1:2:1 Maths Tuition

Quadratic By Formula.....

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

 

Implicit Actions.....

Query:

Differentiate the implicit function....  x³ + y³ + 3xy² = 8, with respect to x.

Response:

 

 

Know Your Parameters.....

Query:

If x=sinθ and y=cos2θ, find d²y/dx².

Response:

 

 

A Stationary Event.....

Query:

Find the stationary points on the curve  y =  x³ - 12x + 5  and determine their nature.

Response:

 

A Turning Point.....

Query:

Find the stationary point on the curve  y = x² + 4x + 9  and determine its nature.

Response:

 

Polynomial Integral.....

Query:

Integrate with respect to x:  √x – 2/x³

Response:

 

Special Trig Equation.....

Query:  How do I set about solving  sinθ + 2 cosθ  = 1?

Response:

 

Just The Merest Touch.....

Query:

Two circles C1 and C2 are given by

(x-2)² + (y+4)²  =  100  &  x² + y² +14x – 16y + 88 = 0.

Show that they touch at the point (-4,4).

Response:

 

Tangent Needed.....

Query:

Find the equation of the tangent to the curve  y = 3x²- 4x + 1 at the point (2,5).

Response:

 

Don't Do It The Hard Way.....

Query:  Find the remainder when x³-2x²-3x+1 is divided by x+2.

Response:

 

Pure Hyperbolics.....

Query:

Find dy/dx if y = tan^-1(sinh x)

Response:

 

Very Complex!

Query: The complex numbers u, v and w are related

by the equation u^-1=v^-1+w^-1.

If v=1-3i, w=2+i, show that u=m(5-i), where m=5/13.

Response:

A Problem Of Progression.....

Query: An arithmetic progression has its first, second and fourth terms as consecutive terms of a geometric progression. Show that the first term of the arithmetic progression is equal to the common difference.

Response:

Just Touching.....

Query: The line y=2x+c is a tangent to the curve y²=8x. Evaluate 'c'.

Response:

Hint = This question is all about the roots of a quadratic equation.

A Power Series.....

Query: Expand (1+0.5x²)^1.5 up to the third term.

Response:

This is achieved using the power series expansion of (1+mx)^p and is valid for -1<mx<+1.

A Straight Line.....

Query: Find the equation of a straight line which passes through the coordinates (-3,-7) and (5,-1), expressing your answer in the form ax+by+c=0?

Response:

Another Trig. Equation To Solve.....

Query: If 8cos²x+2sinx=7, find all the values of x in the range 0 to 360 degrees.

Response:

Go Large.....

Query: Given that A=0.5r(3-2r) show that the maximum value of A as r varies is 9/16.

Response: Click on the graphic below to see the solution....

 

Area By Integration

Query: See if you can solve the following problem. Click on the graphic to view the question only...

 

Solution: Click on the graphic below to view both the question and answer....

 

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.

 

Watch those signs!

Query: Solve these simultaneous equations by an algebraic method.

x²+ y²= 25, 2x + y - 5 = 0.

Solution: Click on the graphic below to see the solution. This is an example of how important it is to remember that...

1. square roots are either positive or negative and
2. you should check to see whether your solution works for both equations.

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.

 

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.