4 \times 3 + 9)

.

a

Calculate the profit. Show each step using BODMAS. [2]

b

Explain what happens to the calculated profit if you add before multiplying inside the cost bracket. Show the incorrect result and state why this matters for budgeting. [2]

c

Identify two ways the expression may not reflect the actual profit at a real bake sale. [2]

Solutions

18QuestionCommon Mistakes in BODMAS ProblemsAssessment Practice

6 marks~9 minCriterion C

A shop sells bags of chips for 3 dollars each and bottles of juice for 2 dollars each.

a

A student evaluates

3 \times 5 + 2 \times 10

and gets 55 dollars. Identify the order-of-operations error the student made and state the correct total. [2]

b

The shop runs a "buy 2, get 1 free" deal on chips. A student writes

3 \times 9 - 3 \times 3

to find the cost of 9 bags. Calculate this cost and explain why the expression correctly models the deal. [2]

c

Describe one situation in which the expression

3 \times 9 - 3 \times 3

would not correctly model the deal. [2]

Solutions

19QuestionApplications of Remainders in ContextAssessment Practice

8 marks~12 minCriterion C

A school has 147 students forming groups of 8 for a workshop. Students left over (fewer than 8) join a separate mixed-age group. The principal claims that only 17 full groups can be formed.

a

Calculate the values of

q

and

r

in

147 = 8 \times q + r

, where

q

is the number of full groups and

r

is the remainder. [2]

b

Show, using two steps of calculation, why the principal's claim that

q = 17

leads to a contradiction. [2]

c

State whether the principal's claim is correct or incorrect. Explain your answer using the division algorithm and identify how many students join the mixed-age group. [4]

Solutions

20QuestionApplications of Remainders in ContextAssessment Practice

6 marks~9 minCriterion D

A school cafeteria uses a 6-day rotating menu cycle. Day 1 falls on the first Monday of term, and the cycle continues through every school day without skipping.

a

Calculate which day of the 6-day cycle falls on the 100th school day. [2]

b

Explain why the remainder method gives a reliable mathematical prediction for this cycle. [2]

c

Identify two real-world factors that could make this prediction inaccurate, and explain which factor is more likely to disrupt the cycle. [2]

Solutions

21QuestionDivisibility Rules for Numbers 2 to 10Assessment Practice

3 marks~5 minCriterion B

The graph below shows the digit sum of each multiple of 3 (circles) and each multiple of 9 (squares) from 1 to 50.

Digit sum means the result of adding all the digits of a number together (e.g. the digit sum of 27 is

2 + 7 = 9

).

a

Identify one digit sum value shown for multiples of 9 on the graph. [1]

b

Explain why the digit sum test can be used to check if a number is divisible by 3. [1]

c

Compare the digit sums of multiples of 3 with those of multiples of 9, and explain what this tells you about the relationship between divisibility by 3 and divisibility by 9. [1]

Solutions

22QuestionProperties of OperationsAssessment Practice

2 marks~3 minCriterion C

The commutative property of addition states that changing the order of addends does not change the sum:

a + b = b + a

.

A student buys 3 pencils at 2 dollars each and 5 erasers at 1 dollar each.

a

Calculate the total cost in both orders to show the commutative property holds. [1]

b

Explain one limitation of using this property to check totals in real life. [1]

Solutions

23QuestionAddition and Subtraction of Whole NumbersAssessment Practice

6 marks~9 minCriterion D

A student has a budget of 245 dollars for school supplies. She spends 89 dollars on books and 37 dollars on stationery. To estimate her remaining money, she rounds each amount to the nearest ten:

250 - 90 - 40 = 120

dollars.

a

Calculate the actual amount of money remaining after both purchases. [2]

b

Calculate the difference between the student's estimate and the actual remaining amount. [1]

c

The student says: "Rounding is always good enough for managing a budget." Identify one situation where rounding could cause a problem in financial planning, and explain why. [3]

Solutions

24QuestionChoosing the Correct OperationAssessment Practice

6 marks~9 minCriterion D

A rectangular parking lot measures 30 m by 50 m. Each parking space, including its share of the access aisle, is 2.5 m wide and 6 m long.

a

Calculate the number of cars the parking lot can hold if the entire area is used for parking spaces. [2]

b

Identify two real-world features of a parking lot that would reduce the number of cars below your answer in part (a). [2]

c

Explain one reason why dividing total area by space area may not give a reliable estimate of parking capacity. [2]

Solutions

25QuestionAdding and Subtracting DecimalsAssessment Practice

5 marks~8 minCriterion B

Look at these four subtractions.

5.4 - 2.1 \qquad 6.8 - 3.5 \qquad 8.2 - 4.9 \qquad 9.6 - 6.3

a

Calculate each subtraction above. [2]

b

Identify one pattern you notice in your four answers and in the pairs of numbers. [1]

c

A student says: "

12.4 - 9.1

must equal

3.3

without me calculating it." Compare this claim with your pattern from part (b) and explain whether the student is correct. [2]

Solutions

26QuestionAdding and Subtracting DecimalsAssessment Practice

4 marks~6 minCriterion D

A student starts the week with 20.00 dollars. They deposit 12.50 dollars from a birthday gift, then spend 3.75 dollars on snacks and 5.20 dollars on a movie ticket. When they count their wallet, they find 23.00 dollars.

a

Calculate the student's expected balance using the transactions above. [1]

b

Identify the difference between the calculated balance and the actual cash amount. [1]

c

Explain two reasons why the calculated balance may differ from the actual cash in the wallet. [2]

Solutions

27QuestionEstimating in Daily Life SituationsAssessment Practice

8 marks~12 minCriterion D

At a school sports day, an aerial photo shows a crowd on a field. A square section measuring

10 \text{ m} \times 10 \text{ m}

is marked on the photo. You count

48

people inside that section. The total crowd area appears to be approximately

8

times the size of the marked section.

a

Estimate the total number of people in the crowd. Show each calculation step clearly. [2]

b

Calculate the crowd density (people per

\text{m}^2

) in the marked section, then use it to explain how you could arrive at the same total estimate a different way. [3]

c

Your estimation assumes people are spread out evenly across the whole crowd area. Compare one situation that would make your estimate too high with one situation that would make it too low. [3]

Solutions

28QuestionMath in Shopping and DiscountsAssessment Practice

8 marks~12 minCriterion C

A jacket is priced at 120 dollars. A store sign shows "30% off." Loyalty members receive a further "20% off" applied to the already-reduced price. A shopper believes the two discounts simply add to give 50% off.

a

Calculate the final price a loyalty member pays. [4]

b

Explain why adding the two percentages gives the wrong answer. [2]

c

Compare the shopper's assumption with the correct method, and suggest one strategy to avoid this mistake when shopping. [2]

Solutions

29QuestionAdding and Subtracting FractionsAssessment Practice

6 marks~9 minCriterion D

A student cuts a piece of length

1\dfrac{3}{5}

m from a wooden plank of length

3\dfrac{1}{3}

m. Their measuring tape is marked only in eighths of a metre.

a

Calculate the remaining length of the plank using the exact measurements. [2]

b

Calculate the remaining length after first rounding each measurement to the nearest

\dfrac{1}{8}

m. Show your rounding clearly. [2]

c

Compare the two remaining lengths from parts (a) and (b). State one limitation of using a measuring tape marked only in eighths of a metre for this task. [2]

Solutions

30QuestionAdding and Subtracting FractionsAssessment Practice

8 marks~12 minCriterion C

Alice and Ben each calculate

\dfrac{3}{4} + \dfrac{5}{6}

.

Alice uses denominator 12:

\quad \dfrac{3}{4} = \dfrac{9}{12}, \quad \dfrac{5}{6} = \dfrac{10}{12}, \quad \text{sum} = \dfrac{19}{12}

Ben uses denominator 24:

\quad \dfrac{3}{4} = \dfrac{18}{24}, \quad \dfrac{5}{6} = \dfrac{20}{24}, \quad \text{sum} = \dfrac{38}{24}

a

Identify one equivalent fraction used by either student and explain why it equals the original fraction. [2]

b

Calculate whether Ben's answer

\dfrac{38}{24}

equals Alice's answer

\dfrac{19}{12}

. Show your working. [2]

c

Compare the two methods. Explain which is more efficient and why, giving at least two reasons. [4]

Solutions

31QuestionAdding and Subtracting Mixed NumbersAssessment Practice

4 marks~6 minCriterion D

A pancake recipe for 4 servings uses

1\frac{1}{2}

cups of flour and

\frac{3}{4}

cup of milk. To make 10 servings, each ingredient is multiplied by the scaling factor

2\frac{1}{2}

.

a

Calculate the amount of flour and the amount of milk needed for 10 servings. [2]

b

A student says the cooking time should also be multiplied by

2\frac{1}{2}

. Explain why multiplying cooking time by the same scaling factor may not give the correct result. Give two reasons. [2]

Solutions

32QuestionAdding and Subtracting Mixed NumbersAssessment Practice

5 marks~8 minCriterion C

Two students each used a different model to find

2\dfrac{3}{4} + 1\dfrac{1}{2}

.

Student A (area model): Shows

\dfrac{3}{4}

and

\dfrac{1}{2}

as separate rectangles, then labels the total as

3\dfrac{1}{4}

.

Student B (number line): Shows a jump of

2\dfrac{3}{4}

then

1\dfrac{1}{2}

, landing on

4\dfrac{1}{4}

.

a

Identify which student's model gives the incorrect answer. [1]

b

Explain the error in that student's method. [2]

c

Calculate

2\dfrac{3}{4} + 1\dfrac{1}{2}

, showing each step clearly. [2]

Solutions

Number Operations and Applications — Free MYP2 Mathematics Practice Questions