Number Operations and Applications — Free IB MYP1 Mathematics Questions

1QuestionExpressions with Brackets and ExponentsConcept Practice

5 marks~8 minCriterion B

Look at these two number sequences.

Sequence A:

2, \ 4, \ 6, \ 8, \ \ldots

Sequence B:

2, \ 4, \ 8, \ 16, \ \ldots

a

Identify the next two terms in Sequence A and the next two terms in Sequence B. [2]

b

Describe the rule you used to find each next term in Sequence A and in Sequence B. [2]

c

Compare the two sequences. Which one grows faster? Describe what you notice in two or three sentences. [1]

Solutions

2QuestionCommon Mistakes in BODMAS ProblemsConcept Practice

4 marks~6 minCriterion C

Two students work out the cost of party supplies.

Student A calculates:

2 \times 5 + 3 \times 4 = 10 + 12 = 22

dollars.

Student B calculates:

5 + 3 = 8

, then

2 \times 8 \times 4 = 64

dollars.

a

Identify the mistake Student B made with the order of operations. [1]

b

Describe how Student B's mistake changes the total cost compared to Student A's answer. [1]

c

Describe one way that getting the order of operations wrong could cause a problem when planning how much money to bring to a shop. [2]

Solutions

3QuestionExpressions with Brackets and ExponentsConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of

3^2

cm and a width of

(2 + 1)

cm.

Calculate the area of the rectangle. [2]

Solutions

4QuestionApplications of Remainders in ContextConcept Practice

2 marks~3 minCriterion B

When you count up in 3s, you get: 3, 6, 9, 12, 15, 18, 21, …

a

List the remainders when each of 3, 6, 9, 12, 15, 18 is divided by 4. [1]

b

Describe the pattern you see in your remainders. [1]

Solutions

5QuestionDivisibility Rules for Numbers 2 to 10Concept Practice

4 marks~6 minCriterion C

Look at the number

7{,}840

.

a

Identify whether

7{,}840

is divisible by

2

, by

5

, and by

10

. [1]

b

Describe the divisibility rule for

2

and the divisibility rule for

5

, and use each rule to explain why

7{,}840

is divisible by both. [1]

c

Compare a number ending in

0

with a number ending in

5

. Describe how each one behaves with divisibility by

2

and by

5

. [2]

Solutions

6QuestionApplications of Remainders in ContextConcept Practice

2 marks~3 minCriterion A

A rectangle is divided into 4 rows and 6 columns of equal squares. Eight of the squares are shaded.

a

Calculate the total number of squares in the rectangle. [1]

b

Describe whether the number of shaded squares is a multiple of the number of rows. [1]

Solutions

7QuestionApplications of Remainders in ContextConcept Practice

2 marks~3 minCriterion D

A teacher has 28 students and wants to make groups of 6 for a project.

a

Calculate the number of complete groups of 6 that can be formed and state how many students are left over. [1]

b

Describe why knowing the number of students left over matters when planning the project. [1]

Solutions

8QuestionChoosing the Correct OperationConcept Practice

5 marks~8 minCriterion B

Mia earns the same amount of money each day doing chores.

Days worked	1	2	3	4
Total earned (dollars)	5	10	15	20

a

Identify how much Mia earns each day. [1]

b

State the rule that gives Mia's total earnings

E

after

d

days. [2]

c

Calculate Mia's total earnings after 10 days. [2]

Solutions

9QuestionChoosing the Correct OperationConcept Practice

2 marks~3 minCriterion A

A rectangle has a top side of

8

cm and a left side of

5

cm.

a

Name the shape shown in the diagram. [1]

b

Describe the length of the bottom side and explain how you know. [1]

Solutions

10QuestionAdding and Subtracting DecimalsConcept Practice

2 marks~3 minCriterion A

The number line below shows the numbers from

0

to

1

, split into ten equal parts.

A point is marked on the line at the arrow.

a

Identify how much each small step is worth on this number line. [1]

b

State the decimal value shown by the arrow. [1]

Solutions

11QuestionAdding and Subtracting FractionsConcept Practice

2 marks~3 minCriterion D

A recipe needs

\dfrac{1}{4}

cup of oil and

\dfrac{1}{2}

cup of milk.

a

Identify a real-life situation where you would need to add fractions. [1]

b

Describe in one sentence why adding fractions is useful in that situation. [1]

Solutions

12QuestionEquivalent FractionsConcept Practice

2 marks~3 minCriterion C

A pizza is cut into 8 equal slices. You eat 2 slices. Your friend says you ate

\frac{1}{4}

of the pizza.

a

Write the fraction of pizza you ate. [1]

b

Show whether your friend is correct by finding an equivalent fraction. [1]

Solutions

13QuestionSimplifying FractionsConcept Practice

3 marks~5 minCriterion B

Look at the two bar models below.

Bar 1 is divided into 12 equal parts, with 8 parts shaded.
Bar 2 is divided into 3 equal parts, with 2 parts shaded.

a

Identify the fraction shown by each bar model. [1]

b

Describe what you notice about the amount shaded in both bars. [1]

c

Describe how Bar 1 shows the process of simplifying a fraction. [1]

Solutions

14QuestionAdding and Subtracting FractionsConcept Practice

2 marks~3 minCriterion A

Two rectangles are each divided into 8 equal parts. In the first rectangle, 3 parts are shaded. In the second rectangle, 2 parts are shaded.

a

State the fraction of the first rectangle that is shaded. [1]

b

Calculate the total fraction shaded when both rectangles are combined. [1]

Solutions

15QuestionApplying Rules to Whole NumbersAssessment Practice

6 marks~9 minCriterion D

A class is holding a bake sale. They sell 8 cupcakes at 3 dollars each and 10 cookies at 2 dollars each. Ingredients cost 9 dollars and packaging costs 5 dollars.

The profit can be found using:

(8 \times 3 + 10 \times 2) - (9 + 5)

a

Calculate the profit step by step using BODMAS. Show all your working. [2]

b

Identify two things that could happen at the real bake sale that might change the actual profit. [2]

c

Describe one way this calculation is helpful for planning the bake sale and one way it might not match what really happens. [2]

Solutions

16QuestionSingle-Step Word ProblemsAssessment Practice

6 marks~9 minCriterion C

Sofia has 24 stickers. She puts 6 stickers on each page.

a

Identify which of these two sentences matches Sofia's sticker problem. [1]

- "How many 6s are in 24?"
- "24 shared into 6 equal groups gives 4."

b

Describe in one sentence why your chosen sentence in (a) matches Sofia's problem. [2]

c

Describe one way the two sentences are the same and one way they are different. [3]

Solutions

17QuestionChoosing the Correct OperationAssessment Practice

6 marks~9 minCriterion D

Samantha buys four items for a party.

Chips: 3 dollars
Dip: 3 dollars
Juice: 5 dollars
Cake: 7 dollars

These are the rounded prices she used to estimate her total.

a

State the estimated total Samantha gets by adding the four rounded prices. [1]

b

The actual prices were: Chips 2.75 dollars, Dip 3.20 dollars, Juice 4.50 dollars, Cake 6.80 dollars. Calculate the actual total cost. [2]

c

Describe one way that rounding each price to the nearest dollar could make Samantha's estimate less useful when she goes shopping. [3]

Solutions

18QuestionAdding and Subtracting DecimalsAssessment Practice

8 marks~12 minCriterion B

Look at these four additions:

0.3 + 0.7

0.45 + 0.55

1.2 + 0.8

3.67 + 0.33

a

Calculate each sum. [2]

b

Describe what you notice about all four answers. [2]

c

Describe what the decimal parts of each pair of numbers have in common. Use your answer to describe when two decimal numbers will add up to a whole number. [4]

Solutions

19QuestionAdding and Subtracting DecimalsAssessment Practice

4 marks~6 minCriterion D

Mia has £12.50 pocket money. She spends £3.75 on Monday, £2.80 on Tuesday, and £4.15 on Wednesday.

a

Calculate how much Mia spends in total over the three days. [1]

b

Mia thinks she has £1.80 left. State whether she is correct. [1]

c

Mia pays for a £0.85 snack with a £1 coin. She gets 10p change instead of 15p because the machine has no 5p coins. Describe how this means the amount of money Mia actually has could be different from what her spending record shows. [2]

Solutions

20QuestionConverting Between Fractions and DecimalsAssessment Practice

8 marks~12 minCriterion C

A student says: "0.3 equals

\frac{3}{10}

, and 0.30 equals

\frac{30}{100}

. Because

\frac{30}{100}

is bigger than

\frac{3}{10}

, the numbers 0.3 and 0.30 are different."

a

Shade a 10 × 10 grid to show 0.3. State how many squares you shaded. [1]

b

Shade a second 10 × 10 grid to show 0.30. Describe what you notice about the two grids. [3]

c

Describe whether the student's claim is correct or incorrect. Use the word equal or not equal and give one reason using the grids or place value. [4]

Solutions

Number Operations and Applications — Free MYP1 Mathematics Practice Questions