G11 Competition !

Pre Calculus 1

100

if

f(x) = 4x^2-x+1

 then f(2x + 1 ) =

f(2x+1) = 16x^2 + 14x +1

200

s(t)=1/(t^2+3t-1). s'(t)=?

(-2t-3)/(t^2+3t-1)^2

300

Complete the square 

F(x) = 2x^2 - 5x + 4

F(x) = 2(x-5/4)^2 + 7/8

400

Find the slope of the normal to the curve y = x^2 +3x - 2 at (4,7).

What is: 

-1/11

500

Find the inverse of 

y = (2x-1)/(2x-5)

f^-1(x) = (5x-1)/(2x-2)

Inverses (mostly)

100

Find the inverse of y = 2x+3

f^-1(x)=(x-3)/2

200

F(x) = (x-1)/3 + x/2

and

F^-1(x) = (6x+2)/5

are inverse ?

yes

300

Find the inverse and state domain

f(x)= -3 root 2 (x-1)

f^-1(x) =( x^2 )/9 + 1

x<=0

400

Find Domain of  F 0 G (x) 

F(x) = 1 / (x+1)

G(x) = x^2 - 10

R\{-3,3}

500

Find the derivative of: y= x²cos x, at x = pi/6.

What is: y' = 

(pi*sqrt3)/6 - pi^2/72

Functions 1

100

find domain 

root 2 ( x-1)

[1, + inf)

200

find domain 

root 2 ( x-1) + root 2 ( x-2 )

[2,inf)

300

Find domain 

y = 1 / (x^2 - 2)

R - { 

- root 2 2, root 2 2

}

400

Domain 

f(x) = root 2(x-4) / (5x-10)

[4,2)U(2,+inf)

500

If We have a rectangle, the length is 3 times the width Knowing that the perimeter is 48, find the length

18

Functions 2

100

( 6x^2 - 3x ) ^2 =

36x^4 - 36x^3 + 9x^2

200

describe transformation

y = 2f(x-4)+3

a =2  VS

h= 4 translation 4 units right

c=3 translation 3 units up

300

Find the minimum value ( y ) 

h(x) = x^2 - 10x + 16

-9

400

In the library there are Math and Physics books. There are 5 more physic books than math books. If the total number of books in the library is 25, how many are math books ?

10

500

The length of a rectangle is 2 meters more than its width. If the area of this rectangle is 24 m^2, then the length of the rectangle is  

6

Misc.

100

Find the solution of 

6x^2 + 5x - 6 = 0

-1.5 , 2/3

200

50 % of 14 is what percent of 35 ?

20

300

The length of a rectangle is 4 meters more than its width. If the area of this rectangle is 5 m^2, then the peremiter of the rectangle is ?

P = 12 cm

400

If Ahmad and Bader has 1210 KD. 4/15 of ahmad’s money is equal to 2/5 bader’s money . Whats bader money

484

500

A square and an equilateral triangle have the same perimiter. The side of the triangle is 2 cm more than that of the square. Find the side of the triangle’s length

x = 8

Calculus

100

f(x)=(-3(3x - 2x^2))/(7x)

f'(x)=?

f'(x)=6/7

200

Find f'(x).

Find the derivative of : y= x * root(x)

f'(x) = (3rootx)/2

300

Find the derivative of:  y= 

(x^2)/(2sqrtx + 1

What is: y' = 

(x(3sqrtx + 2))/(2sqrtx + 1)^2

400

Find the slope of f(x)= (5/x³) - 3(x²)- (1/x) at x = -1

What is -8?

500

Find the derivative of:  f(x)= y=sin(tan 2x)

What is :  2cos(tan 2x)(sec²(2x))

or

[2cos(tan 2x)]/(cos²(2x))