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.....

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....

 

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. 

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).

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.

Eyes Down...

Query: Twenty one identical balls are numbered 1 to 21. They are placed in a bag and two balls are selected without replacement. What is the probability that the numbers on both balls are less than 7?

Response: Click on the graphic for the solution...

Keeping Things In Proportion...

Query: Given that y is inversely proportional to x² and x=15 when y=2, find x when y=50.

Response: Take a close look at the solution below...

 

And The Equation Is?

Query: How do I find the equation of this graph?

Response: You should record the coordinates of points along the graph and try to work out the unique relationship between x & y via the pattern which connects them.

Here, we have the points (12,1), (6,2), (4,3), (3,4), (2,6) & (1,12).

Notice, if you multiply the pair of coordinates each time you get the answer 12. So, the equation is xy=12 or y=12/x.

You could also have recognised this as a transformation of the reciprocal graph, y=1/x.

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.

Another Perfect Square?

Query: How do I find the square root of f(x)=x²-0.2x+0.01?

Response: You should clear the decimals first and then see what the quadratic looks like, once you have whole number coefficients to deal with.

Download Solution [pdf]

Tricky Perimeter Problem...

Query [from KW]:  A circle has a radius of 2X cm and a triangle has sides of [2X+1], 3X and [3X+4] cm. The perimeters are equal. Write an equation in terms of X to represent this fact and hence find the value of X correct to 2 decimal places?

Response: Click on the image graphic to view the solution (opens in new window):

Inequality...

Query: How do I find out the range of x-values for which 2x²<7x+4?

Response: The first step here is to try and solve the inequality by factorisation!

Rearranging to... 2x²-7x-4<0 gives (2x+1)(x-4)<0.

Hence,

1. EITHER 2x+1<0 & x-4>0
2. OR        2x+1>0 & x-4<0

This leads to the solution of -0.5 < x < 4

You should check the solution by trying a suitable value of x (e.g. x=0) back in the original inequality.