BASIC MATHEMATICS

Q.1. Solve the following: (i) 3(2t – 8)=4(7 + t) (ii) x2 – 2x – 48 = 0 (iii) 0≥20–x≥–20 (iv) 4×2 – 100 < 0 (v) Illustrate graphically what is meant by negative and positive slope (vi) Rewrite the equation 3x – 2y = 15 in slope intercept form, also find the x–intercept, y–intercept and sketch the function (vii) Determine the distance between the x-intercept and y–intercept for the equation 3x – 2y = 15.

Q.2. Solve the system of equation:

x + y = 3
2x – y = 12
x – 4y = 13
–2x + 5y = 0

Q.3. Sketch the quadratic function: u = f(v) = 10v2 + 20v – 100

Q.4.(a) A firm sells a single product for $65 per unit. Variable cost per unit are $20 for materials and $27.5 for labor. Annual fixed cost are $100,000. Construct the profit function stated in terms of x, the number of units produced and sold. What profit is earned if annual sales are
20,000 units.

Q.4.(b) An investment of $200,000 is made which earns interest at the rate of 8% per year. If interest is compounded continuously determine the exponential function which states the compound amount as a function of years of investment t. What will this amount grow to if it is invested for 5 years and 10 years.

Q.5(a) Compute the monthly mortgage payment, total payment and total interest if the mortgage loan amounts to $80,000 at the rate of 10% per year for 20 years.

Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population
(c) what is the instantaneous rate of change in the population expected to equal in year 2000.