Ratio, Proportion & Percentages — Free IB MYP2 Mathematics Questions

1QuestionSolving Problems Involving Inverse ProportionConcept Practice

2 marks~3 minCriterion B

The table below shows values of

x

and

y

.

$x$	2	3	4	6	8
$y$	12	8	6	4	?

a

Identify the relationship between

x

and

y

. [1]

b

Calculate the missing value of

y

when

x = 8

. [1]

Solutions

2QuestionUnderstanding Direct Proportion RelationshipsConcept Practice

3 marks~5 minCriterion A

A car travels at a steady speed. The graph of its journey is a straight line through the origin.

Time (hours)	1	2	3	4
Distance (km)	60	120	180	240

a

Identify the type of relationship between distance and time. [1]

b

Explain why the ratio

\dfrac{\text{distance}}{\text{time}}

stays the same for every point on the line. [1]

c

A second car travels 300 km in 4 hours. Compare the speeds of the two cars and state which car is faster. [1]

Solutions

3QuestionApplications of Compound Interest and DepreciationConcept Practice

2 marks~3 minCriterion B

An investment of 100 dollars grows at a compound interest rate (interest calculated on the growing total each year) of

5\%

per year.

Year	1	2	3	4
Value (dollars)	105.00	110.25	115.76	121.55

a

Describe the pattern in the values from one year to the next. [1]

b

Calculate the predicted value of the investment at the end of Year 5. Show your working. [1]

Solutions

4QuestionFinding a Percentage of a QuantityConcept Practice

2 marks~3 minCriterion A

A rectangle is divided into 100 equal squares. Exactly 42 of these squares are shaded.

a

Calculate the percentage of the rectangle that is shaded. Show your working. [1]

b

Calculate the value of

42\%

of

300

. Show your working. [1]

Solutions

5QuestionComparing Percentage Gains and LossesConcept Practice

3 marks~5 minCriterion A

A line graph shows the value of two investments over 4 years.

Investment A: starts at 100 dollars in Year 1, rises to 160 dollars in Year 4.
Investment B: starts at 100 dollars in Year 1, rises to 190 dollars in Year 4.

a

State the formula for percentage increase. [1]

b

Calculate the percentage increase for each investment. [1]

c

Compare the two percentage increases and identify which investment performed better. [1]

Solutions

6QuestionFinding Original Amounts Before ChangeConcept Practice

2 marks~3 minCriterion B

A shop records the final price of four items after a percentage change.

Item A	$+10\%$ change	final price 55 dollars
Item B	$-20\%$ change	final price 40 dollars
Item C	$+25\%$ change	final price 50 dollars
Item D	$-50\%$ change	final price 30 dollars

a

Calculate the original price of each item. [1]

b

Using your results, describe a general rule for finding the original price from the final price and the percentage change. [1]

Solutions

7QuestionFinding Original Amounts Before ChangeConcept Practice

2 marks~3 minCriterion A

A rectangle's length measures 34 cm after being reduced by 15%.

a

Identify the percentage of the original length that 34 cm represents. [1]

b

Calculate the original length of the rectangle. [1]

Solutions

8QuestionApplying Multiple Percent Changes TogetherConcept Practice

2 marks~3 minCriterion A

A jacket has an original price of $50. A shop first increases the price by 10%, then decreases the new price by 10%.

a

Calculate the price of the jacket after the 10% increase. [1]

b

Calculate the final price of the jacket after the 10% decrease is also applied. [1]

Solutions

9QuestionSimplifying Ratios to Lowest TermsConcept Practice

3 marks~5 minCriterion A

A baker uses flour and sugar in three recipes.

Recipe A	Flour $= 6$ cups	Sugar $= 4$ cups
Recipe B	Flour $= 9$ cups	Sugar $= 6$ cups
Recipe C	Flour $= 12$ cups	Sugar $= 8$ cups

a

State the ratio of flour to sugar for Recipe A. [1]

b

Calculate the simplified ratio of flour to sugar for Recipe B and Recipe C. [1]

c

Compare the three ratios and explain what this tells you about the relationship between flour and sugar across all three recipes. [1]

Solutions

10QuestionUnderstanding Direct Proportion RelationshipsAssessment Practice

4 marks~6 minCriterion D

A student converts 50 USD to euros using the equation:

\text{euros} = 0.92 \times \text{USD}

The bank also charges a fixed transaction fee of 3 euros.

a

Calculate the number of euros the student actually receives after the fee is deducted. [1]

b

Explain why the equation above does not accurately model this real currency exchange. [2]

c

Compare the proportional model with the real exchange process and identify one limitation of the model. [1]

Solutions

11QuestionReal-Life Applications of ProportionalityAssessment Practice

3 marks~5 minCriterion C

The graph below shows the distance travelled over time for two objects, A and B.

Object A — Time (hours): 0, 1, 2, 3, 4, 5 | Distance (km): 0, 10, 20, 30, 40, 50

Object B — Time (hours): 0, 1, 2, 3, 4, 5 | Distance (km): 0, 5, 15, 20, 30, 35

a

Identify which object shows a directly proportional relationship between distance and time. [1]

b

Explain how the graph of your answer to part (a) confirms that the relationship is directly proportional. [1]

c

Compare the two graphs and explain why Object B does not show direct proportion. [1]

Solutions

12QuestionSolving Percentage Increase and Decrease ProblemsAssessment Practice

2 marks~3 minCriterion C

A video game costs 40 dollars. A store applies a 25% discount, then adds 8% sales tax (a government charge on the sale price).

a

Calculate the final price the customer pays. Show each step clearly. [1]

b

Explain why using a single percentage change of −17% does not give the same final price. [1]

Solutions

13QuestionFinding a Percentage of a QuantityAssessment Practice

4 marks~6 minCriterion D

A school surveyed 240 students about their preferred lunch option. The results showed that 65% preferred Option A. On the day of the survey, 150 students actually chose Option A in the cafeteria.

a

Calculate the number of students the survey predicted would choose Option A. [2]

b

Compare the predicted number with the actual number, and explain one reason for the difference. [2]

Solutions

14QuestionIdentifying Percentage Markups and DiscountsAssessment Practice

6 marks~9 minCriterion C

A store adds a 15% markup to the cost price of every item to set the marked price. During a sale, a 25% discount is applied to the marked price. The manager claims the jacket's final price is 10% above the cost price, reasoning that

25\% - 15\% = 10\%

.

The cost price of the jacket is 80 dollars.

a

Calculate the final sale price of the jacket. Show each step clearly. [2]

b

Calculate the actual percentage change from the cost price to the final price. Explain why the manager's method of subtracting percentages gives the wrong answer. [3]

c

The store uses the same 15% markup for every product it sells. Compare this fixed-markup model with a flexible approach, and give one reason why a single markup rate may not suit all products. [1]

Solutions

15QuestionIdentifying Percentage Markups and DiscountsAssessment Practice

3 marks~5 minCriterion B

A store applies a markup (an amount added to the original price) to every item it sells. The graph below shows three items with points at original prices of 10 dollars, 20 dollars, and 40 dollars.

a

Identify the selling price for the item with an original price of 20 dollars. [1]

b

Calculate the percentage markup for any two items shown on the graph. [1]

c

A rival store offers the same items at a flat 45% markup. Explain which store charges more, using your results from part (b). [1]

Solutions

16QuestionCalculating Percentage ChangeAssessment Practice

4 marks~6 minCriterion D

A video game's price rises from 25 dollars to 30 dollars. A jacket's price falls from 40 dollars to 32 dollars.

a

Calculate the percentage change in price for each item. Show your working. [2]

b

Both percentage changes are equal in size. Compare the impact of these two changes on a shopper's budget and explain which change is more harmful. [2]

Solutions

17QuestionReal-World Applications of Reverse PercentageAssessment Practice

6 marks~9 minCriterion C

A jacket's sale price is 85 dollars after a 15\% discount.

Aisha says: "Divide the sale price by $0.85$ to find the original price."
Ben says: "Multiply the sale price by $1.15$ to find the original price."

a

State an equation that relates the original price

P

and the sale price

S

after a 15\% discount. [1]

b

Calculate the original price using Aisha's method. Show your working. [2]

c

Compare both methods using the sale price of 85 dollars. Explain why Ben's method gives the wrong answer. [3]

Solutions

18QuestionUsing Equations to Solve Reverse PercentagesAssessment Practice

6 marks~9 minCriterion D

A laptop costs 118 dollars after 18% sales tax (a charge added on top of the original price) is included.

a

State an equation for this situation, using

x

for the pre-tax price. Do not solve it. [1]

b

Calculate the pre-tax price by solving your equation. Show all working. [2]

c

The tax rate is later said to be either 17.5% or 18.5% due to rounding. Calculate the pre-tax price for each rate, then compare the two results and explain whether the reverse percentage model is still reliable. [3]

Solutions

19QuestionUsing Discounts in Shopping ScenariosAssessment Practice

2 marks~3 minCriterion B

A store sells items priced at 50 dollars, 100 dollars, 150 dollars, and 200 dollars, offering discounts of 10%, 20%, 30%, and 40%.

Original price (dollars)	50	100	150	200
10% discount sale price (dollars)	45	90	135	180
20% discount sale price (dollars)	40	80	120	160
30% discount sale price (dollars)	35	70	105	140
40% discount sale price (dollars)	30	60	90	120

a

Identify the pattern linking the original price, the discount percentage, and the sale price. [1]

b

Write an equation for the sale price in terms of the original price and the discount percentage. [1]

Solutions

20QuestionCalculating Profit and Loss with PercentagesAssessment Practice

6 marks~9 minCriterion D

A shop owner buys an item for 200 dollars and sells it at a 25% markup (markup means the amount added to the cost price). During a sale, the marked price is reduced by 10%. A 5% sales tax is then added to the reduced price.

a

Calculate the final price paid by the customer. [2]

b

Calculate the owner's actual profit percentage based on the cost price. [2]

c

The owner expects a 25% profit from every sale. Explain one reason why the actual profit percentage differs from 25%, and describe how this affects the owner's earnings. [2]

Solutions

21QuestionApplying Multiple Percent Changes TogetherAssessment Practice

4 marks~6 minCriterion C

A store sells a jacket for 80 dollars. It applies a 20% discount, then a further 15% discount on the reduced price.

a

Calculate the final price of the jacket after both discounts are applied. [2]

b

A customer claims the total discount is

20\% + 15\% = 35\%

, giving a final price of 52 dollars. Explain why this reasoning is incorrect. [2]

Solutions

22QuestionDefining Ratios and Their NotationAssessment Practice

6 marks~9 minCriterion B

Four bags contain red and blue counters.

Bag 1	2 red	4 blue
Bag 2	3 red	6 blue
Bag 3	4 red	8 blue
Bag 4	5 red	10 blue

a

State the ratio of red to blue counters for Bag 1 in simplest form. [1]

b

Calculate the simplified ratio of red to blue counters for Bag 3, showing your working. [2]

c

Compare the ratios across all four bags and explain whether they are equivalent, using the variables

r

(red) and

b

(blue) to express any pattern you find. [3]

Solutions

23QuestionDefining Ratios and Their NotationAssessment Practice

5 marks~8 minCriterion C

A student claims that

3:4

and

9:12

are equivalent ratios. Their reasoning: since

3 + 6 = 9

and

4 + 8 = 12

, the ratios must be the same.

a

Identify the single multiplier that converts

3:4

into

9:12

. [1]

b

Calculate the cross-products of

\dfrac{3}{4}

and

\dfrac{9}{12}

and state whether the ratios are equivalent. [2]

c

Explain the flaw in the student's reasoning. [2]

Solutions

24QuestionDefining Ratios and Their NotationAssessment Practice

5 marks~8 minCriterion D

A cake recipe uses a flour-to-sugar ratio of

2:3

.

a

State whether

10:15

is equivalent to

2:3

. Show your working. [1]

b

Calculate the simplest form of

8:12

and explain whether it matches the recipe ratio. [2]

c

Each measuring cup has a

\pm 5\%

error. Compare how this error could affect the two scaled-up versions of the recipe differently. [2]

Solutions

Ratio, Proportion & Percentages — Free MYP2 Mathematics Practice Questions