Let's Go for a Ride! (My Turn) by Ivan Bulloch, Diane James, Lydia Monks, Daniel Pangbourne PDF

By Ivan Bulloch, Diane James, Lydia Monks, Daniel Pangbourne

ISBN-10: 1854345710

ISBN-13: 9781854345714

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Any answer we obtain must be checked to see if it is reasonable. For example: ² if we are finding a length then it must be positive and we reject any negative solutions ² if we are finding ‘how many people are present’ then clearly the answer must be an integer. We employ the following general problem solving method: Step 1: If the information is given in words, translate it into algebra using a variable such as x for the unknown. Write down the resulting equation. Be sure to define what the variable x represents, and include units if appropriate.

2x ¡ 1 d f (x) = b f (x) = 3 1 x+1 1 x e f (x) = ¡ p c f : x 7! p x f f : x 7! 1 3¡x 4 Use technology to help sketch graphs of the following functions. Find the domain and range of each. p x¡2 d y = x2 ¡ 7x + 10 g f : x 7! 5x ¡ 3x2 h f : x 7! x + j y = x3 ¡ 3x2 ¡ 9x + 10 k f : x 7! cyan 1 x i y= 3x ¡ 9 x2 ¡ x ¡ 2 x+4 x¡2 l y = x2 + x¡2 magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 n f : x 7! x4 + 4x3 ¡ 16x + 3 100 50 1 x3 75 25 0 5 95 100 50 75 25 0 5 m y = x3 + p c f : x 7! 4 ¡ x p f f(x) = x2 ¡ 4 1 b f : x 7!

B Find the coordinates of the vertex. c Find the axes intercepts. d Hence sketch the function. 10 An open square-based container is made by cutting 4 cm square pieces out of a piece of tinplate. If the volume of the container is 120 cm3 , find the size of the original piece of tinplate. 11 Consider y = ¡x2 ¡ 5x + 3 and y = x2 + 3x + 11. a Solve for x: ¡x2 ¡ 5x + 3 = x2 + 3x + 11. b Hence, or otherwise, determine the values of x for which x2 + 3x + 11 > ¡x2 ¡ 5x + 3. 12 Find the maximum or minimum value of the following quadratics, and the corresponding value of x: b y = ¡2x2 ¡ 5x + 2 a y = 3x2 + 4x + 7 13 600 m of fencing is used to construct 6 rectangular animal pens as shown.

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Let's Go for a Ride! (My Turn) by Ivan Bulloch, Diane James, Lydia Monks, Daniel Pangbourne


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