To estimate the height of a mountain above a level plain at

Question

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Q1. Factorize and slove the quadratic equations:

a) 2x² + 5x - 12 = 0

b) x² - 4x + 3 = 0

Q2. A woman rows a boat upstream from one point on a river to another point 8km away in 1 hour. The return trip with the current takes only 40 minutes. How fast would she be rowing if she were rowing in still water (as if there is no current), and what speed is the current flowing?

Q3. Solve the linear system. 

Q4. In an electric network the mesh current i₁, i₂ and i₃ are found by using Kirchhoff's Law and can be stated as

Solve for i₁, i₂ and i₃.

Q5. a) Find the length of an arc that subtends an angle of 60^o at the centre of a circle whose radius is 10 cm, correct    to 2 decimal places.

b) Find the area of a sector with a central angle of 30^o for a circle whose radius is 6cm, correct to 2 decimal places.

Q6. A signal generator produced the following sinusoidal wave

y = 5 sin (x + π/2)

a) What is the amplitude, period and phase shift of this wave?

b) Sketch the wave by hand.

Q7. To estimate the height of a mountain above a level plain, at one point the angle of elevation to the top of the mountain is measured to be 30^o. At another point which is two thousand metres closer to the mountain along the plain, it is found that the angle of elevation is 45^o. Estimate the height of the mountain.

Q8. Solve the exponential and logarithmic equations for 2, correct to two decimal places

a) 2(e^2x-1 - 3) = 10

b) ln(5 - x) + 1 = 0

c) log₁₀(3x + 4) = 1