1:2:1 Maths Tuition

An Age-Old Problem.....

Query: A man is now four times the age of his son. Eight years ago the product of their ages was 108. What is the father's age now?

Response:

Tempus Fugit.....

Query: How long is a million seconds?

Response: There are 60 seconds in 1 minute, 60 minutes in 1 hour and 24 hours in 1 day.

So, in 1 day there are 60x60x24=86400 seconds.

By working out 1,000,000 divided by 86400, this gives the answer of 11.574 days, which is approximately 11 days 13 hours and 47 minutes (to the nearest minute).

How Do I Find The Mean Of This Data?

Query: I've got data for the number of children absent from a certain class. The data is already in a table [supplied]. How do I find the mean of this data?

Response: Please click the graphic to view the data and the calculations to arrive at the mean. 

Estmating Height...

Query: How do I estimate the height of this mast (see diagram)?

Response: The man's height has to be estimated first. Next, you calculate how many men of the same height (i.e. standing on each other's heads) it would take to reach the top of the mast.

Click on the graphic below to see how you would show this.

Rotational Symmetry...

Query: What is the order of rotational symmetry of this shape?

Response: If you rotate the shape you can see that it will fit its own outline four times in each complete revolution.

Hence the order of rotational symmetry is 4.

Monitoring Heartbeats...

Query: John's pulse rate is taken every 6 hours over a three day period. The graph shows his pulse rate in beats per minute. [Please click on the graph to see it full size]

Find the difference between his lowest and highest pulse rate on the 3rd of May.

Response: From the graph the highest rate is 102 and the lowest is 97. Hence the difference is 102-97=5 beats per minute. 

How Much Is The Fare?

Query: I'm given that the cost of a taxi fare is made up of a fixed charge of $4.20 and 45 cents per mile travelled. How do I find the cost of a 30 mile journey?

Response: You'll need to work out 30 x 45 cents (use $0.45 in a calculator) and then add the $4.20 fixed charge to this.

The answer is $17.70.

Like Shares?

Query: Cliff and Elvis support their local football team and decide to share the cost of a field season ticket for next season. The season ticket costs £240 and they split the cost in the ratio 3:2. Calculate how much Elvis pays?

Response: Elvis pays two-fifths of £240, i.e. £96. 

What goes Into The Pie?

Query: A Market Gardener uses 24 hectares of land to grow vegetables. Peas occupy 7ha., Sprouts 3ha., Broad Beans 6ha. & Potatoes 8ha. Draw this information onto a Pie Chart.

Response: Please click on the graphic to view the solution.

Rotational Symmetry...

Query: What is the order of rotational symmetry of this shape?

Response: If you rotate the shape you can see that it will fit its own outline twice in each complete revolution.

Hence the order of rotational symmetry is 2.

Did They Collide?

Query: A travel graph shows the 50 km. journeys of Ken and Wendy. Ken travels by bike and Wendy completes the journey by car. What time did Wendy pass Ken? [Click on the graphic to view the full size question].

Response: Look at the point on the graph where they appear to 'crash' into each other! Reading the time scale for this apparent collision, it looks like it happened at 1306 hours, i.e. 6 minutes past one in the afternoon.

Scales can be very difficult to read, so make sure you carefully calculate what each division of the graph paper represents.

In this case 1 hour is split into 10 divisions, so each must be 6 minutes. Remember to show the answer on the graph by dropping a dotted line from the intersection onto the time axis.

How Many Cuppas?

Query: A tea urn is shaped like a cylinder with a circular cross-section of diameter 35cm and height 60cm. It is filled with tea. How many cups of capacity 150 cubic cms. can be served from the urn?

Response: The answer is 384 cups. Please click on the graphic below to view the solution.

 

Fuel Economy?

Query: Beth owns a Ford Mondeo. One month she travels 1190 miles and uses 35 gallons of petrol. How many miles per gallon is this equivalent to?

Solution: Please click on the graphic below.

Spin Out Of Control...

Query [from LukeP]:

The spinner gives the following output data: w,b,b,w,r,r,g,b,w,b,r,g,g,r,w,w,r,g,w,b.

I have to find the median colour of the 20 spins? 

Response: I fear there is no median here, as the data is not numerical. Please go back to the source of the question and raise a query.

Remember: The median is the middle value of ordered data and it is only possible to order numbers.

Looks Like A Similar Calculation?

Query [from Kyle2]: I've been given a number fact and I'm meant to work out the answer to a calculation that looks like it. Help!

Response: We've printed the question and the solution below...

Not A Perfect Square Yet!

Query: How do I find the smallest number which is needed to multiply by 2160 to get a perfect square?

Response: The key to solving this is to break down the number to a product of primes and then make each power EVEN.

This type of question has cropped up a few times recently - so we'll be posting a video response soon. In the meantime, click on the image graphic to view the full handwritten solution.

A Chance Lesson...

We're grateful to DWS for drawing our attention to the following video lesson, posted on YouTube, about the basics of probability by keithpeterb.

It's well worth a viewing, especially if you're looking for a quick revision of the basics of this topic, but you'll have to ignore the references to exercises and units!

Here We Go: A, B, C,....

Query: This fair spinner gives the following output:

A, B, A, C, A, C, D, A, A, C, A, B.

Write down the probability of getting an A and what do you expect to happen to this probability as the number of spins increases?

Response: The letter A has occurred 6 out of the 12 spins, so p(A)=6/12=0.5

As the number of spins increases, there should be a strong tendency for p(A) to reach 0.25, if the spinner is as fair as you say.

Heavy Metal...

Query [From LAL]: A 20cm square sheet of metal has equal quadrants cut from the corners, as shown in the diagram. The area left is 246 sq.cm and we need to find the radius of the circle from which the quadrants are taken. [use pi as 22/7]

Response:

• Area of the square is 20x20=400 sq cm
• Take away area that remains
• Quadrants add up to 154 sq cm.
• Four quadrants equal 1 circle
• Calculate the radius of this circle.

The answer is 7 cm.

Keeping Afloat...

Submitted Question [from TracyJ]: The probability of a swimmer winning a race is 84% and he swims 50 races in a season. How many races would you expect him to win?

Repsonse: By multiplying the probability of an event happening by the number of 'identical' events, you arrive at the expected number of successes.

So, your answer of 42 wins was actually correct (i.e.50x0.84), but I can understand how you felt it couldn't be that easy!

A Perfect Square...

Query [from KP]: I've reduced 540 into prime factors and written them as 2 squared times 3 cubed times 5. I've now been asked to suggest the smallest number which I must multiply 540 by to get a perfect square? Solid!

Response: It is true that 540=2²x3³x5.

The condition for a number to be a perfect square is that it has a whole number square root.

So you will need to make all the indices into even numbers...

• the power of 2 is already even, so no action needed.
• the power of 3 needs to be increased from 3 to 4 (i.e. times by 3)
• the power of 5 needs to be increased from 1 to 2 (i.e. times by 5)

The smallest square root which is a multiple of 540 is therefore: 2²x3⁴x5²=8100.

Not All Expressions Are Created Equal!

Query [from Mr.K]: I helped my son with a question and he had it marked wrong by his teacher. He was asked to convert five more than w into an Algebraic expression. My answer was 5>w. Is this wrong?

Response: It is wrong, but I can see why the confusion has occurred, as your answer is an inequality, not an expression.

So, although 5>w seems correct, it is in fact a symbolic translation of the statement five is more than w and not five more than w, which was originally set.

The required answer was 5+w (or w+5, which also works).

HINT: It is often worth trying out some actual values for the unknown letter(s) or variable(s). In this case, different values of w can then be tested against the information of the initial question, to check the logic of your answer.

For example, 5 more than 3 is 8, 5 more than 10 is 15, 5 more than 23 is 28.

Now think about the flawed logic leading to the inequalities: 5>3, 5>10 & 5>23?

1:2:1 Challenge (Problem 07/2007)...

From an ordinary pack of 52 playing cards I randomly take some Spades, Hearts and Clubs and lay them face upwards on a table.

• If on each Club I place either a Heart or a Spade, there are 15 cards over.
• If on each spade I place either a Heart or a Club, there are 7 cards over.
• If on each Heart I place either a Spade or a Club, there are 11 cards over.

How many cards of each suit were chosen?

The solution will be posted on Friday, October 12th at 12 noon (GMT).

1:2:1 Challenge (Solution 06/2007)...

The answer is:  A=2, B=3, C=4, D=8 & E=9.

Download Explanation [pdf]

No correct answers were received. We'll make the next one a little easier!

1:2:1 Challenge (Problem 06/2007)...

Although this is a simple problem at first glance, you will definitely need to use all your powers of deduction to figure it out.

You are told that four times the number ABCD gives the answer EBEA, where each letter stands for a different single digit!

What digits do the letters A,B,C,D & E represent?

Again, no prizes on offer, but can you crack the fiendish logic required? The solution will be posted on Friday, October 5th at 12noon GMT.