Find at least 3 solutions to each of the Equation and graph them in the provided cartesian plane.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1. (6 marks)

Solve the following equations. Show your work!

a) 3𝑥#$%/𝑥&2 = 𝑥#/2𝑥

b) 3 + 𝑥#5/6#𝑥= $ 2

Question 2. (5 marks) Consider the equation

3𝑦2𝑥 = 3𝑥 + 9𝑦2 + 4.

a) Find the 𝑥-intercept(s) of this equation, if any. (Give both coordinates.)

Question 3. (10 marks) Consider the equation

3−𝑦 + 1 = −3𝑥2 + 2𝑥 (Equation (1))

0 = 4𝑥 − 𝑦 − 2 (Equation (2))

a) Complete the following sentences by choosing the right statement. No justification required.

i) The graph of Equation (1) is:

• A straight line having a positive slope

• A straight line having a negative slope

• A parabola curving upward

• A parabola curving downward

• None of the above

ii) The graph of Equation (2) is:

• A straight line having a positive slope

• A straight line having a negative slope

• A parabola curving upward

• A parabola curving downward

• None of the above

c) Find at least 3 solutions to each of the Equations (1) and (2), and graph them in the provided cartesian plane.

Find 𝑐 such that the points (−1,3), (2, −4) and (𝑐, 7) all lie on a common straight line. (Show your work!)

The length of a rectangular pool is 3 meters less than twice its width. If the pool’s perimeter is 66 meters, find its length and width.

(To answer this question, first define the necessary variables and set up the necessary equation(s). Show your work!)

Tessa has 48 ft of fencing available to construct a fence that will divide her garden in two rectangular sections as shown in the figure. Find the largest total area that can be enclosed.

(To answer this question, first define the necessary variables and set up the necessary equation(s). Show your work!)

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