Post-LearningAssessment

Year 8 Module 4: Proportional Reasoning

Name: ………………………………………………………………….

Class: ……………………………………………………………………

Teacher: ……………………………………………………………….

What have we learnt this half term?

Unit 7: Percentage Change In this Unit you consolidated your understanding of percentages including percentages greater than 100, expressing a

quantity as a percentage of another and comparing two quantities using percentages. You also learnt to increase or decrease a quantity by a given percentage and use reverse percentages to find an original quantity.

Unit 8: Ratio and Rate In this Unit you learnt to compare two or more quantities by ratio and to relate ratios to fractions. You are also able to

give equivalent ratios and divide a quantity in a given ratio. You can apply your understanding of ratio to the relationship between distance, time and speed.

Pre-Learning Assessment Mark:

50

Post-Learning Assessment Mark:

50Teacher Comment:

1) (a) 25% of this square is shaded.

You need: A Pen A Pencil A Ruler

You DO NOT need: A Calculator

What fraction of the square is shaded?

....................... % (1)(b) What percentage of this square is shaded?

....................... % (1)

2) Each diagram in this question is drawn on a square grid.

50% of this diagram is shaded.

Shade 60% of each of the diagrams below

(2)

3) The scale shows both percentages and decimals.

Fill in the missing decimals in the gaps below. The first one is done for you.

60% is the same as .......0.6......

70% is the same as ..................(1)

7% is the same as ..................(1)

4) 12of the diagram below is shaded.

(a) Look at this diagram:

What fraction is shaded?

…………………… (1)

What percentage is shaded?

.............................. % (1)

(b) Shade 45 of the diagram below:

(1)

What percentage of the diagram have you shaded?.............................. % (1)

5) Each diagram below was drawn on a square grid.(a) Write what percentage of each diagram is shaded.

The first one is done for you.

…………………%

…………………% (1)

…………………% (1)

(b) Explain how you know that1212% of

this diagram is shaded.

…...…………………………………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………………….. (1)

(c) Shade6212% of this diagram.

75

(1)6) Work out the missing values.

10% of 48 = ..................

5% of 48 = ..................

2 12% of 48 = ..................

(2)7) (a) Work out 10% of 280

....................... (1)(b) Work out 15% of 280

You can use part (a) to help you.

...................... (1)

8) This is how Carly works out 15% of 120 in her head.

(a) Show how Carly can work out 17 12% of 360 in her head.

(2)(b) Work out 45% of 640. Show your working.

(2)

9) The table shows whether pupils in a class get the bus to school.

Bus to school Do not get bus to schoolBoys 3 2Girls 5 10

(a) What percentage of the boys do not get the bus to school?

..................... % (1)

(b) What percentage of the pupils in this class get the bus to school?

..................... % (2)

10) The average total lung capacity of an adult male is 6 litres of air.The average total lung capacity of an adult female is 40% less than that of an adult male. What is the average total capacity of a female lung?Show your working, and write your answer to the nearest litre.

........................... l (2)

11) Five years ago Jayla paid £270 per week to rent a flat.Prices have increased by 30% since then.What is the current weekly rent for her flat?

£……………………….. (2)

12) (a) Look at this information about exchange rates:

You can get 50 Thai Baht for 1 British Pound.

Write the missing number in this sentence.

450 Thai Bhat can be converted to ...................... British Pounds.(1)

(b) 13 out of 20 people who converted money at the currency exchange used cash rather than card for the transaction. What percentage of the group is this?

...................... % (1)13) Work out the number of boys and girls in each class below.

(a) In class 8M, there are 32 pupils. There are three times as many boys as girls.

Number of boys Number of girls..................... .....................

(1) (b) In class 8K, there are 27 pupils.

There are three less boys than girls.

Number of boys Number of girls..................... .....................

(1)(c) In class 8T, there are 7 boys.

The ratio of boys to girls is 1 : 3

Number of boys Number of girls..................... .....................

(1)

14) (a) Nigel pours 3 cartons of orange juice and 1 carton of apple juice into a big jug.

What is the ratio of orange juice to apple juice in Nigel's jug?

orange juice : apple juice = ..................... : .....................(1)

(b) Lesley pours 3 cartons of apple juice and 2 12 cartons of orange juice into another

big jug.What is the ratio of apple juice to orange juice in Lesley's jug?

apple juice: orange juice = ..................... : .....................(1)

15) Janie looks at the nutritional information on some cereal.The box of cereal weighs 600 grams. 20% of the cereal is sugar. 15% is fat.

(a) How many grams of sugar does this packet of cereal contain?

.....................grams (2)

(b) How many full 70 gram servings can Janie get from this box of cereal?

.................servings (1)

(c) The ratio of sugar to fat in this cereal is 20 : 15Write this ratio in its simplest form.

............................... (1)

16) A Christmas tree has both red and gold decorations.

In total there are 126 decorations on the tree.The ratio of red decorations to gold decorations is 3 : 4How many gold decorations are there?

………………………………. (2)17) Simone’s cat is 9 months old.

Her dog is exactly 6 months older, so this month it is 15 months old.This month, the ratio of her cat’s age to her dog’s age is 9 : 159 : 15 written as simply as possible is 3 : 5

(a) When Simone’s cat is 18 months old, what will be the ratio of her cat’s age to her dog’s age?Write the ratio as simply as possible.

........................ : .....................(1)

(b) When her dog is 21, what will be the ratio of the Dog’s age to the cat’s age?Write the ratio as simply as possible.

........................ : .....................(1)

(c) Could the ratio of the cat’s age to the dog’s age ever have been 1 : 2?Tick ( ) Yes or No.

Yes No

Explain how you know.

(1)

18)

(a) A peregrine falcon flies 360 kilometres in 9 hours. What is its average speed in kilometres per hour?

…………………..……..…mph (1)

(b) A car travels 12 miles in 15 minutes. What is the car’s speed in miles per hour?

…………………..……..…mph (1)19) Mo takes 14 minutes to run 7 times round a 400 metre track.

Assuming he runs at a constant speed, how long does he take to run 1 kilometre?

…...........................…..…….. (3)20) Nat runs at a speed of 12 miles per hour. She runs an 18 mile course.

If she decreases her running speed by 4 miles per hour, how much more time will she take?

…...........................…..…….. (2)