Reference no: EM133984248

Relevant Course Objectives:

• Apply main mathematical operations of (addition, subtraction, multiplication and division) to function.
• Find the inverse of a function.
• Form composite functions.
• Find domain and range of functions.
• Use the remainder and factor theorem.
• Find factors of a polynomial using long or synthetic division.
• Solve quadratic equations using completing the square, factorization or the quadratic formula.
• Solve logarithmic and exponential equations.
• Solve linear inequalities.
• Solve system of linear inequalities.
• Identify arithmetic and geometric sequences.
• Find the nth term of an arithmetic sequence and geometric sequence.
• Apply the knowledge of functions to problems involving supply, demand, production, revenue and cost.
• Identify the appropriate functions, equations and sequences which are to be used in problem solving in the Social Sciences.
• Use solutions to linear, quadratic, exponential and logarithmic equations to determine market equilibrium price and quantity.

Problem Set A

Question 1. Determine which of the following: Linear, Quadratic, Constant, Rational, Absolute Value or Polynomial best describes each function below.
a. f(t) = 25 - p
b. q(p) = 7p² - 4|5p - 4|
c. h(r) = (3r²/4) - t⁴
d. r(s) = (12s⁵ - 5s)/(6s⁷ + m)

Question 2. State whether the relation {(2,2), (-1,5), (5,2), (2,4)} is a function. Give a reason for your decision.

Question 3. The diagram below shows the function Q(p) drawn to scale.

Answer the following questions referring to the above diagram:
a. How many functions made up the diagram?
b. State the domain for each individual function that is drawn above.
c. Determine the value of Q(-1).
d. State the range of the function.

Question 4. Use synthetic division to determine whether (q - 3) is a factor of the polynomial q⁴ - 2q² + 2.

Question 5. Given that q(p) = 6p - 3 and w(p) = 7p + p² + 12, determine:
a. h(p) = q(p) / w(p)
b. q(p - 4) = -9
c. State why p = -3 cannot be included in the domain of h(p).

Problem Set B

Question 1. Find the inverse of h(t) = -2t / (4 - 3t).

Question 2. Given the diagram below,

provide answers to the following questions:
a. Identify two points that the straight-line passes through.
b. What is the nature or type of the quadratic's roots?
c. Determine the equation of the straight-line drawn in blue.
d. Determine the function/equation of the quadratic.
e. The straight-line and quadratic intersect at two points, one point is (0,1). Determine the second point.

Question 3. Solve the inequality: 48 < -13p + p².

Problem Set C

Question 1. Solve the following:
i. e^{2r - 1} = 3
ii. log₄(t + 3) = 3 - log₅ 125

Question 2. Determine the range of values for t that will satisfy the inequality (t - 2)/(t - 5) > 1. Get AI-free online assignment help by the best tutors.

Question 3. The fifth term of a GP is 16, the third term is 4 and the sum of the first ten terms is positive. Calculate:
i. First term
ii. Common difference
iii. Sum of the first ten terms

Problem Set D

Question 1. Graphically solve the system of linear inequalities:
4q ≥ 8 - 2p
p - 4 > q
p ≤ 8

Question 2. The sum of first n terms of an arithmetic progression is S_n = n(3n - 4). Determine:
i. Sum of the first four terms.
ii. Value of the fourth term.

Question 3. Solve the pair of equations:
xy = 2
x + y - 3 = 0

Problem Set E

Question 1. Express in terms of log p, log q and log r: log(pr²/q³).

Question 2. Determine whether the given points (0,2), (2,5) and (3,7) fall on the same straight-line.

Question 3. Classify the following sequence: r - 5, 5, r + 5, ...

Question 4. Make h the subject of the formula: 7/(5h² - 2) = m.

Question 5. Given that a quadrilateral ABCD has points (3, -1), (6, 0), (7, 3) and (4, 2) respectively:
i. Identify the diagonals of the quadrilateral ABCD.
ii. Determine whether the diagonals are perpendicular.