1:2:1 Maths Tuition

Watch The Bubble Grow.....

Query:

The diameter of a sphere is increased by 5%. Find the percentage increase in the surface area of the sphere.

Response:

 

Tax Write-Off.....

Query:

Machinery in a factory is estimated to lose each year 20% of its value at the start of the year. Find the original cost of a machine which is worth £3840 after two years’ use.

Response:

 

Computing Power.....

Query:

In the 1980s, the largest known prime number was calculated by a Cray computer. It took 3 hours to complete the task, working at 400 million calculations per second! Work out how many calculations were done by the computer, giving you answer in standard form.

 Response:



Another - What Did He Get Next?

Query: Rob’s marks in 5 tests were 60%, 55%, 45%, 40% and 50%. What mark must he get in the last test to gain an overall mean of 55%?

Response:

Tempus Fugit II.....

Query: How long is a billion seconds?

Response: The UK billion is 1,000,000,000 (thousand million).

There are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in 1 day and 365.25 days in a year.

So, in 1 year there are 60x60x24x365.25=31,557,600 seconds.

By working out 1,000,000,000 divided by 31,557,600, this gives the answer of 31.68808781 years.

So, a billion seconds is approximately 31 years, 251 days.

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).

What Did He Get Next?

Query: Arthur's marks in four modules were 68%, 58%, 51% and 75%.What average mark must he get in the last two modules in order to gain an overall mark of 60%?

Response: Please click on the graphic below....

 

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.

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.

Tricky Area Question...

Query: How do I find the shaded area, given that the circular shapes are quarters (i.e. quadrants) of circles whose radii of 12 cm. are equal to the side length of the square ABCD, with centres A and C.

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

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.

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.

 

Squaring The Circle...

Query: A circle had a diameter of 18cm. The length of a square is eight-ninths of the diameter. Calculate the area of the square.

Response: Please click on the graphic below.

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.

Much Interest!

Query [from Mr. Howells]: If I borrow money at 6.8% APR on an interest-only basis, how long will it take for the debt to double?

Response: If this rate of annual interest is fixed for the duration of the loan, then each year the debt owing increases by a factor of x1.068.

Hence, you will have doubled the debt after t years, where (1.068)^t>2. This means that after 11 years your debt will have increased to beyond double the sum raised.

NOTE: This timing will not vary, irrespective of how much you originally borrow.

An Approximation That Isn't...

Query [from Jon]: Why can't I use 2x10⁸ as an approximation for 1.98x10⁸?

Response: I know it's tempting to do this. However, you should consider the true values of the standard form numbers you're meant to be comparing.

First,   1.98 x 10⁸ = 198,000,000 (198 million)

Secondly, 2 x 10⁸ = 200,000,000 (200 million)

These numbers are 2,000,000 (2 million) away from each other in value!

Awkward Fractions Rooted...

Query [from KK]: How do I find out two and a quarter raised to the power of two and a half, expressing it as a ratio p/q, without using a calculator?

Response: Do the following...

• Convert two and a quarter to a top heavy (improper) fraction
• You can see that the numerator and denominator are both perfect squares, i.e. 9/4.
• The power of two and a half is actually the power of 5/2 (which is the 5th power of the half power)
• The half power is found by taking the square root, which is 3/2 (or -3/2).
• Raising this to the fifth power gives 3⁵/2⁵ = 243/32 (or -243/32)
• Hence, p=243 & q=32.
• Notice that the negative answer is valid, e.g. p=-243 & q=32.

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...

An Odds On Certainty?

I would never have thought that going to the races would be considered an useful mathematical exercise.

Well, if you follow this link to the recent video story which appeared in the Education Guardian (UK) website you will find out that someone obviously does!

I presume that actually betting on the races is optional and on a positive note, the children might begin to realise the true probability of picking a winner, with any luck.

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.

1:2:1 Challenge (Solution 12/2007)...

The answer is that Jamie must be 28 years of age - a little old for birthday cakes with candles!

Using a calculator, it is possible to applying the keying sequence 1+2+3+4+5+6+7+8+9+10+...... and keep checking the total, until the magic 406 is reached.

Alternatively, 406 is the total of an Arithmetic Progression (AP) with a=1 & d=1.

So, you can apply the formula for S_n (the sum of n terms) and then solve it for n.

1:2:1 Challenge (Problem 12/2007)...

On every birthday, Jamie's doting parents have baked him a special cake with a lit candle for every year of his current age. As part of the ritual they blow out the candles whilst others present sing "Happy Birthday" to Jamie.

Up to the present time, they have actually blown out a total of 406 lit candles. How old must be Jamie now?

Send your answers to us using the comment link below. No prizes are offered, just congratulations! But can you solve it?

The solution will be posted on Friday, November 16th at 12 noon GMT. 

1:2:1 Challenge (Solution 11/2007)...

The missing number is 10 - you must take the sum of the absolute differences (i.e. positive value) between the three top numbers in each box to produce the bottom numbers...

Box 1:  [4-2]+[6-4]+[6-2]=8

Box 2:  [7-1]+[7-2]+[2-1]=12

Box 3:  [9-4]+[9-1]+[4-1]=16

Box 4:  [6-2]+[6-1]+[2-1]=10

There were several correct answers without solutions. Well done to Lu & TF, who got both the right answer and the reasoning behind it.

1:2:1 Challenge (Problem 11/2007)...

In each of the 4 boxes below, the top 3 numbers combine to generate the bottom number...

Can you figure out the rule (which is the same for each box) and find the missing number? There are no prizes on offer, just the satisfaction of cracking the code. It's not as easy as it looks. Happy computing!

The solution will be posted on Friday, November 9th at 12 noon GMT.