2 km. 4.5 cm. where the measures are in centimetres. Points A and B are at a distance of 12 cm from the major axis.

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1 1 Miriam made the following poster for sports week at her school. She has drawn an ellipse to represent a football. The equation of this ellipse is 1 36 where the measures are in centimetres. 1 1 Points and are at a distance of 1 cm from the major ais. What is the length, in centimetres, of segment? Michael wants to take part in an airplane race around two plons, the tops of which are km apart. To have the best chance of winning, he estimates that the sum of the distances separating him from the plons should alwas be 3 km. Epress algebraicall the ideal route for Michael's airplane. km 3 Last ear nita dined at the revolving restaurant in the CN Tower in Toronto. ssuming that the restaurant's diameter is 60 metres and that it revolves at a speed of 0. km/h, how man revolutions did nita complete during the hours and 30 minutes she was seated in the restaurant? In the figure, a circle is tangent to a parabola. The verte of the parabola corresponds to the origin of the Cartesian plane. The center of the circle corresponds to the focus of the parabola. The equation of the directri d of the parabola is = -.. Segment is perpendicular to the -ais and tangent to the circle. The Cartesian plane is scaled in centimetres. What is the measure of segment? tunnel in the shape of a parabola cuts through a mountain. The maimum width of the tunnel is 0 meters and its maimum height is 16 meters. Several reinforcement beams have been placed horizontall along the tunnel at a height of 10 meters. What is the length of reinforcement beam? d 16 m 10 m 0 m 6 The logo of a compan that sells cherries is drawn in the Cartesian plane below. bowl is represented b a portion of a parabola. cherr is represented b a circle whose equation + ( 1) = 1. The height of the logo is. cm. The -ais is the ais of smmetr of the parabola. The circle passes through the focus of the parabola.?. cm What is the width of this logo?

2 7 On a designer's "sketch pad" a car's steering wheel is represented b the following design. The central part of the wheel is the space between two branches of a hperbola, the distance between whose foci is 18 cm. The width through the centre of the wheel is 6 cm. The segment is 10 cm from the centre of the wheel. What is the length of segment? 6 cm O 10 cm 8 The line whose equation is = 0 is tangent to a circle with centre C(3, ). What is the equation of this circle? 9 The fence surrounding an amusement park is in the shape of a parabola. Each point that lies on this fence is the same distance from Route 173 as it is from restaurant R, located inside the park. The distance between Route 173 and restaurant R is 00 metres. The length of the amusement park is 800 metres. What is the width of the amusement park? Route graphic designer draws the plan of a butterfl that will be used in a children's comic strip. The bod of the butterfl is represented b an ellipse whose equation is: 1 9. E G D musement Park R 800 m Width 11 The wings are presented b a hperbola. The vertices of the hperbola are also the vertices of the ellipse. The distance between the two foci of the hperbola is 1 cm. In addition, the width of the wings of the butterfl (m ED ) is cm. What is the length (m GH ) of the wings of the butterfl? The lcan Compan logo is represented in the Cartesian plane below. H This logo was drawn using the equation of the absolute value function f and a parabola. The height of the logo is 7 m. What is the equation of the parabola? 1 The distance between the foci of an ellipse centred at the origin is 96 metres. Two of the vertices of this ellipse coincide with the foci of a second ellipse represented b the equation: 1 6. What is the equation of the first ellipse?

3 13 In the diagram on the right, the equation of the ellipse is 1. The circle has a radius of 3 m. The centre C of the 6 00 circle is located directl above the focus F of the ellipse. Line segment C F T V FT is tangent to the circle at point T. m FT = m. ll unit measures are in metres. What is the equation of the circle? (The diagram is not drawn to scale.) 1 designer has suggested a massive entrance to welcome athletes to the Olmpic Games, as shown in the Cartesian plane, scaled in metres. The athletes will enter through an arch that is in the form of a parabola and is 1 m high. The parabola can be represented b the rule of directri 10 WELCOME 1 m 10 m correspondence 0. The entr has the word WELCOME written on a line segment 1 m wide. The line segment is part of the directri of the parabola. The outer part of the entr is in the form of an absolute value function with verte 10 m above the top of the arch. What is the width of the base of the entrance? m The ellipse shown here is centred at the origin of a Cartesian coordinate sstem that is scaled in metres. The height of the ellipse is 1 metres and its width is metres. The line represented b the rule 3 intersects the ellipse at points P 1 and P. What is the distance between points P 1 and P? Given u (3, ), and v (1, - ) P 1? 1 m What are the components of the resultant of the following vector operation? P u v 17 The Egptians used an ingenious pulle sstem to move the blocks of stone used in the construction of pramids. To minimize the work needed to displace the blocks, the applied a force oriented at 6. (Work (Nm) is the scalar product of the force vector and the displacement vector.) What work is needed to displace a block of stone horizontall for a distance of 00 m, if the force applied to it is 100 N oriented at 6 o? 100 N 6 m 00 m

4 18 The following diagram shows the side view of a new obstacle course at a neighbourhood park. The first part of the obstacle course is a slide in the form of a semi-parabola whose verte is located at point (10, ). Its curve is represented b the rule: f Height (m) Slide f Climbing challenge g The second part of the obstacle course, beginning at the minimum of function f, is a wall-climbing challenge in the form of an absolute value function, g. It reaches a maimum height of metres, 10 metres awa from the lowest point of the slide. safet net is stretched under the obstacle course from point to point. What is the length of the safet net? Safet net? Distance (m) 19 Given vectors u and v shown below. u Which of the following vectors represents the resultant, r, of u v? ) r C) r v ) r D) r 0 sailboat faces two distinct forces, wind and current, whose components on a Cartesian plane are (8, 1) and (, -) respectivel. wind a) What is the measure of the angle between the two forces? current b) What is the measure of the resulting force? 1 Given vectors u and v where: u = with (-, 7) and (3, -), and v = (6, 3). Find u + v. Two unit vectors, u and v, form a 60 angle as shown. What is the magnitude of the vector w if w u 3v? v 60 u

5 N (-1, 3) 3 W On a computer screen, an alien ship was travelling at a ver rapid speed. When it reached point (3, -), it suddenl eploded with one piece moving to point (-1, 3) and the other to point C(, 1). What is the sum of vectors u and v? Give the magnitude and direction. In the diagram on the right, the terminal point of P lies on the ais and S E v u (3, -) C(, 1) (1, 8) P = 0. What is the magnitude of P? (3, ) n airplane is fling due north at 00 km/h. Suddenl, the wind starts blowing from the northwest at 0 km/h. What is the resulting speed and direction of the airplane? W N-W N N-E E P(, 0) 6 Given: u -1, 1 and 1, components of u u 3v? v. What are the S-W S S-E 7 Given u v =. The magnitude of u is 1 cm and its direction is 70. The direction of v is 10. What are the components of v? u v 8 Consider v 8 and, whose vertices are (-, ) and (8, 8). The scalar product of the two vectors is 10. What is the measure of the angle between the two vectors? 9 Given u =, with (, ) and (3, 3) and v = (1, -). Simplif the following vector epression: ( u v ) v 30 Peter and Marie are pulling on an object. The forces the applied are 100 N and 0 N respectivel but in different directions: 0 and 10. The situation is represented below. Tim is going to replace them. What force must Tim appl to produce the same effect on the object (strength and direction)? 0 N N 31 In the polgon below, CG is a square. D and G are the midpoints of sides CG and F, respectivel. Side is parallel to side EF. Using the properties of C 3 vectors, show that C C FE GF GE. Given the real functions defined b f 1 and g 1. D E What is the solution set of f > g? G F

6 N 33 n airplane leaves airport and must fl to airport. In the Cartesian plane on the right, these airports are represented b points and respectivel. The scale of the graph is in kilometres. During the flight, the plane encounters a stead wind. This wind is represented b the vector v = (0, -1). The pilot steers the plane so as to negate the effect of the wind. t what angle relative to the east should the pilot point the plane in order to reach airport? O E S (10, 1) (00, 00) 3 Solve the following inequalit in : 1 3 The rule of a rational function f is f() = What are the equations of the asmptotes of function f? 36 n merican spacecraft completed three circular orbits around the Earth before continuing on its journe towards the moon following a trajector which is tangent to its previous path. In the adjacent diagram, the Earth's center is represented b point. Point is the spacecraft's position at the moment it began its journe towards the moon. What is the equation of the spacecraft's trajector towards the moon. (8, ) (1, 6) 37 n object is thrown into the air. The height it reaches is a function of the time elapsed epressed b the formula: h 10 60, where h is the height in metres and is the time in seconds. In which interval of time will the projectile be located at a height more than 80 m? What is the solution set of the following inequalit within? 3 > 0 Sonia is replacing some of the water in her aquarium without removing the fish. When she started working, the aquarium contained 60 litres. fter 3 seconds, litres of water remained in the aquarium. This is the minimum quantit of water needed to ensure that the fish will not be harmed. Then, using a pump, Sonia filled the aquarium to its maimum capacit of 70 litres. Sonia noted that the relation between the time elapsed, in seconds, and the quantit of water in the aquarium, in litres, corresponds to an absolute value function. Throughout this process, for how man seconds was the quantit of water in the aquarium less than 3 litres? 0 Two missiles are launched seconds apart. The paths the follow over a span of 8 seconds can be represented b two different square root functions, as illustrated. How man seconds after the nd projectile has been launched, will it be higher than the 1 st projectile? Height (m) (0, 3) (6, ) 1 Consider the rational function f 1 What is the solution set of the inequalit f 0? (, 0) (, 1) 6 8 Time (s)

7 8 cm cm glassblower wants to appl a gold leaf strip around a cocktail glass. The gold leaf strip will be applied cm from the rim of the glass. The side view of this glass is represented in the following Cartesian plane. The scale of the graph is in centimetres. The rule f 10 6 is associated with the top part of the glass. The maimum diameter of the glass is 8 cm. What is the diameter of the glass at the point where the gold leaf strip will be applied? f() = Gold leaf strip 3 The curve of a skateboard ramp is defined b a square root function whose verte is (3, 1) and which passes through the point (1, 3). In order to make the ramp more secure, a metal bar was propped up under it. The rule of the line representing the metal 6 bar is g( ). t what height from the ground is this metal bar attached to 7 the ramp? f() (3, 1) ramp Each morning, the traffic on a certain highwa increases, reaches a peak, and then decreases again. This situation is represented mathematicall b the function: V t t 8 6 V(t) = the number of vehicles passing per minute t = the time, in hours, since midnight metal bar (1, 3) 6 7 To ensure a smooth and safe flow of traffic, a police officer has been assigned to monitor this section of highwa when the volume of traffic is at least 3 vehicles per minute. For how man hours should the police officer be on dut to ensure the safe flow of traffic? fter fling for 10 seconds, a hawk swoops down, catches a mouse, and immediatel takes off with its pre. The path of the hawk's descent has been determined to be in the shape of a rational function and the path of its ascent is in the shape of a square root function. The point of ascent corresponds to the verte of the square root function. Four seconds after the hawk catches the mouse, it is 8 m above the ground. The rational function is f. How man metres above the ground will the hawk be 9 seconds after it catches its pre? circular garden is represented b the equation ( 3) + ( + ) = 1. What is the equation of the footpath tangent to the garden at point (8, -1)? Two missiles are being tested at a militar base. One missile followed the path described b f 3 1 before self-destructing. The second missile followed the inverse path of the first, before it self-destructed. What is the rule of correspondence for the path of the second missile? 10 8 Given function f with equation: f. What is the solution set of f <?

8 P(w) Profit in thousands of dollars 30 9 n car dealer's weekl profit P(w) for the last 3 weeks is graphed. What profit did the dealer realize in the 9 th week? 0 n absolute value function whose verte is V(, 3) passes through point D(7, -3), as shown in the figure on the right., and C are the intercepts of the function with the aes. What is the area of triangle OC? f() O V (,3) D (7,-3) w Weeks 1 3 The graph, with the aes C graduated in meters, represents a slide that spans 31 metres in length. Three posts placed 8 meters apart support the first part of the slide. This part of the slide is represented b a square root function with verte (0, 1). The second part of the slide is linear and forms an angle of with the horizontal. s shown in the graph the second post is 8 meters awa from the first, which is located on the -ais. What is the height of the second post? Jonas is plaing with his remote control plane. From 0 to seconds, its path is that of a square root function, f(), whose verte is located at (0,3). From to 9 seconds, the plane follows the path of an absolute value function, g(). The following diagram shows the path of the plane over 9 seconds with respect to height, in meters. What is the value of f g 6, rounded to the nearest tenth? Carol's father made a slide during the winter. Placed on a Cartesian plane scaled in metres, the slide follows a square root function, as shown below. The top of the slide,. m above the ground, coincides with the verte of the square root function. The foot of the slide is 16 m horizontall from the top. Carol starts going down the slide. However, her scarf becomes jammed in the sled causing her to stop at a horizontal distance of 10 m. t what height did she stop? 1 10 (0, 1) h =? 1 st part nd part (31, 0) Height (m) 3 0 Path of plane 9 Time (s). m 1 10 m h (16, 0)