Algebra and Expressions — Free IB MYP1 Mathematics Questions

1QuestionCombining Like TermsConcept Practice

2 marks~3 minCriterion B

The diagram shows a row of squares growing one square at a time.

Shape 1 has 1 square. Shape 2 has 2 squares. Shape 3 has 3 squares.

a

Identify how many squares Shape 4 has. [1]

b

Describe, in one sentence, how the number of squares changes each time the shape number goes up by one. [1]

Solutions

2QuestionCombining Like TermsConcept Practice

2 marks~3 minCriterion A

A rectangle has side lengths of

(2x + 3)

cm and

(x + 5)

cm. Its perimeter is 40 cm.

Using

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

, calculate the value of

x

. [2]

Solutions

3QuestionExpanding Single Bracket ExpressionsConcept Practice

6 marks~9 minCriterion A

You are buying 5 packs of juice for a class party. Each pack costs 8 dollars, and the delivery fee is 3 dollars per pack. The total cost can be written as

5(8 + 3)

.

a

Calculate the total cost by expanding

5(8 + 3)

. Show all your working. [2]

b

Describe what the numbers 8 and 3 inside the brackets represent in this situation. [2]

c

The delivery fee changes to 2 dollars per pack. Write the new expression for the total cost and describe how it is different from

5(8 + 3)

. [2]

Solutions

4QuestionExpanding Single Bracket ExpressionsConcept Practice

2 marks~3 minCriterion B

The diagram shows a rectangular garden with a length of

4

m and a total width of

(x + 3)

m. A dividing line splits it into two smaller rectangles: one of width

x

m and one of width

3

m.

a

State the area of each smaller rectangle. [1]

b

Describe how the two smaller areas show that

4(x + 3) = 4x + 12

. [1]

Solutions

5QuestionChecking Solutions for Word-Based ExpressionsConcept Practice

2 marks~3 minCriterion D

You have 20 dollars to spend at a school canteen. A sandwich costs 5 dollars, a juice costs 3 dollars, and a cookie costs 2 dollars.

a

Calculate the correct total cost of one sandwich, one juice, and one cookie. [1]

b

Your classmate says the total is 12 dollars. Describe one reason why checking your answer by substituting the actual prices is useful. [1]

Solutions

6QuestionCreating Algebraic Expressions from Word ProblemsConcept Practice

2 marks~3 minCriterion B

A student makes square patterns using tiles. The number of tiles in each pattern follows the sequence:

1, \ 4, \ 9, \ \ldots

a

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

b

Describe the rule for finding the total number of tiles for any side length. [1]

Solutions

7QuestionChecking Solutions for Word-Based ExpressionsConcept Practice

2 marks~3 minCriterion A

A rectangle has two short sides of

(x + 3)

cm each and two long sides of

2x

cm each.

A student says the perimeter is

(6x + 6)

cm.

a

Calculate the perimeter by adding all four sides. [1]

b

Substitute

x = 4

into your answer from (a) and into

(6x + 6)

. State whether the student is correct. [1]

Solutions

8QuestionUsing Substitution in Real-World FormulaeConcept Practice

2 marks~3 minCriterion C

A rectangular garden has a length

l

and a width

w

.

a

State the formula for the perimeter

P

of the rectangle, using

l

and

w

. [1]

b

Describe what the number 2 represents in the formula

P = 2l + 2w

. [1]

Solutions

9QuestionUsing Substitution in Real-World FormulaeConcept Practice

4 marks~6 minCriterion B

A savings account uses the formula

I = P \times R \times T

, where

I

is the interest earned.

Account details:
Starting amount: 500 dollars
Interest rate: 3
Time: 2 years

a

Name what

P

,

R

, and

T

stand for in this formula. [1]

b

Describe what happens to

I

when you substitute

P = 500

,

R = 3

, and

T = 2

into the formula. [1]

c

Compare the interest earned when

T = 2

and when

T = 4

. What do you notice? [2]

Solutions

10QuestionEvaluating Algebraic Formulas with Given ValuesConcept Practice

3 marks~5 minCriterion A

A rectangular garden has a length of 8 m and a width of 5 m. The perimeter is found using

P = 2l + 2w

where

l

is the length and

w

is the width.

a

State the value of

l

and the value of

w

for this garden. [1]

b

Calculate the perimeter

P

of the garden. Show your working. [2]

Solutions

11QuestionDefining Constants and CoefficientsConcept Practice

4 marks~6 minCriterion C

A student uses this equation to work out their weekly allowance:

\text{Total} = 5w + 10

where

w

is the number of chores completed, and all amounts are in dollars.

a

Name what the number

10

represents in this equation. [1]

b

Describe what the number

5

tells you about how the allowance is calculated. [1]

c

The student says this equation works for any number of chores. Describe one way the equation for a friend's allowance could be different, and explain why. [2]

Solutions

12QuestionBuilding Expressions from Verbal DescriptionsConcept Practice

6 marks~9 minCriterion B

A gardener plants trees in rows. Row 1 has 3 trees, Row 2 has 5 trees, and Row 3 has 7 trees. Each row has 2 more trees than the row before it.

a

Identify the number of trees in Row 4 and Row 5. [2]

b

Describe, in one sentence, the rule that connects the row number

n

to the number of trees in that row. [2]

c

Calculate the number of trees in Row 10 using the expression

2n + 1

. [2]

Solutions

13QuestionUnderstanding the Use of Letters in MathConcept Practice

4 marks~6 minCriterion A

A fruit stall sells pears and apples. There are 12 more apples than pears. The total number of fruits is 50. Let

p

= number of pears and

a

= number of apples.

a

State one equation that shows the total number of fruits. [1]

b

State one equation that links the number of apples to the number of pears. [1]

c

Calculate the number of pears and the number of apples. Show your working. [2]

Solutions

14QuestionCreating Expressions from Situational ProblemsConcept Practice

2 marks~3 minCriterion B

A shop arranges square tiles in a growing pattern.

Pattern 1: 1 tile
Pattern 2: 3 tiles
Pattern 3: 5 tiles
Pattern 4: 7 tiles

a

State the number of tiles in Pattern 5. [1]

b

Write an expression for the number of tiles in Pattern

n

. [1]

Solutions

15QuestionConstructing Expressions with BracketsConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of

(x + 3)

cm and a width of

5

cm.

Its perimeter is given by

2(x + 3) + 2(5)

.

Calculate the perimeter of the rectangle when

x = 4

. [2]

Solutions

16QuestionUsing the Distributive PropertyAssessment Practice

5 marks~8 minCriterion C

A garden has two sections side by side, both with a width of 3 m. One section is 4 m long and the other is

x

m long.

a

Identify the expression that shows the total area of the garden as a single multiplication. [1]

b

Calculate the total area of the garden when

x = 5

, using both expressions below. Show your working.

3(4 + x) \qquad \text{and} \qquad 3 \times 4 + 3 \times x

[2]

c

Describe one way in which the expression

3(4 + x)

and the expression

3 \times 4 + 3 \times x

are the same and one way in which they are different. [2]

Solutions

17QuestionUsing the Distributive PropertyAssessment Practice

6 marks~9 minCriterion D

A rectangular garden bed has a length of

(x + 3)

metres and a width of

(x + 2)

metres, where

x

is a whole number.

a

Name the expression for the area of the garden bed. [1]

b

Calculate the area when

x = 4

. Show your working. [2]

c

A friend says: "This formula will always give the exact area of any real garden."

Describe one reason why this might not be true, and give an example of a garden feature that would cause a problem. [3]

Solutions

18QuestionCreating Equivalent Expressions through ExpansionAssessment Practice

6 marks~9 minCriterion D

You are tiling a rectangular patio. The width is 5 metres. The length is (x + 3) metres, where x is the length (in metres) of an extension that will be built later.

a

[2 marks] Write an expression for the area of the patio in expanded form.

b

[2 marks] The tiles cost 20 dollars per square metre. Write an expression for the total cost of the tiles in expanded form.

c

[4 marks] Suppose you measure the extension length x with a tape measure that has an accuracy of ±0.1 m. Evaluate the real-world significance and limitations of using the algebraic expression from part (b) to predict the total cost. In your response, discuss how the measurement error affects the reliability of the cost estimate and suggest one way to improve the accuracy of the prediction.

Solutions

19QuestionCreating Equivalent Expressions through ExpansionAssessment Practice

6 marks~9 minCriterion C

A gardener uses the expression $2(x+3)$ to calculate the number of paving stones needed for a straight rectangular path of width $x$ meters. The path is shown in the diagram.

a

[2 marks] Explain why the expression

2(x+3)

gives the number of stones for a straight rectangular path, assuming each stone covers 1 square meter.

b

[2 marks] The actual path has a curved section and a small flower bed in the middle, as shown in the diagram. Discuss whether the model

2(x+3)

is still valid for this actual path. Identify one limitation of the model.

c

[2 marks] Suggest a different expression that would be more accurate for the actual path, and explain why your expression is better.

Solutions

20QuestionWriting Multi-Step Expressions from SituationsAssessment Practice

4 marks~6 minCriterion C

A rectangle has a length of 10 cm and a width of

w

cm.

a

Name the unknown measurement in the rectangle. [1]

b

Describe the expression for the perimeter of the rectangle. [2]

c

Compare the perimeter when

w = 3

with the perimeter when

w = 6

. [1]

Solutions

21QuestionSolving Problems Using Substitution TechniquesAssessment Practice

2 marks~3 minCriterion D

Your class is planning a picnic. The total cost in dollars is:

\text{Total cost} = 8 \times \text{number of students} + 15

The $15 is a fixed booking fee. The $8 covers food and drinks for each student.

Describe one reason why this formula may give the wrong total cost if some students bring their own lunch. [2]

Solutions

22QuestionBuilding Expressions from Verbal DescriptionsAssessment Practice

4 marks~6 minCriterion D

A baker uses the expression

5c + 3m

to find the total cost in dollars for making

c

cakes and

m

muffins.

a

Identify the constant in the expression

5c + 3m

. [1]

b

Calculate the total cost for 4 cakes and 6 muffins using

5c + 3m

. [1]

c

The cost per cake can go up or down by 1 dollar each day. Describe one way the expression

5c + 3m

is limited and one way the baker could change it to give a better estimate. [2]

Solutions

23QuestionConstructing Expressions with BracketsAssessment Practice

4 marks~6 minCriterion D

A rectangular garden has length

l

metres and width

w

metres. A semicircular flower bed is attached to one of the shorter sides, replacing that side with a curved edge.

a

Name the measurement that the curved edge replaces. [1]

b

Give an example of what the total perimeter of the garden looks like as an expression, using brackets, when the curved edge is included. [2]

c

Describe one way the expression with the curved edge gives a different result from the plain rectangle formula

2(l + w)

. [1]

Solutions

24QuestionConstructing Expressions with BracketsAssessment Practice

3 marks~5 minCriterion C

You are buying packs of stickers and packs of pencils for a party. Each pack of stickers has 3 stickers. Each pack of pencils has 2 pencils. You buy 4 packs of stickers and 5 packs of pencils, then give away 2 packs of stickers.

a

Write an expression with brackets that shows the total number of stickers and pencils you have left after giving away the sticker packs. [1]

b

Describe what the brackets in your expression tell you to do first, and why this matters. [1]

c

A friend works out the total without brackets, getting the answer 8. Compare this with your answer and describe what your friend calculated incorrectly. [1]

Solutions

Algebra and Expressions — Free MYP1 Mathematics Practice Questions