1:2:1 Maths Tuition

Quadratic By Formula.....

Let us show you how to solve a quadratic equation by using the formula:

 

Awkward Change Of Subject.....

Query: Can you demonstrate how to change the formula 1/p = 2/q + 3/r , to make 'r' the subject?

 Response:

 

Leaves On The Line?

Query:

A train normally travels a journey of length 60 miles at a certain average speed.

One day, due to bad weather, the train’s average speed is reduced by 10 mph so that the journey takes 3 hours longer.

Find the train’s normal average speed in mph?

Response:

 

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:



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:

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:

An Annulus Problem....

Query: Two concentric circles have radii of r cm and 6 cm (where r>6). If the area between the circumferences is 64π, find the size of the radius r.

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.

Watch The Signs!

Query: A tricky change of subject question, i.e. find y in terms of x if

x=(y-1)/(y+1)

Response: Try it yourself - one solution is given below.....

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....

 

A Strange Sequence?

Query: If x is an even integer, write down the next three even integers.

Hence show that the sum of any four consecutive even integers is divisible by four.

Solution: Try this for yourself, but if you can't establish the result, click on the graphic below to see the solution.

 

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.

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.

How Do I Get From A To C?

Query: Describe fully the transformation which takes shape A onto shape C. [Please click on the graphic to see the full size question].

Response: It can be seen that the shape A has been turned to arrive at position C, so a favoured method is to use tracing paper to investigate it further.

Proceed as follows: Trace the shape A and place it directly over A. Now put your pencil point on the point (0,0) and rotate the paper. Does the shape A cover position C? In this case it does, but in another question you would have to try other 'centres' with your pencil point, until one works.

You'll see that the transformation which maps A onto C is a clockwise rotation of 90^o centered at the origin (0,0).

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.