By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI established arithmetic specification, has been up-to-date to check the necessities of the recent necessities, for first educating in 2004.
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Specify the transformations in the order in which they are used and, where there is more than one stage in the sketching of the curve, state each stage. State the equation of the line of symmetry. (i) 2 y = –2x 2 (ii) y = 4 – x2 (iii) y = 2x – 1 – x 2 For each of the following curves (a) sketch the curve (b) identify the curve as being the same as one of the following. y = ±sin x, (i) (iii) (v) 3 (i) (ii) (iii) 4 (i) (ii) y = ±cos x, y = cos(–x) y = sin(180° – x) y = sin(–x) or (ii) (iv) y = ±tan x y = tan(–x) y = tan(180° – x) Write the expression x 2 – 6x + 14 in the form (x – a)2 + b where a and b are numbers which you are to find.
13 The general quadratic curve You are now able to relate any quadratic curve to that of y = x 2. 5 (i) (ii) (iii) Write the equation y = 1 + 4x – x 2 in the form y = a[(x + p)2 + q]. Show how the graph of y = 1 + 4x – x 2 can be obtained from the graph of y = x 2 by a succession of transformations, and list the transformations in the order in which they are applied. Sketch the graph. SOLUTION (i) 32 / a[(x + p)2 + q] If 1 + 4x – x 2 then –x 2 + 4x + 1 / ax 2 + 2apx + a(p 2 + q) Comparing coefficients of x 2: a = –1.
This mapping is said to be many-to-one. A mapping can also be one-to-one, one-to-many or many-to-many. The relationship between the people and their UK passport numbers will be one-to-one. The relationship between the people and their items of luggage is likely to be one-to-many, and that between the people and the countries they have visited in the last 10 years will be many-to-many. Mappings In mathematics, many (but not all) mappings can be expressed using algebra. Here are some examples of mathematical mappings.