1:2:1 Maths Tuition

A Composite Problem.....

Query: Why isn't it always possible to define a composite function completely from the domains of the functions involved.

Response: Consider the worked example below...

 

Indices Challenge.....

Query: I need to simplify the following algebraic terms to lowest terms...

Divide the fraction [16a²b³/3ac⁴ ] by the fraction [32ab⁴/25c²].

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

Circular Measure...

Query: A sector of a circle radius r subtends an angle of theta at the centre. The perimeter of the sector is 3m and the area is A sq.m. Show that A=0.5r(3-2r).

Response: Please click on the graphic to view 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.

An Arithmetic Progression Or Series?

Query: The sum of the first three terms of an AP is 15 and the sum of the first five terms is 40. Find the first term and the common difference.

Response: Always write down the first few terms of the series, so that you know what you're dealing with. Please view the graphic for the solution.

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.