Pass MATHS GCSE with ease and achieve the best marks?

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• What are quadratic equations? Using examples

A quadratic equation is an polynomial , second degree.

A quadratic equation can have 2 different solutions or  1 solutions or no solutions.

We can use a scientific calculator, Casio fx991EX to solve a quadratic equation .

Move to Menu and bring down the arrow key to the rectangle A, click on = and  click on 2 , Polynomial,click on 2 for degree, as it is a quadratic equation and enter the value of a,b,c as quoted.

Press equal and the solutions x1 and x 2 will appear on the screen or only x for a single solution.

x^2 +2x+1=0 , solution x=-1

x^2 -5x+6=0   , solution x1=2 and x2= 3

If you do not use a calculator , you need to apply the formula for the discriminant of the equation , Discriminant = b^2 -4ac , where a,b,c, are the values in the quadratic formula and for the solutions .

If the Discrimiant is >0 , we have 2 solutions  x=( -b+-square root( b^2-4ac))/2a

If the Discriminant =0 , we have 1 solution x -b/2a 

If the Discriminant is<0 , no solutions .

• What are Circle Theorems? A guide with examples
• The angle is a semi circle is 90 degree.  Any right angle triangle can be found inside a circle where the diameter is the triangle hypotenus.
• Opposites angles of a cyclic quadrilateral add up to 180 degree.
• Angles in the same segment are equal.
• The angle at the centre of the circle is twice the angle on the circumference.
• The perpendicular from a chord to the centre of the circle bisects the chord.
• The angle between the tangent and a chord is equal to the angle in the alternate segment.- Alternate segment .theorem.
• Calculating the interior and exterior angles of a polygon
• In a regular polygon all the sides are equal and all the angles are equal .
• If a regular polygon has n sides , then each exterior angle is 360/n.
• We can use the fact the angles on a straight line add up to 180 degree to work 
• out the size of the interior angles.
• For a polygon with n sides, 
  • Sum of the interior angles=180 x (n-2)
  • Sum of the exterior angles = 360/n
• What are the laws of indices for multiplication and division? A guide with examples
• Indices include square roots, cube roots and powers.
• When you multiply two  same number, you add the indices .
• a^m xa^n= a^m+n
• a^m/a^n= a^m-n
• When you divide two same number , you subtract the indices.
• 3^2  x 3 ^5 = 3 ^2+5= 3^8
• 4^9/4^2= 4^7
• Power of zero = 1 and power of 1= to itself.
• 8^0=1  and 8^1= 8

Negative power: a^-n= 1/a^n

a^-1= 1/a

• Here are the topics you need to know for GCSE maths
• Number:  Factors and primes, indice, fractions , decimals, standard form, surds,....
• Algebra: Factorising, linear equation, arithmetic sequences, quadratic equations, simultaneous equations,inequalities, equation of a circle, functions, inverse functions, velocity time graphs.....
• Ratio and Proportion :  Ratio , proportion, percentage change, speed, density.
• Geometry and measures: Angles and properties, trigonometry, angle in polygons, circles, surface area , bearings, the sin and cosine rules, Pythagoras, vectors.....
• Probability and Statistics :Mean , median and mode, interquartile range, box plots,  probability, tree diagrams.....
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• Best textbooks for A-Level Maths
• Revise Edexcel AS Mathematics, C1,C2, M1,S1 D1
• A level year 2, Mathematics , Edexcel .