Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Homework 

Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool? (We assume that all large pumps are similar and all small pumps are also similar.) 

Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm. 

A circle of center (-3 , -2) passes through the points (0 , -6) and (a , 0). Find a. 

Find the equation of the tangent at ( 0 , 2) to the circle with equation 

(x + 2)2 + (y + 1)2 = 13

An examination consists of three parts. In part A, a student must answer 2 of 3 questions. In part B, a student must answer 6 of 8 questions and in part C, a student must answer all questions. How many choices of questions does the student have? 

Solve for x 

x2 - 3|x - 2| - 4x = - 6

The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) and point C is the x-intercept of the parabola. If the equation of the parabola is given by y = -x2 + 4x + C, find C so that the area of the triangle ABC is equal to 32 square units. 

problem 3. 

The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. Find k. 

A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). Find the equation of this parabola. 

When the polynomial P(x) = x3 + 3x2 -2Ax + 3, where A is a constant, is divided by x2 + 1 we get a remainder equal to -5x. Find A. 

When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B. 

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