Probability of stopping on a star : Result The probability of winning a prize is. Work : (example) There are 12 candies in the jar.
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1 Mathematics 0/ REVIEW - Contents Question Item Objective Type Skill 008 PRO.0 Extended answer Problem solving 0 PRO.0 Extended answer Applications 050 GEO.0 Extended answer Problem solving 055 PRO.0 Extended answer Problem solving 5 00 GEO.0 Extended answer Problem solving 0 GEO.0 Extended answer Problem solving 8 PRO.0 Extended answer Problem solving - Correction key Work : (example) Number of large congruent sector : 9 Number of sectors with a star : These sectors together form large sector Number of congruent sectors : Probability of stopping on a star : 0 Result The probability of winning a prize is 0. Work : (example) There are candies in the jar. First draw, P(black candy) Second draw, P(green candy) P(black candy and green candy) P(black candy) P(green candy) Result The probability is. Area of disk Radius of circle r r Area of hexagon Area of blacken part Area of hexagon area of disk Answer The area of the black part of the logo is 5.8 cm Probability of winning soap Probability of winning cream Probability of winning a prize Answer The probability of winning a prize is.
2 5 Apothem of hexagon radius of circle m m Area of the regular hexagon A 5 m m 585 m Area of the circle A m m m area 585 m m 5.0 m Cost 5.0 m $.5/m $9.80 Answer: Excluding taxes, planting the grass will cost $9.80. Accept an answer in the interval [9, ] Side length 9. m 8. m Area of square A (8. m)(8. m) 5.9 m Area of regular pentagons 59.9 m 5.9 m 5 m Area of regular pentagon 5 m 0.5 m Length of apothem m 5 a a m Length of beam apothem + side of square + apothem m + 8. m + m 0. m Answer: The length of each beam is 0. m. Do not penalize students who rounded off their answers. Using a tree diagram (St, St) (St, Sh) (St, B) (Sh, St) (B, St) Probability of hitting at least striped rectangular area % Answer: To the nearest percent, the probability of winning a prize is %.
3 Mathematics 0/ REVIEW To win a prize in a roulette game, the wheel must stop on a star. The diagram below shows the roulette wheel used in the game. The sectors with stars are congruent. Together, their area is the same as the area of each of the other sectors. What is the probability of winning a prize in this roulette game? Work Result : The probability of winning a prize is. A jar contains black candies, green, red, yellow and blue. The candies are all the same shape and size. Lisa draws candies in succession without putting the first one back into the jar. What is the probability that she draws a black candy followed by a green one? Work Result : The probability is. A company s logo is shown on the right. B The area of sector AOB is 5. cm and angle AOB measures 0. A Each side of the regular hexagon measures cm. O What is the area of the black part of the logo? Answer Area of the shaded part of the logo is cm.
4 Customers at a local pharmacy can win a prize by spinning the wheels shown below. Wheel Wheel Soap 0 Soap Cream Cream Better luck next time! If both wheels stop on the same prize, the customer wins that particular prize. What is the probability of winning a prize? Show your work Answer The probability of winning a prize is. 5 A circular pool with a fountain in the centre has been installed in a town park. A fence in the form of a regular hexagon is constructed so that the pool touches each side of the hexagon, as shown in the diagram on the right. The pool has a diameter of m. The length of each side of the regular hexagon is 5 m. Fountain The town wants to plant grass in the areas that are shaded in the diagram. 5 m The cost of the grass is $.5/m. Excluding taxes, what will it cost the town to plant the grass around the pool? Answer: Excluding taxes, planting the grass will cost $. A hotel has a deck on its property. The deck was formed by constructing regular pentagons around a square area, as shown in the diagram below. The outside perimeter of the deck is 9. m. The area of the deck is 59.9 m. Beams A building inspector told the hotel owners that beams must be installed under the deck for more support. These beams are to run from the centre of one regular pentagon to the centre of the opposite regular pentagon. How long is each beam? Show your work.
5 A contest at a fair consists of tossing a dart at the board shown in the sketch below. Each rectangle on the board is the same size. To win a prize, the dart must land inside one of the striped rectangles at least once in two throws. Rounded to the nearest percent, what is the probability that a person will win a prize after tossing a dart twice? Answer: To the nearest percent, the probability of winning a prize is.
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