Tag Archives: 11 plus Maths

Problem Questions

‘Problem questions’ are often the most difficult in 11+ and 13+ Maths papers.

There are several different kinds, but they all have one thing in common: they all ‘hide’ the sums that you have to do.

That means the first thing you have to do is work out the actual calculations you’re being asked for.

Here’s an example from a 10-11+ Bond book that I was going through today with one of my pupils:

What is the nearest number to 1000, but smaller than 1000, into which 38 will divide with no remainder?

He couldn’t answer it, so I told him something I always say in these situations. There are three ways of answering a question in Maths:

  1. Use a proper mathematical technique.
  2. Use trial and error.
  3. Guess!

Method 1

The first method is usually the most efficient and reliable. In this case, you need to do two calculations:

  1. 1000 ÷ 38 (ignoring any remainder)
  2. Multiply the answer by 38.

The first step should be done using long division and should give the answer 26.

 

 

 

 

 

 

 

The second should be done by long multiplication and give the answer 988.

Method 2

It’s all very well saying you have to use ‘proper’ Maths, but what if you don’t know how to do it? That’s when trial and error comes in handy.

Trial and error just means thinking of a number that you think is ‘about right’ and then adding or subtracting from it if the answer is too low or too high.

In this case, there’s no easy answer, but you might round up 38 to 40, and 40 goes into 1,000 25 times. However, that still leaves a difference of 25 lots of 2, which is 50, so the actual total is only 950. If you add on another 38, you get 988, which is the answer.

Method 3

If you’re doing a multiple choice paper, the worst mistake in the world is to leave an answer blank. It only takes a second to guess A, B, C, D or E, so it’s worth doing because you’ll always have a 20% chance of getting it right—and that beats zero!

The key is to make sure your guesses are at least possible. For example, if the question asks for a number between 1 and 10, don’t guess 12!

For this question, it isn’t easy to guess, but the answers to a lot of questions at 11+ or 13+ level can be narrowed down quite easily to a common fraction or a single-digit number.

As Sherlock Holmes once told Dr Watson, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth!”

Quiz

  1. Mark is 11 and Julie is 9 years old. If they get £80 pocket money shared according to their ages, how much does each of them get?
  2. If a dress costs £240 after VAT at 20% is added on, what is the original price?
  3. Candy floss is on sale at £2 for three sticks at Stall A and £2.50 for five sticks at Stall B. Which stall is cheaper per stick?
  4. A garden measures 10 x 8 metres in total. There’s a lawn surrounded by a path 1 metre wide around the outside. What’s the area of the grass?
  5. If school starts at 9.15am and there are four 45-minute lessons in the morning followed by three lessons of 1 hour 15 minutes in the afternoon with an hour for lunch, what time do the children go home? 

     

     

     

    If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.

Working out values from a pie chart

Working out Values from a Pie Chart

This is a typical question from a Dulwich College 11+ Maths paper that asks you to work out various quantities from a pie chart.

To answer questions like this, you have to be comfortable working with fractions and know that there are 360 degrees in a circle.

So how should you start?

The first question asks for the fraction of the school children who liked tennis.

To work this out, you just need to take the following steps:

  1. Put the number of degrees showing the tennis segment over 360 to create a fraction.
  2. Simplify the fraction.

The number of degrees is 45, so the fraction is 45/360.

The first step to simplifying fractions is to see if the numerator goes into the denominator, which it does in this case: 45/45 = 1 and 360/45 = 8, so the fraction is 1/8 in its lowest terms.

(By the way, for a complete guide to simplifying fractions, just read Working with Fractions.)

The second question asks how many of the children preferred cricket.

To answer this, you should be able to learn a bit from the first question.

To work this out, you just need to take the following steps:

  1. Put the number of degrees showing the cricket segment over 360 to create a fraction.
  2. Multiply that fraction by the number of school children in the survey, which is 240.

As with the first question, you need to work out the fraction of the children in the survey you’re dealing with.

In this case, it’s 60/360 or 1/6.

To find out the number of children, you just have to multiply by 240, which is 1/6 x 240 = 40.

The final question asks you to estimate (or guess) how many of the children would say their favourite sport was football out of the whole school of 1200 pupils.

To work this out, you just need to take the following steps:

  1. Work out the number of degrees taken up by the football segment of the pie chart.
  2. Put the number of degrees over 360 to create a fraction.
  3. Multiply that fraction by the number of children in the school, which is 1200.

To work out the number of degrees, it’s easier if you spot that the first half of the pie chart is composed of just football and tennis.

There are 180 degrees in total for that half, so taking away 45 degrees for the tennis-lovers gives you 135 degrees.

This works out at a fraction of 135/360 or 3/8.

Now, we only have data for the 240 children who’ve been surveyed, but that’s why we’re being asked to estimate the answer.

We have to assume that the other kids at school share the same preferences as the ones in the survey.

If we do that, all we need to do is multiply 3/8 by 1200 to get 3/8 x 1200 = 450.

And that’s it…!

 

 

 

 

If you’re looking for past papers with answers, especially in the run-up to 11+/13+ exams, GCSEs or A-levels, you can visit my Past Papers page and subscribe for just £37.99 a year.