Number Concepts & Systems — Free IB MYP2 Mathematics Questions

1QuestionDefining Irrational NumbersConcept Practice

2 marks~3 minCriterion A

The diagram shows a right triangle with legs measuring 2 cm and 3 cm.

a

Calculate the length of the hypotenuse. [1]

b

State whether this length is rational or irrational, and explain how the definition of an irrational number supports your answer. [1]

Solutions

2QuestionEstimating Products and QuotientsConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

7.8

cm and

4.2

cm.

a

State the value of each side length rounded to the nearest whole number. [1]

b

Estimate the area of the rectangle by multiplying your rounded values. Give your answer in cm². [1]

Solutions

3QuestionComparing and Ordering DecimalsConcept Practice

2 marks~3 minCriterion B

Consider the decimal sequence:

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

a

State the next two terms of the sequence. [1]

b

Describe the rule that generates this sequence. [1]

Solutions

4QuestionDecimal Place Value and PrecisionConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

3.64

cm and

2.47

cm.

a

State the length of the longer side rounded to the nearest tenth of a centimetre. [1]

b

Calculate the perimeter of the rectangle using each side length rounded to the nearest tenth. [1]

Solutions

5QuestionInequalities and SymbolsConcept Practice

2 marks~3 minCriterion A

The number line below shows points marked at

-3

,

0

, and

5

.

a

Identify the inequality symbol needed when an open circle is used on a number line. [1]

b

Write the inequality that represents the shaded region shown on the number line. [1]

Solutions

6QuestionInequalities and SymbolsConcept Practice

3 marks~5 minCriterion C

A number line shows points at

-3

and

4

. The inequality

x < -3

is shown to the left of

-3

, and

x > 4

is shown to the right of

4

. Both regions are shaded.

a

Identify one value of

x

that satisfies

x < -3

and one value that satisfies

x > 4

. [1]

b

Explain why no single value of

x

can satisfy both

x < -3

and

x > 4

at the same time. [1]

c

Compare the two shaded regions and describe what this tells you about the solution set for both inequalities together. [1]

Solutions

7QuestionApplications of Square Numbers in GeometryConcept Practice

2 marks~3 minCriterion A

A square patio has a side length of 7 m.

a

Identify the formula used to calculate the area of a square. [1]

b

Calculate the area of the patio. Show your working. [1]

Solutions

8QuestionSquare Numbers and Their PatternsConcept Practice

2 marks~3 minCriterion B

The dot arrangements below show the first four square numbers.

Arrangement 1: 1 dot
Arrangement 2: 4 dots
Arrangement 3: 9 dots
Arrangement 4: 16 dots

a

State the relationship between the side length

n

and the total number of dots, using mathematical notation. [1]

b

Explain why these numbers are called "square numbers." [1]

Solutions

9QuestionFinding Factors of a NumberConcept Practice

3 marks~5 minCriterion B

A factor of a number divides into it exactly, with no remainder.

a

List all the factors of

24

. [1]

b

Factors of

24

can be arranged into pairs. State what each pair multiplies to give, and write out all four pairs. [1]

c

Compare the sizes of the two numbers in each factor pair. Describe the pattern you notice. [1]

Solutions

10QuestionFinding Factors of a NumberConcept Practice

2 marks~3 minCriterion A

A rectangle has an area of 24 square units and a width of 3 units.

a

Calculate the length of the rectangle. [1]

b

List all factor pairs of 24. Identify which factor pair represents the dimensions of this rectangle. [1]

Solutions

11QuestionAbsolute Value of an IntegerConcept Practice

2 marks~3 minCriterion A

The absolute value of a number is its distance from zero on the number line, always written as a positive value.

a

Identify the absolute value of

-4

. [1]

b

Explain what this value tells you about the position of

-4

on the number line. [1]

Solutions

12QuestionRational Numbers as Terminating and Repeating DecimalsAssessment Practice

3 marks~5 minCriterion B

The table shows five fractions and whether their decimal form is terminating (T) or repeating (R).

Fraction:

\dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{1}{4},\ \dfrac{1}{6},\ \dfrac{1}{7}

Decimal type: T, R, T, R, R

a

Identify the prime factors of the denominator 6. [1]

b

Explain why

\dfrac{1}{4}

gives a terminating decimal but

\dfrac{1}{6}

gives a repeating decimal. [1]

c

Compare the denominators that give terminating decimals with those that give repeating decimals, and state the rule that predicts which type will occur. [1]

Solutions

13QuestionRational Numbers as Terminating and Repeating DecimalsAssessment Practice

4 marks~6 minCriterion C

A student measures a table and records its length as

1.333...

m.

a

Explain why the fraction

\dfrac{4}{3}

is equal to the repeating decimal

1.333...

[2]

b

The student claims the table's length is exactly

\dfrac{4}{3}

m. Explain whether this claim can be justified, given that the ruler has millimetre markings. [2]

Solutions

14QuestionIrrational Numbers in Square Roots and PiAssessment Practice

4 marks~6 minCriterion D

A student measures the circumference of a circular garden as

C = 15.7

m (precision:

\pm 0.1

m) and uses

C = 2\pi r

to calculate the radius as

r = 2.5

m.

a

State whether the calculated radius is exact or approximate. [1]

b

Calculate the radius using

\pi \approx 3.1416

instead of

3.14

, and explain how this affects the result. [2]

c

Compare the reliability of the measured circumference with the reliability of the calculated radius. [1]

Solutions

15QuestionRounding Whole NumbersAssessment Practice

6 marks~9 minCriterion C

Two students disagree about rounding

4\,789

to the nearest ten.
Aisha says the answer is

4\,790

. Ben says the answer is

4\,800

.

a

Identify which student is correct. State the rounding rule for the nearest ten and use the ones digit of

4\,789

to support your answer. [2]

b

Draw a number line from

4\,780

to

4\,800

, marking

4\,789

on it. Explain how the number line shows which multiple of ten

4\,789

is closest to. [2]

c

Compare rounding to the nearest ten with rounding to the nearest hundred. Explain which process gives

4\,800

and why Ben's answer uses the wrong process. [2]

Solutions

16QuestionEstimating Products and QuotientsAssessment Practice

5 marks~8 minCriterion D

A student plans a school bake sale and estimates the cost of 8 packets of chocolate chips, each priced at 19.90 dollars, by rounding to 20 dollars:

20 \times 8 = 160 \text{ dollars}

a

Calculate the actual total cost of 8 packets at 19.90 dollars each. [1]

b

The student's estimate gives an error of 0.80 dollars. Calculate the percentage error and explain whether the estimate is accurate enough for budget planning. [2]

c

Describe an alternative estimation strategy and compare it to the student's method, stating which gives a more useful result. [2]

Solutions

17QuestionEstimating Products and QuotientsAssessment Practice

3 marks~5 minCriterion B

The table shows four products and their estimates, found by rounding each factor to one significant figure.

Exact product	12	47	83	126
Estimated product	10	50	80	130

a

Identify which exact product has the largest difference from its estimated product. [1]

b

Calculate the percentage error for the pair (47, 50). [1]

c

Compare how close the estimated products are to the exact products as the values increase. [1]

Solutions

18QuestionReading and Writing Numbers in WordsAssessment Practice

4 marks~6 minCriterion C

A bank statement shows a deposit written as: "three thousand four hundred and five dollars and sixty-seven cents."

a

State this amount as a decimal number of dollars. [1]

b

Explain why banks write monetary amounts in words as well as numerals. [1]

c

Compare the advantages and disadvantages of writing amounts in words on bank statements. [2]

Solutions

19QuestionComparing and Ordering DecimalsAssessment Practice

6 marks~9 minCriterion D

Three athletes finish a swimming race with these recorded times:

Athlete A:

23.450

s
Athlete B:

23.500

s
Athlete C:

23.405

s

a

State the order in which gold, silver, and bronze medals are awarded. [1]

b

Explain why recording times to three decimal places (thousandths of a second) helps ensure a fair result in close races. [2]

c

Compare the precision of a stopwatch (accurate to

\pm 0.01

s) with the level of detail shown in the recorded times above. What does this suggest about relying on the thousandths digit alone to rank athletes? [3]

Solutions

20QuestionInequalities and SymbolsAssessment Practice

4 marks~6 minCriterion D

A student measures a plant's height using a ruler marked in whole centimetres only and records it as 12 cm. The actual height lies somewhere in the range

11.5 \leq \text{height} \leq 12.5

(in cm).

a

State what the notation

\leq

means in the inequality above. [1]

b

Explain why the inequality

11.5 \leq \text{height} \leq 12.5

is a more honest record of the measurement than writing "height = 12 cm." [2]

c

Identify one real-world limitation of using this inequality to describe the plant's height. [1]

Solutions

21QuestionInequalities and SymbolsAssessment Practice

5 marks~8 minCriterion B

Given

a = -3

,

b = 1

, and

c = 4

, where

a < b

and

b < c

.

a

Identify the positions of

a

,

b

, and

c

on the number line below by labelling each point. [1]

b

Explain why

a < c

is true for these values, using the number line. [2]

c

Compare the statement "if

a < b

and

b < c

, then

a < c

" with what your number line shows. Does this pattern hold for any real numbers? Give a reason. [2]

Solutions

22QuestionApplications of Square Numbers in GeometryAssessment Practice

6 marks~9 minCriterion D

Two students each measure the side of a square garden bed. Student A records 3.2 m; Student B records 3.3 m. The true side length is 3.25 m.

a

Calculate the actual area of the garden bed. Show your working. [1]

b

Calculate the percentage error in area for each student's measurement. State which measurement is more accurate. [3]

c

Identify one reason why the formula

A = \text{side}^2

may not give the exact area of a real garden bed. Explain how the shape of a real garden bed can differ from a perfect square. [2]

Solutions

23QuestionComposite Numbers and Their PropertiesAssessment Practice

5 marks~8 minCriterion C

A student claims: "Every composite number is the product of exactly two prime numbers."

A composite number has more than two factors. A prime number has exactly two factors: 1 and itself.

a

State the prime factorisation of 12, 18, and 30. [2]

b

Identify one example from part (a) that disproves the student's claim, and explain why the claim is incorrect. [2]

c

Compare the student's claim with the correct statement about prime factorisation of composite numbers. [1]

Solutions

24QuestionFinding Factors of a NumberAssessment Practice

4 marks~6 minCriterion D

A gardener plans a rectangular flower bed with an area of

36 \text{ m}^2

. She wants the side lengths to be whole numbers (integers).

a

List all pairs of integer side lengths that give an area of

36 \text{ m}^2

. [2]

b

The gardener considers using side lengths of

5.5 \text{ m}

and

6.5 \text{ m}

instead. Explain one advantage and one disadvantage of allowing non-integer side lengths in this design. [2]

Solutions

25QuestionPrime Factorization Using Factor TreesAssessment Practice

6 marks~9 minCriterion C

A student drew a factor tree for 72, shown below.

72

8 \quad \times \quad 9

2 \times 4 \qquad 3 \times 3

\quad\quad 2 \times 2

The student says the prime factors of 72 are 2, 2, 2, 3, and 3.

a

Identify one error in the student's factor tree. [1]

b

Draw a complete factor tree for 72, stopping only when every branch ends in a prime number. Write the prime factorisation in index form. [3]

c

Explain why any correct factor tree for 72 must always give the same prime factors. [2]

Solutions

26QuestionAbsolute Value of an IntegerAssessment Practice

4 marks~6 minCriterion C

A hiker leaves base camp, climbs

+150

m to a ridge, then descends

-200

m to a valley floor.

The hiker says: "My total vertical distance traveled is

350

m, because I add the absolute value of each change."

a

Calculate the hiker's total vertical distance traveled using absolute values. [2]

b

The hiker then climbs back up

+200

m to return to base camp. Explain why the absolute value model now underestimates the total vertical distance traveled, and state the correct total. [2]

Solutions

27QuestionOpposites and Zero on the Number LineAssessment Practice

6 marks~9 minCriterion B

The opposite of an integer is the number the same distance from zero on the other side of the number line. For example, the opposite of

+3

is

-3

.

A point starts at integer

n

. It moves to its opposite, then moves to the opposite of that result.

a

State the opposite of

-7

. [1]

b

Starting at

-7

, show the two opposite moves on a number line and identify the final position. [3]

c

A different point follows the same two moves and ends at

+4

. Compare the starting position with the ending position and explain what this tells you about any integer after two opposite moves. [2]

Solutions

28QuestionComparing and Ordering IntegersAssessment Practice

8 marks~12 minCriterion D

A student's bank account shows these balances over three weeks:

Week 1:

-15

dollars
Week 2:

+8

dollars
Week 3:

-3

dollars

Each Monday the student receives a

+10

dollar allowance; each Friday a

-5

dollar subscription fee is charged.

a

State the three balances in order from least to greatest. [2]

b

Calculate the net change in balance from Week 1 to Week 3, and find the adjusted Week 3 balance after including the allowance and subscription fee. [3]

c

Explain one way the integer model gives an incomplete picture of the student's real financial situation. [3]

Solutions

Number Concepts & Systems — Free MYP2 Mathematics Practice Questions