Pure Maths A Level

Front 1

If f''(X) is less than zero for an interval, the function is .....

Back 1

Concave for that given interval.

Concave means the gradient is decreasing.

Front 2

If f''(X) is greater than zero for an interval, the function is....

Back 2

Convex for that interval.

Convex means the gradient is increasing.

Front 3

How do you know where a point of inflection is?

Back 3

The point of inflection will be at the point where f''(X) changes sign. (+ To - or vice versa.)

Front 4

Differential of sin(kx)?

Back 4

Kcos(kx)

Front 5

Differential of cos(kx)?

Back 5

-ksin(kx)

Front 6

Differential of e^kx?

Back 6

Ke^kx

Front 7

Differential of ln(X)?

Back 7

1/x

Front 8

Product rule for y=f(X)g(X)?

Back 8

F(X)g'(X)+g(X)f'(X)

Front 9

Chain rule for y=f(g(X))?

Back 9

F'(g(X))*g'(X)

Front 10

Implicit differentiation for the y part.

Back 10

Differentiate everything by d/dx, then do one of these three things.

Front 11

How do you prove a number is rational?

Back 11

It can be expressed as a/b where a and b are both integers.

Front 12

How would you express 5/(X+1)(X+4) as a partial fraction.

Back 12

Firstly split it into a/(X+1) +b/(X+4).

Then give them both a common denominator. Set a(X+4) + b(X+1) = 5.

Solve by substituting X =-4 and -1.

Front 13

What is the critical factor for a function?

Back 13

Each X value must have one y value

Front 14

The inverse of f(X) , f^-1(X), is a reflection of f(X) in what line?

Back 14

X=Y

Front 15

What is the formula for the nth term of an arithmetic sequence?

Back 15

Un= a+ (n-1)d where a is the first term and d is the difference.

Front 16

What is the formula for the nth term of a geometric sequence?

Back 16

Un=ar^n-1. Where a is the first term and r is the common ratio.

Front 17

What is 1+tan²x equal to?

Back 17

Sec²x

Front 18

What is 1+cot²x equal to?

Back 18

Cosec²x

Front 19

How can you rewrite acos(X) ± bain(X)?

Back 19

•Rsin(x±æ)

•Rcos(x±ß)

Where Rcos(æ)=a and Rsin(æ)=b

Front 20

Where are the routes of a function?

Back 20

At the coordinates where f(X) =0

Front 21

How do you rearrange f(X) =0 so that you can use iteration to find its root?

Back 21

Rearrange it into the form X=g(X).

From there use the iterative formula Xn+1 = g(Xn)

Front 22

What should you do when integrating something in the form k f'(X)/f(X)?

Back 22

Try differentiating ln(X) and then adjust your answer to find the constants.

Front 23

What should you do when trying to integrate k f(X)f'(X)^n ?

Back 23

Try f(X)^n+1 and adjust constants.

Front 24

How do you find the angle, o, between the X plane and the vector A?

Back 24

Cos(o)=X/|A|