Mathematics. Guide

Transcription

1 Mathematics Guide Contents Question Item Objective Tpe Skill 083 ALG.0.0 Multiplechoice answer Concepts 06 ALG Multiplechoice answer Applications ALG.0.04 Multiplechoice answer Applications ALG.0.06 Multiplechoice answer Applications ALG.0.04 Multiplechoice answer Concepts 6 05 ALG.0.04 Multiplechoice answer Concepts 7 05 ALG.0 Shortconstructed answer Applications ALG.0.06 Shortconstructed answer Applications 0585 ALG.0.04 Shortconstructed answer Applications ALG.0.04 Multiplechoice answer Concepts 050 ALG.0.03 Multiplechoice answer Concepts 3 ALG.0.04 Shortconstructed answer Concepts ALG.0 Etended answer Problem solving ALG.0 Etended answer Problem solving ALG.0 Etended answer Problem solving 6 68 ALG.0.05 Etended answer Applications 7 3 ALG.0 Etended answer Problem solving Correction ke

2 A B 3 A 4 A 5 A 6 C 7 It will cost $3.5 to send the parcel.

3 8 The temperature of the rod is 80.6 degrees Fahrenheit. 0 f. 3 The inverse of this function is ( ) 0 C B The range of f () is, 5]

4 3 Eample of an appropriate solution Equation of the square root function Verte (0,,4) Point (6, 0) f ( ) A b( h) 0 A ( 6 0) 0 a a.4.4 4a 0.6 A k.4 b So, f() Coordinates of the point where she stops (0, h) f ( ) h h Answer: Carol stops at a height of 0.5 m.

5 4 Eample of an appropriate solution Inequalities representing the constraints Polgon of constraints Number of sweaters 500 B 50 A C O 500 Number of caps Coordinates of vertices A, B, and C A(50, 50), B(50, 50) and C(350, 50) Profit according to the function P 3 7 and vertices A, B and C A P $500 B P $500 C P $00 Answer: The team must sell 50 caps and 50 sweaters to maimize its profit.

6 5 Eample of an appropriate solution The supplier s new constraint is or Polgon of constraints Q T S P R 0 Objective function Z Vertices of the polgon of constraints Sstem of equations Vertices Value of objective function Profit 0 $ Q (0, 30) 0.0(0).40(30) 67 (maimum profit before additional constraint) 0 S (0, 80) 0.0(0).40(80) 333 $ $5 T(60, 30) 0.0(60).40(30) 5 (maimum profit with additional constraint) R(30,0) 0.0(30).40(0) 477 $477

7 0 0 P(0,0) 0.0(0).40(0) 07 $07 Difference in profit $67 $5 $35 Answer: The profit would decrease b $35.

8 6 Eample of an appropriate solution Draw ( ) 3 ( ) f using verte and intercept. Flip (, ) of verte and intercept Find rule of inverse f f 0 ( ) a( h) ( ) a( ) a( ) a a k (, ) (0, ) (, 0) V(, ) f ( ) ( ), Answer: The rule of correspondence for the path of the second missile is f. f ( ) ( ), or ( ) ( ), [, [ Alternate solution Domain: ], ] Range: [, [

9 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ [,, : 3 : f f Answer: The rule of correspondence for the path of the second missile is ( ) [ [,,.

10 7 Eample of an appropriate solution Find the equation of the absolute value function Verte (, 0) point (0, ) a 0 a 0 8 a 8 0 Find the value when or or Find the equation of the square root function Starting point (.5, ) point (3.5, 3) a 3 a a a So.5

11 Find the time when the height is 5 m Answer: The ball hits the wall 6.5 seconds after it was hit b the racket. Note: Students who use an appropriate method in order to determine the starting point of the square root function have shown the have a partial understanding of the problem. Do not penalize students who rounded their final answer.

12 Name : Group : Date : Mathematics Question Booklet Which of graphs below represents the equation f() []? A) C) f() f() B) D) f() f()

13 The altitude f(t) of a radiocontrolled model airplane is given b the equation f 4 ( t) t 3t 4 where t is the time of the flight in minutes and f(t) is in metres. Rounded to the nearest tenth, for how man minutes has the airplane maintained an altitude equal to or greater than 7 metres? A).0 min C) 4. min B).8 min D) 3.4 min 3 The function g is defined b the following rule: g ( ) 4 0 What is the rule of its inverse g? 0 4 A) g ( ) C) g ( ) B) g ( ) D) g ( ) 8 4

14 5 3 Given the rational function ƒ() 5. What are the equations of the asmptotes of this function? A) 3 C) 3 B) 5 D) A function is represented b the rule f().which of the following graphs represents f ()? 3 A) C) B) D)

15 7 The cost C, in dollars, to send a parcel is given b the function C() [.75].5 where is the mass in kg. How much will it cost Danielle to send a parcel that weighs 4.4 kg? 0 Given the function f ( ) 3. What is the rule of correspondence of the inverse of this function? 0 Given the function defined b the equation ( ) f. What is the domain of this function? A) R B) [6, C) [, D) [4,

16 The graph on the right represents function f The rule of this function is of the form ( ) a b( h) k f. Which of the following statements is FALSE? A) a ], 0[ C) h ]0, [ B) b ]0, [ D) k ]0, [ A rocket is shot into the air b a submarine located at the verte of the following square root function: The rocket follows the path of the square root function. What is the range of f ()? f ( ) 3 5

17 3 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,.4 m above the ground, coincides with the verte of the square root function. The foot of the slide is 6 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 0 m..4 m 4 0 m h (6, 0) At what height did she stop? 4 To raise mone, the rugb team sells caps and sweaters. In order to avoid saturating the market, the team can sell no more than 500 articles. The number of caps sold must be greater than or equal to the number of sweaters sold. The manufacturer requires an order of a minimum of 50 sweaters. The team will make a profit of $3 on each cap and $7 on each sweater. How man caps and how man sweaters must the team sell to maimize its profit?

18 5 Secondar 5 students are organizing a fundraising activit in order to lower the cost of their grad dance. During a volleball tournament, the plan to sell bottles of water and juice at a stand. The following constraints are to be respected: At least 0 bottles of water and at least 0 bottles of juice must be sold. The cannot store more than 480 bottles at the stand Letting be the number of bottles of water to be sold and, the number of bottles of juice to be sold, the students transformed the constraints into the following inequalities: The profit on each bottle of water is $0.0 and on each bottle of juice it is $.40. To determine their maimum profit, the students drew the graph of the polgon of constraints, shown above. Before deliver, the supplier imposed a new condition: The students had to order a maimum of twice as man bottles of juice as bottles of water. This new constraint will lower their maimum profit. B how much would the profit decrease because of the supplier s new condition?

19 6 Two missiles are being tested at a militar base. One missile followed the path described b ( ) 3 ( ) f before selfdestructing. The second missile followed the inverse path of the first, before it selfdestructed. What is the rule of correspondence for the path of the second missile?