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Maths A Level: "Sketch the curve of the function f(x) = 2x^3 - 2x - 12 and show that the equation f(x)=0 has one root; calculate the root."

Consider the curve y = 2x^3 - 2x - 12.1) y-intercept. When x=0, y= -12 3) when x tends to infinity...y tends to infinity and when x tends to negative infinity...y tends to negative infinity 4) stationary ...

Answered by Joseph I. • Maths tutor

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Prove that the square of an odd number is always 1 more than a multiple of 4

(2x-1)² = 4x²- 4x + 1= 4(x²-x)+1The part of the expression which is: 4(x²-x) indicates that the value is a multiple of 4. The number 1 is then added which means...

Answered by Gokul P. • Maths tutor

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4y^2 = 256, Find a value for y

y^2 = 256/4 = 64
therefore, y = sqrt(64) = 8

Answered by Kai P. • Maths tutor

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Solve the simultaneous equations: 2x + y = 12; x - y = 6

We add the two equations together (left-hand sides and right-hand sides separately). By doing this we get: 2x + y + (x - y) = 12 + 6. By rearranging and simplifying: 3x = 18.If we divide both sides by 3 w...

Answered by Rebeka D. • Maths tutor

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A class of pupils were asked about how they travelled to school on a particular day. 1/6 of the pupils were driven to school in a car. 2/5 of the pupils took the bus. The rest of the pupils walked to school. Calculate the fraction of pupils who walk

The total amount of student would be represented by 1 or 100%. The pupils are split into three categories meaning the total must add up to 1. Therefore to find the remaining pupils who walked to school we...

Answered by Jane Z. • Maths tutor

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