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1. Solve the following system of equations:

MTH-4111 Pretest B. 1. Solve the following system of equations:. 5 marks. 8 m. y. 30 m. x.

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1. Solve the following system of equations:

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  1. MTH-4111 Pretest B 1. Solve the following system of equations: 5 marks

  2. 8 m y 30 m x 2. A ship is moored to a pier by a chain. The chain hangs in the shape of a parabola part of which is submerged. The chain sinks below the water surface 5 meters from the pier and re-emerges 25 meters from the pier. The chain is attached to the top of the pier which is 2 meters above water level. The bow of the ship is an oblique line. The top of the bow is 30 meters from the pier and 8 meters above the surface of the water. The bow enters the water 40 meters from the pier. At what point does the chain attach to the bow of the ship? 10 marks

  3. A) C) B) D) 3. Two functions are described below. 5 marks f(x) = mx + bwhere m < 0 g(x) = ax2 + cwhere a > 0 and b = c. Which of the following graphs represents the function operation, f – g?

  4. h g A) C) B) D) 5 marks • Functions g and h are represented graphically to the right. • Identify the graph below that corresponds to g • h.

  5. The equations for the diagonals of a parallelogram are indicated in the diagram that is provided. A (-5, -7) and B (3, -5) are two of the vertices of the parallelogram. What is the perimeter of the parallelogram? y = 2x + 3 B(3, -5) A(-5, -7) 5 marks

  6. A (-3, 4) B (3, 2) D (-1, -2) C (5, -4) B (2, 5) A (-3, 3) D (-4, -1) C (6, -2) 6. Prove that the following quadrilateral is a rhombus. 10 marks 7. The vertices of an irregular quadrilateral are as follows: A (-3, 3), B (2, 5), C (6, -2) and D (-4, -1). Calculate its area. 10 marks

  7. CONCLUSION: G D (0,a) C (a,a) F H A (0,0) E B (a,0) 8. Complete the demonstration of the following proposition using geometric analysis. 5 marks The area of square ABCD is twice the area of square EFGH. HYPOTHESIS: y STATEMENTS JUSTIFICATIONS x 1. The coordinates of E, F, G and H are: 1. Midpoint Formula:

  8. STATEMENTS C JUSTIFICATIONS 36º B D A E 9. Complete the demonstration of following proposition: 5 marks The following diagonals of the regular pentagon form an isosceles triangle with a vertex angle of 36º. CONCLUSION: HYPOTHESIS:

  9. A B C G H F D E • ACDF and ABHG are similar trapezoids and the ratio of their areas is . Trapezoid GHEF is equivalent to parallelogram BCDE. • Given that the height of trapezoid ACDF is 12 cm and its large base is 20 cm, what is the length of the base of parallelogram BCDE? 10 marks

  10. 38° F I H G D E • ΔFDE is equivalent to rhombus IFHG. • ΔFDE ~ ΔFHG • Find the perimeter of ΔFDE. 10 marks

  11. 6 cm 8 cm 10 cm • A mother is sharing a some Tropicana orange juice between her 2 sons. However she only has 2 glasses which are both cylindrical yet have different shapes. She tries to assure her sons that she will share the juice equally between them. She fills one glass having a diameter of 6 cm to a height of 10 cm. The other glass has a diameter of 8 cm. • a) How high must she fill it to keep her promise? • b) The juice comes from a container that is a rectangular prism with a height of 19 cm whose base is a square with 10 cm sides. If after serving the juice, the container is empty, How high was the juice inside the container? 10 marks

  12. A company called Party Poppers plans to produce cardboard party hats for the New Years’ Eve celebrations. They have 2 different proposals. A cone-shaped hat with a diameter of 15 cm and a height of 20 cm and a cylindrical-shaped hat with the same diameter and height. If they have 100 square meters of material to work with, how many hats can they make for each proposal? HINT: Remember the hats will be open at one end. 10 marks

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