Number Concepts & Systems — Free IB MYP1 Mathematics Questions

1QuestionEven Odd and Prime NumbersConcept Practice

2 marks~3 minCriterion B

Look at these sums of prime numbers:

2 = 2

(even)

2 + 3 = 5

(odd)

2 + 3 + 5 = 10

(even)

2 + 3 + 5 + 7 = 17

(odd)

a

Identify the pattern in whether these sums are even or odd. [1]

b

Describe whether

2 + 3 + 5 + 7 + 11

will be even or odd, and give one reason why. [1]

Solutions

2QuestionIntegers and Their UsesConcept Practice

5 marks~8 minCriterion C

The temperature in a city changes each day for five days.

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Temperature change (°C)	$+3$	$-5$	$+7$	$-2$	$+4$

a

List the two days when the temperature went down. [1]

b

Calculate the total temperature change over the five days. Show each step of your working. [3]

c

A friend says: "The temperature went up more days than it went down, so the total change must be more than

+10°C

." Describe why your friend is wrong. [1]

Solutions

3QuestionEven Odd and Prime NumbersConcept Practice

2 marks~3 minCriterion A

The grid below shows 3 rows and 4 columns of dots.

a

Calculate the total number of dots in the grid. [1]

b

Identify whether the total is even or odd, and describe how you know. [1]

Solutions

4QuestionIrrational Numbers in Square Roots and PiConcept Practice

2 marks~3 minCriterion B

Look at this sequence:

\sqrt{1},\ \sqrt{4},\ \sqrt{9},\ \sqrt{16}

a

Identify what type of numbers appear under the square root signs. [1]

b

Describe how you know what the next term in the sequence will be. [1]

Solutions

5QuestionRational Numbers as Terminating and Repeating DecimalsConcept Practice

3 marks~5 minCriterion C

A pizza is cut into 12 equal slices. Mia eats 7 of them.

a

Write the fraction of pizza Mia eats as a decimal. Use long division to show your working. [1]

b

Describe whether your decimal is terminating or repeating, and explain how you know. [1]

c

Write the decimal using bar notation, and explain what the bar tells you. [1]

Solutions

6QuestionRational Numbers as Terminating and Repeating DecimalsConcept Practice

2 marks~3 minCriterion A

A cashier shares 10 dollars equally among 4 people.

a

Calculate how much each person receives. [1]

b

Describe why the decimal 2.50 is called a terminating decimal. [1]

Solutions

7QuestionRational Numbers as Terminating and Repeating DecimalsConcept Practice

2 marks~3 minCriterion A

A rectangle is divided into 8 equal parts. Three parts are shaded.

a

Identify the fraction of the rectangle that is shaded. [1]

b

Calculate the decimal value of this fraction and describe whether it terminates or repeats. [1]

Solutions

8QuestionEstimating Products and QuotientsConcept Practice

3 marks~5 minCriterion B

A student estimates division answers by rounding the starting number to a compatible number.

Starting number	$198$	compatible number: $200$	divisor: $5$	estimate: $40$	actual answer: $39.6$
Starting number	$412$	compatible number: $400$	divisor: $8$	estimate: $50$	actual answer: $51.5$

a

Identify whether the compatible number

200

is greater than or less than

198

. [1]

b

Describe what happens to the estimated answer when the compatible number is greater than the starting number. [1]

c

Compare the two estimates above and describe how the direction of rounding affects whether each estimate is too high or too low. [1]

Solutions

9QuestionEstimating Products and QuotientsConcept Practice

2 marks~3 minCriterion D

You want to buy 8 movie tickets. Each ticket costs approximately 12 dollars.

a

Calculate the estimated total cost of 8 tickets. State whether 100 dollars is enough to pay. [1]

b

Describe whether your estimate is an overestimate or an underestimate if the actual ticket price is 11.50 dollars. [1]

Solutions

10QuestionRounding Whole NumbersConcept Practice

3 marks~5 minCriterion C

The bar chart shows the number of people who attended a school concert each year. The attendance figures have been rounded to the nearest hundred.

Year 1:

400

— Year 2:

500

— Year 3:

500

— Year 4:

600

a

Identify the trend in attendance shown by the rounded figures. [1]

b

Describe what it means to round a number to the nearest hundred. [1]

c

Give an example to show how rounding to the nearest hundred could hide a real change in attendance between two years. [1]

Solutions

11QuestionEstimating Products and QuotientsConcept Practice

2 marks~3 minCriterion A

The diagram shows an irregular shape drawn on a grid. Each square represents

1 \, \text{cm}^2

.

a

State the number of complete squares and the number of partial squares inside the shape. [1]

b

Calculate the estimated area of the shape in

\text{cm}^2

. [1]

Solutions

12QuestionDecimal Place Value and PrecisionConcept Practice

3 marks~5 minCriterion C

A student rounded

3.456

to different numbers of decimal places and recorded the results below.

Decimal places	1	2	3
Rounded value	$3.5$	$3.46$	$3.456$

a

Identify the incorrect rounded value. [1]

b

State the correct rounded value for that number of decimal places. [1]

c

Describe the rounding rule you used to find the correct value. [1]

Solutions

13QuestionComparing and Ordering DecimalsConcept Practice

2 marks~3 minCriterion B

Look at this number sequence:

0.1, \quad 0.3, \quad 0.5, \quad 0.7, \quad \ldots

a

State the next two numbers in the sequence. [1]

b

Describe the rule you used to find them. [1]

Solutions

14QuestionComparing and Ordering DecimalsConcept Practice

2 marks~3 minCriterion A

Segment A measures

3.4

cm and Segment B measures

3.04

cm.

a

Identify which segment is longer. [1]

b

Describe how you know, using the tenths digit of each measurement. [1]

Solutions

15QuestionDecimal Place Value and PrecisionConcept Practice

2 marks~3 minCriterion D

A shopkeeper's till calculates that a customer owes 4.673 dollars in a cash transaction.

a

State why the shopkeeper rounds this amount to 4.67 dollars. [1]

b

Describe one way that rounding prices in cash transactions can be unfair to customers. [1]

Solutions

16QuestionOrdering Positive and Negative NumbersConcept Practice

3 marks~5 minCriterion B

A thermometer shows these temperatures on a cold winter day:

Top:

7°C

— Upper middle:

3°C

— Middle:

0°C

— Lower middle:

-2°C

— Bottom:

-5°C

a

Identify the coldest temperature shown on the thermometer. [1]

b

Identify the warmest temperature shown on the thermometer. [1]

c

Describe the relationship between a temperature's position on the thermometer and its value. [1]

Solutions

17QuestionRounding Numbers to Nearest 10 100 1000Concept Practice

2 marks~3 minCriterion D

A teacher is buying packets of crisps for a class party. There are 28 students in the class.

a

State the number of students rounded to the nearest ten. [1]

b

Describe whether this rounded number is an overestimate or an underestimate, and explain why this helps the teacher buy enough crisps for everyone. [1]

Solutions

18QuestionInequalities and SymbolsConcept Practice

2 marks~3 minCriterion A

A balance scale has 5 kg on the left side and 3 kg on the right side. The left side tips down.

a

State which side is heavier. [1]

b

Write the correct symbol (

<

or

>

) to complete the statement below. [1]

5 \text{ kg} \ \underline{\hspace{1cm}} \ 3 \text{ kg}

Solutions

19QuestionComposite Numbers and Their PropertiesConcept Practice

2 marks~3 minCriterion D

A factory packs 24 chocolates into rectangular boxes.

a

List two factors of 24 (not 1 or 24). [1]

b

Describe one reason why having many factors makes 24 a better choice than 23 for packaging chocolates. [1]

Solutions

20QuestionSquare Numbers and Their PatternsConcept Practice

5 marks~8 minCriterion B

The dot diagrams below show the first four square numbers.

1 \times 1

: 1 dot

\quad

2 \times 2

: 4 dots

\quad

3 \times 3

: 9 dots

\quad

4 \times 4

: 16 dots

a

Name the next square number after 16. [1]

b

Describe the rule that connects the side length of a square to its number of dots. [2]

c

A

5 \times 5

square has 25 dots and a

10 \times 10

square has 100 dots. Describe one way these two squares are the same and one way they are different. [2]

Solutions

21QuestionApplications of Square Numbers in GeometryConcept Practice

2 marks~3 minCriterion A

The square below has a side length of 5 cm.

Calculate the area of the square. [2]

Solutions

22QuestionFinding Multiples of a NumberConcept Practice

5 marks~8 minCriterion C

A student says: "All multiples of 6 are also multiples of 3 and 2, so the LCM of 6, 3, and 2 is 6."

a

List the first five multiples of 6, of 3, and of 2. [2]

b

Identify the smallest number that appears in all three lists. [1]

c

Describe whether the student's claim is correct, and explain why using your lists. [2]

Solutions

23QuestionFinding Factors of a NumberConcept Practice

4 marks~6 minCriterion A

A teacher is organising

24

students into equal-sized teams for a sports day. No student should be left out.

a

List all the factors of

24

. [2]

b

The teacher wants to make teams of

5

. Identify whether this is possible, and give one reason for your answer. [1]

c

Describe one reason why the factors of

24

might not all work as team sizes in a real sports day. [1]

Solutions

24QuestionFinding Factors of a NumberConcept Practice

2 marks~3 minCriterion B

A teacher has 24 students and wants to split them into equal-sized groups.

a

List all the possible group sizes. [1]

b

Describe what all these group sizes have in common. [1]

Solutions

25QuestionLowest Common Multiple LCMConcept Practice

4 marks~6 minCriterion D

Two buses stop at the same bus stop. Bus A arrives every 6 minutes. Bus B arrives every 9 minutes. Both buses arrive together at 8:00 AM.

a

List the first four multiples of 6 and the first four multiples of 9. [1]

b

Calculate the lowest common multiple (LCM) of 6 and 9, and state the first time after 8:00 AM when both buses arrive together. [2]

c

Describe one reason why the two buses might not actually arrive together at the time you calculated. [1]

Solutions

26QuestionOpposites and Zero on the Number LineConcept Practice

6 marks~9 minCriterion B

Look at these five integers:

6

,

-4

,

3

,

-7

,

0

.

a

State the opposite of each integer. [2]

Integer	$6$	Opposite: \_\_\_\_
Integer	$-4$	Opposite: \_\_\_\_
Integer	$3$	Opposite: \_\_\_\_
Integer	$-7$	Opposite: \_\_\_\_
Integer	$0$	Opposite: \_\_\_\_

b

On the number line below, label the five integers above and their opposites. [2]

c

Describe what you notice about where an integer and its opposite sit on the number line. [2]

Solutions

27QuestionAbsolute Value of an IntegerConcept Practice

2 marks~3 minCriterion A

Point

P

is marked at

-5

on the number line below.

\longleftarrow \quad -6 \quad -5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad \longrightarrow

\hspace{52pt} P

a

Identify the distance of point

P

from

0

on the number line. [1]

b

Describe what the absolute value of a number tells you. [1]

Solutions

28QuestionEven Odd and Prime NumbersAssessment Practice

2 marks~3 minCriterion D

A school gives each locker a code made by multiplying two different prime numbers, for example

2 \times 7 = 14

.

a

State one reason why a code like 14 is harder to guess than a code made from even numbers. [1]

b

Describe one reason why this system would not work well for a large school with hundreds of lockers. [1]

Solutions

29QuestionOrdering Positive and Negative NumbersAssessment Practice

5 marks~8 minCriterion C

The table shows the high and low temperatures (°C) for one week.

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
High (°C)	5	2	−1	3	−3	0	4
Low (°C)	−2	−4	−6	−1	−7	−3	1

a

List all 14 temperatures in order from lowest to highest. [2]

b

Identify the coldest day and state its high temperature. [1]

c

A student says: "The coldest day had a high temperature lower than the coldest low temperature of the week." Describe whether this claim is correct, and explain why. [2]

Solutions

30QuestionComposite Numbers and Their PropertiesAssessment Practice

5 marks~8 minCriterion C

A student says: "A number is composite if it ends in an even digit."

a

Name one factor of 15 that is neither 1 nor 15. [1]

b

List all the factors of 12. [2]

c

Describe why a number ending in an even digit is not always composite. Give one example to support your answer. [2]

Solutions

31QuestionOpposites and Zero on the Number LineAssessment Practice

4 marks~6 minCriterion D

A weather app shows a city's temperature drops from

3°C

to

-3°C

.

a

State how far each temperature is from

0°C

on the number line. [1]

b

Describe what makes

3

and

-3

opposites on the number line. [1]

c

Describe one reason why

-3°C

feels much colder to a person than

3°C

, even though both are the same distance from

0°C

. [2]

Solutions

32QuestionRepresenting Integers on Number LineAssessment Practice

5 marks~8 minCriterion C

Ali says the distance between

-8

and

3

on a number line is

5

.
Bella says the distance is

11

.

a

Calculate the distance between

-8

and

3

on the number line. [1]

b

Identify which student is correct. [1]

c

Describe what mistake the other student made, and explain why the correct answer makes sense using the number line. [3]

Solutions

Number Concepts & Systems — Free MYP1 Mathematics Practice Questions