Algebra and Expressions — Free IB MYP2 Mathematics Questions

1QuestionCreating Algebraic Expressions from Word ProblemsConcept Practice

2 marks~3 minCriterion B

An L-shaped figure is built from squares. The table shows the pattern.

Figure number	1	2	3	4
Number of squares	3	5	7	9

a

Identify the number of squares in Figure 5. [1]

b

Write an algebraic expression for the number of squares in Figure

n

. [1]

Solutions

2QuestionChecking Solutions for Word-Based ExpressionsConcept Practice

4 marks~6 minCriterion C

A mobile phone plan charges a fixed monthly fee of 40 dollars plus 0.15 dollars per minute of calls. The total monthly cost in dollars is:

C = 40 + 0.15m

where

m

is the number of minutes used.

a

State whether a customer who used 200 minutes would pay a total of 65 dollars. Show your substitution. [2]

b

Calculate the total cost for a customer who uses 320 minutes. Show all working. [2]

Solutions

3QuestionChecking Solutions for Word-Based ExpressionsConcept Practice

2 marks~3 minCriterion A

A rectangle has a width of

(x + 2)

cm and a length of

(x + 5)

cm.

The perimeter of a rectangle is given by:

P = 2 \times (\text{length} + \text{width})

When

x = 3

, calculate the perimeter of the rectangle. Give your answer in centimetres. [2]

Solutions

4QuestionEvaluating Algebraic Formulas with Given ValuesConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths

a = 5

cm and

b = 3

cm. The perimeter of a rectangle is given by

P = 2(a + b).

Calculate the perimeter of this rectangle. [2]

Solutions

5QuestionBuilding Expressions from Verbal DescriptionsConcept Practice

2 marks~3 minCriterion B

Each apple costs 2 dollars and there is a fixed fee of 1 dollar.

Number of apples ( $n$ )	1	2	3	4
Total cost ( $C$ ) in dollars	3	5	7	9

a

Identify the expression for

C

in terms of

n

. [1]

b

Calculate the total cost when

n = 5

. [1]

Solutions

6QuestionDefining Constants and CoefficientsConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

3

cm and

x

cm, giving an area of

3x

cm².

a

Identify the variable in the expression

3x

. [1]

b

The number

3

in

3x

is called a coefficient — a number that multiplies a variable. State the value of the coefficient. [1]

Solutions

7QuestionConstructing Expressions with BracketsConcept Practice

3 marks~5 minCriterion A

A party organiser uses the relationship:

\text{Cost} = 50 + 15 \times (\text{number of guests})

where Cost is in dollars. Guests are seated equally across 4 tables, with

n

guests per table.

a

State the total number of guests in terms of

n

. [1]

b

Write an algebraic expression with brackets for the total cost in terms of

n

. [1]

c

A second venue charges a total cost of

50 + 15(5n)

dollars. Explain which venue costs more when

n = 3

, showing your working. [1]

Solutions

8QuestionForming Expressions with Multiple TermsConcept Practice

2 marks~3 minCriterion B

The table below shows the number of unit squares in square grids of increasing size.

Side length ( $n$ )	1	2	3
Number of unit squares	1	4	9

a

Identify the pattern shown in the table. [1]

b

Write an algebraic expression for the total number of unit squares in an

n \times n

grid. [1]

Solutions

9QuestionInterpreting Algebraic Expressions in ContextConcept Practice

2 marks~3 minCriterion C

A café's daily profit (in dollars) is modelled by the expression

3.50x - 25

, where

x

is the number of smoothies sold.

a

Identify what the values

3.50

and

25

each represent in this context. [1]

b

Calculate the profit when

x = 20

, showing your working. [1]

Solutions

10QuestionChecking Solutions for Word-Based ExpressionsAssessment Practice

4 marks~6 minCriterion D

A bike shop charges a 20 dollar deposit plus 3 dollars per hour. A student models the total cost in dollars as

20 + 3m

, where

m

is the number of hours rented, and claims this works for any value of

m

.

a

Identify two real-world limitations of this model. [2]

b

Calculate the cost given by the model for

m = 0.5

hours and for

m = 24

hours. For one of these durations, explain why the model may not reflect the actual cost. [2]

Solutions

11QuestionSubstituting Values into Simple ExpressionsAssessment Practice

4 marks~6 minCriterion B

Parity means whether a number is odd or even.

a

Complete the table by substituting

n = 1, 2, 3, 4, 5, 6

into

2n + 1

and

3n

. [1]

$n$	1	2	3	4	5	6
$2n + 1$	\_\_	\_\_	\_\_	\_\_	\_\_	\_\_
$3n$	\_\_	\_\_	\_\_	\_\_	\_\_	\_\_

b

Describe the parity pattern you see in each row of your table. [1]

c

n = 10

is an even number. State whether

2(10) + 1

and

3(10)

are odd or even, then calculate both values to verify. [2]

Solutions

12QuestionSubstituting Values into Simple ExpressionsAssessment Practice

4 marks~6 minCriterion C

A kayak rental company charges a flat fee of 25 dollars plus 10 dollars per half-hour (30-minute block). A student models the cost

C

(in dollars) for

h

hours as

C = 25 + 10h

.

a

Calculate the cost for a 3-hour booking using the student's formula. [1]

b

Calculate the actual cost for a 3-hour booking using the company's pricing structure. [1]

c

Compare the student's formula with the company's pricing structure for bookings of 2.5 hours and 3.5 hours. State which booking shows a difference and explain why. [2]

Solutions

13QuestionSubstitution with Negative and Decimal ValuesAssessment Practice

6 marks~9 minCriterion D

A scientist uses the formula

F = 1.8C + 32

to convert temperatures from Celsius to Fahrenheit. A thermometer has a systematic error (a fixed, consistent offset) of

-2°\text{C}

, meaning every reading is

2°\text{C}

lower than the true temperature. The scientist records

-10°\text{C}

in Antarctica.

a

Calculate the Fahrenheit value for the recorded temperature

C = -10

. Show your substitution clearly. [2]

b

The true temperature is

-8°\text{C}

after correcting for the error. Calculate the Fahrenheit value for the true temperature, then state the difference in Fahrenheit between your two results. [2]

c

The systematic error of

-2°\text{C}

was measured in a warm laboratory. Explain why this error value may not be reliable when the thermometer is used in Antarctica. [2]

Solutions

14QuestionBuilding Expressions from Verbal DescriptionsAssessment Practice

2 marks~3 minCriterion D

A fruit seller uses the expression

3a + 2b = 5.50

where

a

is the cost of one apple (in dollars) and

b

is the cost of one banana (in dollars).

Explain one real-world limitation of using this expression to model the fruit seller's prices. [2]

Solutions

15QuestionRecognizing Like and Unlike TermsAssessment Practice

6 marks~9 minCriterion C

Tom buys apples at

a

dollars each and bananas at

b

dollars each. He writes his total cost as

3a + 2b + 5a

and simplifies it to

5a + 5b

.

a

Identify the error in Tom's simplification. [1]

b

Explain why

3a

and

2b

cannot be combined. In your answer, refer to what

a

and

b

represent. [2]

c

Compare the correct total cost with Tom's incorrect total cost when

a = 2

and

b = 3

. State whether Tom overestimates or underestimates, and describe one practical consequence. [3]

Solutions

16QuestionCreating Expressions from Situational ProblemsAssessment Practice

5 marks~8 minCriterion D

A student runs a school bake sale, selling brownies for

1.50

each and cookies for

0.75

each. The expression

1.5b + 0.75c

models the total amount raised in dollars, where

b

is the number of brownies and

c

is the number of cookies sold. A rounded version,

2b + c

, is used to estimate the total quickly.

The student sells

12

brownies and

20

cookies. The pizza party costs

45

dollars.

a

Calculate the actual total raised using

1.5b + 0.75c

. [1]

b

Calculate the estimated total using

2b + c

. State whether each model suggests the student has raised enough for the pizza party. [2]

c

Compare the two models and explain how rounding could lead to a wrong decision about buying the pizza party. [2]

Solutions

Algebra and Expressions — Free MYP2 Mathematics Practice Questions