# MODEL SOLUTIONS

These model solutions are for Practice Test 2 from the Department of Education website.

You can access the full test here.

##### On-Screen Question 13
To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class.

What proportion of the class have the same reading age as their actual age? Give your answer as a decimal to one decimal place.

##### On-Screen Question 14
To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class.

Circle the pupil who has the greatest difference between their reading age and actual age.

##### On-Screen Question 15
To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class.

What is the range of reading ages for pupils in the class?

(a) 13 months; (b) 19 months; (c) 21 months

##### On-Screen Question 16
At a staff meeting, the head teacher presented the following table, showing the number of pupils in each class in a school who are having extra music lessons.

What percentage of pupils in the school are having extra music lessons?

##### On-Screen Question 17
A teacher calculated the mean points score achieved by pupils in an end of Key Stage 2 mathematics test.

There were 48 pupils in the year group.

The mean points score is given by the formula:

What was the mean points score for the year group?

The total points for Levels 3 and 4 have been done for you.

##### On-Screen Question 18
A teacher is planning a group outing to see a play in a nearby city.

She has been given details of costs and travel.

There are 25 in the group, including pupils and teachers.

A group booking for 25 theatre tickets costs £185.

Return train tickets cost £5.65 each.

How much will each person have to pay for the outing to cover the cost of travel and theatre ticket?

##### On-Screen Question 19
To set targets for the following year, the mathematics department analysed the percentage of mathematics GCSE grades A* – C achieved by pupils in the school.

Tick all the true statements:

• The mean percentage of GCSE grades A* – C for the last 5 years of the chart was 51%.
• The percentage of GCSE grades A* – C increased each year from 2004 – 2011.
• The percentage of mathematics GCSE grades A* – C more than doubled from 2004 – 2011.

##### On-Screen Question 20
A school parents’ evening starts at 16:30 on each of two consecutive days.

A teacher has a total of 24 appointments lasting 10 minutes each and takes a 20 minute break each evening. The teacher filled all the available appointment slots on the first evening and finished at 19:00.

What is the earliest time the teacher can expect to finish on the second evening?

##### On-Screen Question 21
A teacher produced the following table to show the marks achieved in an end of year geography test by pupils in three Year 7 classes.

Tick all the true statements:

• Some pupils in Class A achieved less than 12%.
• At least one pupil in Class C achieved less than 20%.
• All pupils in Class B achieved at least 40%.

##### On-Screen Question 22
As part of a review programme a teacher compared the marks for 10 pupils in each of two English tests.

Circle the letters in the table for the pupils who scored at least 10 percentage points more in Test 2 than in Test 1.

##### On-Screen Question 23

A teacher presented the following box-and-whisker diagram as part of a staff discussion on pupils’ performance. The diagram shows the percentage test marks in mathematics for a revision test for two class groups.

Tick all the true statements:

• The range of percentage marks was greatest in class A.
• The median percentage mark in Class A was 15 percentage points less than the median percentage in Class B.
• The interquartile range was the same in both classes.

##### On-Screen Question 24
A teacher plans a school trip to Brussels, which involves using a ferry from Ostend. The teacher wants to be in Ostend no later than 18:00. She expects their coach to travel from Brussels to Ostend, a distance of 120km, at an average of 50 miles per hour.

Using the approximation of 5 miles equals 8 kilometres, what is the latest time that the coach should leave Brussels? Give your answer using the 24-hour clock.