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CAT Practice Excellence

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Question One You are to explore the sequence of numbers given by the rule: 2n 2 + 3n - 1 Find the rule for the difference between any two consecutive terms for the sequence 2n 2 + 3n - 1. You should show all your working.

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Question One You are to explore the sequence of numbers given by the rule: 2n 2 + 3n - 1 Find the rule for the difference between any two consecutive terms for the sequence 2n 2 + 3n - 1. You should show all your working.

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Question Two

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An artist uses tiles to create different designs. For the design below, she uses square tiles some of which are black, others have crosses and the rest are white. The first four designs are shown below.

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There are 3 equations that can be formed to calculate the number of black, crossed and white tiles for each design (n).

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Prove that the total number of tiles in any of the designs, n, is given by the equation (2n + 1) 2. The equations are: Black Tiles = 4n + 1 Crossed tiles = 2(n 2 - n) White tiles = 2(n 2 + n)

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Prove that the total number of tiles in any of the designs, n, is given by the equation (2n + 1) 2. The equations are: Black Tiles = 4n + 1 Crossed tiles = 2(n 2 - n) White tiles = 2(n 2 + n)

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Question 5 The diagram shows the path of a jet of water from a parkʼs water sprinkler. The furthest distance that the water travels is 50 metres and can be described by the equation: y = 0.5x - 0.01x 2, where x is the horizontal distance traveled and y is the vertical maximum height that the water reaches.

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Question 5 The diagram shows the path of a jet of water from a parkʼs water sprinkler. The furthest distance that the water travels is 50 metres and can be described by the equation: y = 0.5x - 0.01x 2, where x is the horizontal distance traveled and y is the vertical maximum height that the water reaches. The point mid-way between S and D is the highest point of the water (H). Find the greatest height (MH) that the water reaches.

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Question 5 The diagram shows the path of a jet of water from a parkʼs water sprinkler. The furthest distance that the water travels is 50 metres and can be described by the equation: y = 0.5x - 0.01x 2, where x is the horizontal distance traveled and y is the vertical maximum height that the water reaches. The point mid-way between S and D is the highest point of the water (H). Find the greatest height (MH) that the water reaches.

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Question 5 The diagram shows the path of a jet of water from a parkʼs water sprinkler. The furthest distance that the water travels is 50 metres and can be described by the equation: y = 0.5x - 0.01x 2, where x is the horizontal distance traveled and y is the vertical maximum height that the water reaches. M is at x = 25

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Question 5 The diagram shows the path of a jet of water from a parkʼs water sprinkler. The furthest distance that the water travels is 50 metres and can be described by the equation: y = 0.5x - 0.01x 2, where x is the horizontal distance traveled and y is the vertical maximum height that the water reaches. M is at x = 25

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Question 5 At one end of the park is a 2.25 m high fence. The water is just managing to go over this fence. If the park caretaker moves the sprinkler so that the water just reaches the base of the fence how far will the sprinkler have to be moved?

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Question 5 At one end of the park is a 2.25 m high fence. The water is just managing to go over this fence. If the park caretaker moves the sprinkler so that the water just reaches the base of the fence how far will the sprinkler have to be moved?

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Move it back 5 m

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