AA Hl Review 2

Calculus

100

f(t)=3sec²t+5t

Find f'(t)

6sec²t tan t +5

200

A normal to the graph of y = arctan(x-a), x>0, has equation y = -2x + c. Find the value of c. 

4+pi/4

300

The function f is given by f(x) = (x⁵+2)/x. There is a point of inflection on the graph at P. Find the coordinates of P. 

GDC Allowed

(-0.803, -2.08)

400

Integrate the function 6/(x²+6x+13).

3arctan((x+3)/2)+c

500

Consider the differential equation dy/dx = -y/x,      y(1) = 2

Use Euler's method with h=0.2 to find the approximate value of y(2).

0.889

Trig

100

solve cos x = 1/2, 0 < x < 4pi

pi/3, 5pi/3, 7pi/3, 11pi/3

200

Let f(x) = 4sin(3x+pi/2). For what values of k will the equation f(x) = k have no solutions? 

GDC allowed

k>4, k< -4

300

Let x be the angle for which sin x+ cos x = 4/3.

Find sin 2x. 

7/9

400

Given that 2 sin4x - 3 sin2x = 0, and sin 2x is not equal to 0, find the value of cos²x.

7/8

500

Solve the equation cos 3x = cos (0.5x), 0<x<pi

0, 4pi/5, 4pi/7