By Paul Urban, David Martin
Mathematics for the overseas pupil: arithmetic HL has been written to mirror the syllabus for the two-year IB degree arithmetic HL direction. it isn't our goal to outline then path. academics are inspired to take advantage of different assets. we have now constructed the publication independently of the overseas Baccalaureate association (IBO) in session with many skilled academics of IB arithmetic. The textual content isn't recommended by means of the IBO.
This moment version builds at the strengths of the 1st variation. many fantastic feedback have been obtained from academics worldwide and those are mirrored within the alterations. every now and then sections were consolidated to permit for higher potency. alterations have additionally been made in keeping with the advent of a calculator-free exam paper. a lot of questions, together with a few to problem even the easiest scholars, were further. particularly, the ultimate bankruptcy includes over 2 hundred miscellaneous questions, a few of which require using a portraits calculator. those questions were integrated to supply tougher demanding situations for college kids and to offer them adventure at operating with difficulties that can or would possibly not require using a portraits calculator
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Extra info for Mathematics for the International Students: IB Dipolma HL Core
1, f (x) ! 0 (from above) x ! ¡1, f (x) ! 0 (from below) x ! 0 (from right), y ! 1 x ! 0 (from left), y ! ¡1 1 is asymptotic to the x-axis x and to the y-axis. The graph gets closer to the axes as it gets further from the origin. EXERCISE 1G 1 2 4 , g(x) = , h(x) = on the same set of axes. x x x Comment on any similarities and differences. CDR Friday, 13 July 2007 12:44:50 PM DAVID3 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 1 2 4 2 Sketch the graphs of f(x) = ¡ , g(x) = ¡ , h(x) = ¡ on the same set of axes.
C 2, 6, 12, 20, .... B SEQUENCES OF NUMBERS 1 st row 2 nd row 3 rd row Consider the illustrated tower of bricks. The top row, or first row, has three bricks. The second row has four bricks, and the third row has five bricks. cyan magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 If un represents the number of bricks in row n (from the top) then u1 = 3, u2 = 4, u3 = 5, u4 = 6, ...... CDR Monday, 22 October 2007 3:47:19 PM PETERDELL IB_HL-2ed 55 SEQUENCES AND SERIES (Chapter 2) The number pattern: 3, 4, 5, 6, ......
X = 4. As ¡4(1)2 is < 0 we put a ¡ sign here. As the factor is ‘squared’ the signs do not change. 100 - x black x IB_HL-2ed 31 FUNCTIONS (Chapter 1) Example 9 x¡1 : 2x + 1 Draw a sign diagram for x¡1 2x + 1 is zero when x = 1 and undefined when x = ¡ 12 : + So, -\Qw_ 1 x¡1 = 2x + 1 For x = 10, x 9 21 >0 Since (x ¡ 1) and (2x + 1) are single factors the signs alternate. CDR Thursday, 12 July 2007 12:52:26 PM DAVID3 IB_HL-2ed 32 FUNCTIONS (Chapter 1) 2 Draw a d g j m sign diagrams for: (x + 4)(x ¡ 2) ¡(x + 1)(x ¡ 3) x2 ¡ 9 x2 ¡ 3x + 2 6 ¡ 16x ¡ 6x2 b e h k n x(x ¡ 3) (2x ¡ 1)(3 ¡ x) 4 ¡ x2 2 ¡ 8x2 ¡2x2 + 9x + 5 c f i l o 3 Draw sign diagrams for: a (x + 2)2 d ¡(x ¡ 4)2 g 4x2 ¡ 4x + 1 b e h (x ¡ 3)2 x2 ¡ 2x + 1 ¡x2 ¡ 6x ¡ 9 c f i 4 Draw sign diagrams for: x+2 a x¡1 x(x + 2) (5 ¡ x)(1 ¡ 2x) 5x ¡ x2 6x2 + x ¡ 2 ¡15x2 ¡ x + 2 ¡(x + 2)2 ¡x2 + 4x ¡ 4 ¡4x2 + 12x ¡ 9 b x x+3 c 2x + 3 4¡x d 4x ¡ 1 2¡x e 3x x¡2 f ¡8x 3¡x g (x ¡ 1)2 x h 4x (x + 1)2 i (x + 2)(x ¡ 1) 3¡x j x(x ¡ 1) 2¡x k x2 ¡ 4 ¡x l 3¡x 2x2 ¡ x ¡ 6 m x2 ¡ 3 x+1 n x2 + 1 x o x2 + 2x + 4 x+1 p ¡(x ¡ 3)2 (x2 + 2) x+3 q ¡x2 (x + 2) 5¡x r x2 + 4 (x ¡ 3)2 (x ¡ 1) s x¡5 +3 x+1 t x¡2 ¡4 x+3 u 3x + 2 x ¡ 3 ¡ x¡2 x+3 E INEQUALITIES (INEQUATIONS) 2x ¡ 1 x+3 6 are examples of inequalities.
Mathematics for the International Students: IB Dipolma HL Core by Paul Urban, David Martin