Ratio, Proportion & Percentages — Free IB MYP1 Mathematics Questions

1QuestionConcept Practice

3 marks~5 minCriterion D

A pancake recipe for 4 servings uses 240 g of flour.

a

State how many grams of flour are needed for one serving. [1]

b

Calculate the amount of flour needed for 7 servings. Show your working. [1]

c

Describe one reason why doubling a recipe does not always mean doubling every ingredient. [1]

Solutions

2QuestionConcept Practice

2 marks~3 minCriterion A

A map of a park uses the scale

1 \text{ cm} = 50 \text{ m}

. The path from the entrance to the fountain measures

4 \text{ cm}

on the map.

a

Calculate the real distance, in metres, from the entrance to the fountain. [1]

b

Describe what happens to the scale if the map is printed at a smaller size. [1]

Solutions

3QuestionConcept Practice

6 marks~9 minCriterion B

Four squares are drawn in a row. Their side lengths are

1

cm,

2

cm,

3

cm, and

4

cm.

Side length (cm)	$1$	$2$	$3$	$4$
Area (cm $^2$ )	___	___	___	___

a

Identify the area of each square. [2]

b

Describe how the area changes as the side length increases by

1

cm each time. [2]

c

Describe whether the relationship between side length and area is a direct proportion. Give a reason using the numbers from your table. [2]

Solutions

4QuestionFinding a Percentage of a QuantityConcept Practice

5 marks~8 minCriterion C

A shop sells two items.

Item A costs 200 dollars and is on sale for 15\% off.
Item B costs 100 dollars and is on sale for 30\% off.

a

Calculate the discount amount on Item A. [1]

b

Calculate the discount amount on Item B. [2]

c

A student says: "The discount on Item A is the same as the discount on Item B." State whether this claim is true or false, and describe what your two answers tell you about the two discounts. [2]

Solutions

5QuestionUnderstanding Percentages as Fractions and DecimalsConcept Practice

2 marks~3 minCriterion B

A shop puts a

30\%

discount on a backpack that costs

40

dollars.

a

Write

30\%

as a fraction and as a decimal. [1]

b

Describe how the dollar saving changes if the original price of the backpack goes up. [1]

Solutions

6QuestionFinding a Percentage of a QuantityConcept Practice

2 marks~3 minCriterion D

A toy costs 30 dollars. A shop offers a

10\%

discount.

a

Calculate the sale price of the toy. [1]

b

Describe whether the discount amount is realistic for a shop to use. [1]

Solutions

7QuestionFinding a Percentage of a QuantityConcept Practice

2 marks~3 minCriterion A

A rectangle has sides of 80 cm and 50 cm.

a

Identify which side length you need to find 25% of to answer this question. [1]

b

Calculate 25% of that side length. Give your answer in centimetres. [1]

Solutions

8QuestionIdentifying Percentage Markups and DiscountsConcept Practice

2 marks~3 minCriterion B

A shop adds a markup to the price of each item.

Original price (dollars)	10	20	30	40
Markup amount (dollars)	3	6	9	12

a

Identify the markup percentage. [1]

b

Describe how the markup amount changes as the original price increases. [1]

Solutions

9QuestionSolving Real-Life Percent Change ScenariosConcept Practice

2 marks~3 minCriterion A

A jacket costs $80. During a sale, the price is reduced by 25%.

a

State the amount the price is reduced by. [1]

b

Calculate the sale price of the jacket. [1]

Solutions

10QuestionIdentifying Percentage Markups and DiscountsConcept Practice

2 marks~3 minCriterion D

A shop sells a jacket for 50 dollars. It offers a 30% discount.

a

Identify one reason why a shop might show a price ending in a whole dollar rather than in cents. [1]

b

Describe what the customer pays for the jacket after the 30% discount is applied. [1]

Solutions

11QuestionSolving Markup and Discount Reversal ProblemsConcept Practice

2 marks~3 minCriterion B

A shop adds 20% to the original price of every item.

Original price (dollars)	10	20	30	40
Selling price (dollars)	12	24	36	48

a

Identify the rule that links the original price to the selling price. [1]

b

Calculate the selling price for an original price of 50 dollars. Show your working. [1]

Solutions

12QuestionFinding Original Amounts Before ChangeConcept Practice

2 marks~3 minCriterion D

A jacket costs 42 dollars after a 30% discount.

a

Calculate the original price of the jacket. [1]

b

Describe one reason why the original price you calculated may not match the price shown on the original price tag in a real shop. [1]

Solutions

13QuestionUnderstanding and Applying Sales TaxConcept Practice

2 marks~3 minCriterion B

A toy costs 10 dollars. The table below shows the total cost after adding different sales tax rates.

Tax rate (\%)	5	8	10	12
Total cost (dollars)	10.50	10.80	11.00	11.20

a

Identify the pattern shown in the table. [1]

b

Calculate the total cost of the toy at a tax rate of 15\%. [1]

Solutions

14QuestionCalculating Profit and Loss with PercentagesConcept Practice

2 marks~3 minCriterion D

A student buys a pack of trading cards for 8 dollars and sells it to a friend for 10 dollars.

a

Give an example of one situation in real life where calculating profit percentage is useful. [1]

b

The student also paid 2 dollars in bus fare to meet the friend. Describe how this extra cost changes whether the student actually made a profit. [1]

Solutions

15QuestionUnderstanding and Applying Sales TaxConcept Practice

2 marks~3 minCriterion C

A student buys a backpack for 25 dollars. The local sales tax rate is 6%. The receipt shows a total of 26.75 dollars.

a

Calculate the correct total cost after adding 6% sales tax. [1]

b

State whether the receipt total is correct or incorrect, and give one reason. [1]

Solutions

16QuestionCalculating Profit and Loss with PercentagesConcept Practice

2 marks~3 minCriterion A

A shop buys a jacket for 50 dollars and sells it for 65 dollars.

a

State the profit the shop makes on the jacket. [1]

b

Calculate the profit percentage using the formula below. [1]

\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100

Solutions

17QuestionDefining Ratios and Their NotationConcept Practice

2 marks~3 minCriterion B

Look at this sequence of ratios:

2:3

,

4:6

,

6:9

,

8:12

.

a

Identify how each ratio in the sequence is made from

2:3

. [1]

b

Write the next two ratios in the sequence. [1]

Solutions

18QuestionDefining Ratios and Their NotationConcept Practice

8 marks~12 minCriterion A

A recipe uses 3 cups of flour and 4 cups of oats. The tape diagram below shows two bars made of equal-sized units.

a

Label each bar in the tape diagram to show the ratio

3:4

. [1]

b

List four equivalent ratios for

3:4

. Include

6:8

and

9:12

in your list. [3]

c

Describe how you can tell that

6:8

and

9:12

are both equivalent to

3:4

. [4]

Solutions

19QuestionDefining Ratios and Their NotationConcept Practice

2 marks~3 minCriterion D

A fruit punch recipe uses 2 cups of orange juice and 3 cups of lemonade.

a

State the ratio of orange juice to lemonade using colon notation. [1]

b

Describe what happens to the taste of the punch if you use too much orange juice. [1]

Solutions

20QuestionAdjusting Quantities Using RatiosConcept Practice

4 marks~6 minCriterion C

A pancake recipe makes enough for 4 people. It needs 120 g of flour and 2 eggs.

a

Identify the scale factor needed to adjust the recipe for 10 people. [1]

b

Calculate the amount of flour needed for 10 people. [1]

c

A friend says: "I just double the eggs, so I'll use 4 eggs for 10 people." Describe why your answer for the number of eggs is different from your friend's answer. [2]

Solutions

21QuestionComparing Ratios in Real-World ScenariosConcept Practice

2 marks~3 minCriterion B

Four paint mixtures are made using red and blue paint.

Mixture A	2 cups red	3 cups blue
Mixture B	4 cups red	6 cups blue
Mixture C	6 cups red	9 cups blue
Mixture D	8 cups red	12 cups blue

a

Identify which mixtures have the same ratio of red to blue paint. [1]

b

Describe the pattern you see in the amounts of red and blue paint across the four mixtures. [1]

Solutions

22QuestionAdjusting Quantities Using RatiosConcept Practice

2 marks~3 minCriterion D

A recipe for 4 people uses 200 g of flour and 2 eggs.

a

Describe how you would use a ratio to work out the amount of flour needed for 10 people. [1]

b

Give one reason why this ratio method may not work perfectly in real life. [1]

Solutions

23QuestionAdjusting Quantities Using RatiosConcept Practice

2 marks~3 minCriterion A

A rectangle has a width of 6 cm. The ratio of width to length is

2 : 3

.

Calculate the length of the rectangle. [2]

Solutions

24QuestionAssessment Practice

6 marks~9 minCriterion C

A fruit punch recipe uses 300 mL of orange juice for every 4 servings.

a

State how many mL of orange juice are needed for 1 serving. [1]

b

Calculate the amount of orange juice needed for 7 servings. Show your working. [2]

c

A student says: "525 mL is needed for 7 servings, so I can double it to get the amount for 10 servings." Describe why the student's method is wrong and give the correct amount for 10 servings. [3]

Solutions

25QuestionCalculating Percentage ChangeAssessment Practice

6 marks~9 minCriterion C

A shop sells a jacket for

\$100

.

a

The price goes up by

10\%

, then comes back down by

10\%

. Calculate the final price. [2]

b

Describe what you notice about the final price compared to

\$100

. [1]

c

A friend says: "Going up by

10\%

then down by

10\%

always gets you back to the start." Compare what happens when you increase by

10\%

then decrease by

10\%

with what happens when you increase by

20\%

then decrease by

20\%

, and use both results to explain whether your friend is right. [3]

Solutions

26QuestionSolving Markup and Discount Reversal ProblemsAssessment Practice

4 marks~6 minCriterion C

A jacket is on sale. The sale price is 60 dollars after a 25% discount.

a

State what percentage of the original price the sale price represents. [1]

b

Calculate the original price of the jacket. [2]

c

A friend says: "I can find the original price by adding 25% to 60 dollars." Describe why this gives the wrong answer. [1]

Solutions

27QuestionFinding Original Amounts Before ChangeAssessment Practice

2 marks~3 minCriterion A

A shop reduces the price of a book by 25%. The sale price is £9.

Calculate the original price of the book. [2]

Solutions

28QuestionSimplifying Ratios to Lowest TermsAssessment Practice

6 marks~9 minCriterion C

A pancake recipe uses

3

cups of flour and

2

cups of milk.
A student halves the recipe and rounds

1.5

cups of flour up to

2

cups, keeping

1

cup of milk.

a

State whether

3:2

is already in its simplest form. Give a reason for your answer. [2]

b

Describe why the ratio

2:1

(rounded amounts) is not the same as the ratio

3:2

(original recipe). [2]

c

Compare what happens to a recipe when you use exact ratios with what happens when you must round amounts to fit your measuring cups. [2]

Solutions

Ratio, Proportion & Percentages — Free MYP1 Mathematics Practice Questions