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Convert 1-i / 2 into trigonometric form

C. How many centimeters are in a meter?

D. What is the mode of the data set below:

5;6;1;4;7;3;8;2;4;3;8;9;4;6;1;2;6;5

E. Calculate the area of the darker shaded outer part below.The larger rectangle is 15cm long and 9 cm wide, the sides of the smallest square are 5cm each.

An aeroplane flies at a ground velocity (i.e. velocity relative to the ground) of 300 km/h N 30o W, in a wind blowing at a velocityof 50 km/h N 20o E. What is the velocity (speed and direction)of the plane relative to the ground? (Use a calculator and round the speed)

to the nearest km/h, and the corresponding angle to the nearest degree.)

1.Find the domain of the function 𝑓(𝑥)=log4(𝑥2+4𝑥−5𝑒𝑥−1).

2. Construct the tangent line to the graph of the function 𝑓(𝑥)=√𝑥+2𝑥 which is perpendicular to the line 𝑥+3𝑦−2=0.

3. Find the maximal intervals of monotonicity of the function 𝑓(𝑥)=arctg(𝑥2−4𝑥).

4. Calculate the integral ∫𝑥2(𝑥3+4)2 𝑑𝑥2−1.

5. Find the particular solution of the differential equation 𝑦′=−(2𝑦+1)⋅tg(𝑥) which fulfills the initial condition 𝑦(𝜋4)=12.

6. Solve the matrix equation 2𝒳+𝒜=3ℬ−𝒜𝒳 if 𝒜=(−4−332), ℬ=(1−121).

Find the initial speed which a projectile must be subjected to give it a maximum horizontal range of 490m. Assume the acceleration due to gravity as g=10m/s

Below are five test items, each belonging in one of the four cognitive levels of CAPS: knowledge, routine procedure, complex procedure or problem solving. Indicate in each case to what cognitive level the question belongs:

(a) What is the temperature difference between 17°C maximum – 3°C minimum?

(b) Ben walks to school in 48 minutes. Nomsa goes by bicycle in half the time that Ben walks. Koki goes by taxi in half the time that Nomsa goes by bicycle. At what time do they all start at home if they all arrive at school at 07:15?

(c)  How many centimeters are in a meter?

(d)  What is the mode of the data set below:

5; 6; 1; 4; 7; 3; 8; 2; 4; 3; 8; 9; 4; 6; 1; 2; 6; 5

(e) Calculate the area of the darker shaded outer part below. The larger rectangle is 15cm long and 9cm wide; the sides of the smaller square are 5cm each.

A ball is thrown vertically upward with a speed of 7.1 m/s. Find:

(9 points)

a. Maximum height reached the ball

b. Its time of flight

c. Velocity the ball would return to its starting point

Jo Ann and her lab partner are completing a free fall lab in physics. Her partner drops the ball in front of the motion sensor to measure its speed. Assuming acceleration is constant and air resistance is negligible, how far does the object fall if it reaches a speed of 9.8 m/s?

An aeroplane heads due north at 500 km/h. It experiences a 80 km/h crosswind flowing in

the direction N60^°E.

(b) Determine the speed of the aeroplane. (Leave your answer in terms of square root) (3)