20 a i The highest power will be 2 with no C1 2 C1 for clear explanation M y x2 C1 C1 for also using an example negative powers, e.g. = + 3x 1, – where 2 is the highest power. ii C1 C1 for clear explanation The highest power will be 3 with no C1 C1 for also using an example y x3 negative powers, e.g. = + 5x2 – 6, the 3 being the highest power. b C1 C1 for clear explanation Find points that cross the axes where possible and then create a table of values including for the turning point and the axis intercepts so that you have sufficient points to plot the curve. c C1 C1 for first explanation x2 1: is always positive for positive or x, negative values of hence 2x2 will also be positive as positive multiplied by positive is positive. The +5 moves y the graph up 5, so = 2x2 + 5 will also C1 C1 for second explanation x. always be positive for all values of 2: Draw the graph and illustrate all the x points on the graph are above the 7 axis. 21 a A quadratic function always has line C1 2 C1 for clear explanation M x2 symmetry because and (–x)2 have y the same value. b C1 C1 for clear explanation A cubic equation does not have a line A3 of symmetry as will have different A values depending on whether is negative or positive. c C1 C1 for clear description Rotational symmetry of order 2 about the point of inflection. 3 y 22 i B1 3 B1 correct letter with correct example M D, = 5x2 y B, = ii B1 B1 correct letter with correct example y A, = 0.5x + 2 iii B1 B1 correct letter with correct example d C, = √A iv B1 B1 correct letter with correct example 4
20 a i ii b c The highest power will be 2 with no negative powers, e.g. y = x2 + 3x – 1, where 2 is the highest power. The highest power will be 3 with no negative powers, e.g. y = x3 + 5x2 – 6, the 3 being the highest power. Find points that cross the axes where possible and then create a table of values including for the turning point and the axis intercepts so that you have sufficient points to plot the curve. 1: x2 is always positive for positive or negative values of x, hence 2x2 will also be positive as positive multiplied by positive is positive. The +5 moves the graph up 5, so y = 2x2 + 5 will also always be positive for all values of x. 2: Draw the graph and illustrate all the points on the graph are above the x axis. C1 C1 C1 C1 C1 C1 C1 2 C1 for clear explanation C1 for also using an example C1 for clear explanation C1 for also using an example C1 for clear explanation C1 for first explanation C1 for second explanation M 7 21 a b c A quadratic function always has line symmetry because x2 and (–x)2 have the same y value. A cubic equation does not have a line of symmetry as A3 will have different values depending on whether A is negative or positive. Rotational symmetry of order 2 about the point of inflection. C1 C1 C1 2 C1 for clear explanation C1 for clear explanation C1 for clear description M 3 22 i ii iii iv D, y = 5x2 B, y = A, y = 0.5x + 2 C, d = √A B1 B1 B1 B1 3 B1 correct letter with correct example B1 correct letter with correct example B1 correct letter with correct example B1 correct letter with correct example M 4
Higher_Skills_Algebra_MarkScheme_Edexcel.docx