8 SETS, VECTORS AND FUNCTIONS

Transcription

1 1 8 SETS, VECTORS D FUCTIOS TSK Given tht e ¼ {1,, 3,..., 0}, list the memers of the following susets: ¼ {prime numers} ¼ {odd numers} c \ d [ e \ f \. The figures in the digrm indicte the numer of elements in ech suset of e Find n() Find n( [ ) c Find n( \ ) d Find n( [ ) 3. In school, there re 10 students in prticulr yer group. Out of those students, 100 study mthemtics nd 60 study physics. 15 students study neither mthemtics nor physics. Drw Venn digrm illustrting this informtion. Find n( \ P) c Find n( [ P) d Find n( [ P ) 4. P Q R Drw three digrms similr to tht given ove. Shde the following: P \ Q P [ (Q \ R) c P \ Q \ R

2 Sets, vectors nd functions 5. Given tht e ¼ {1,, 3,..., 10} nd tht ¼ {1, 4, 6} nd ¼ {, 4, 7, 8}, list the memers of the following sets: \ c \ d ( \ ) e [ TSK If k =, m = 3 nd n = 5 4, find s column vector: 3m 4n c m + k d m + n e 5k n f k +3m +n g 4(m n) h 1 (k +n). Simplify the following vectors: m +n n m +3(m +n) c 1 (m n) +n d p + 3 (q p) e + 3 ( ) +1 f 3 1 ( + c) + 3. ke copy of this grid then write on the letters to H so tht: c e O = O = + OC = d OD = OE = + f OF = O g OG = h OH = Express ech vector in terms of, or c. C C c D d D ƒ 8 5. KL = nd = 5 0 KL is prllel to. Explin why. D c C

3 Sets, vectors nd functions 3 6. KL is rhomus. Express ech vector in terms of m nd n. ƒ K c L ƒ d K K m L n 7. hs co-ordintes (3, 1). ƒ 4 3 = nd P =. Find the co-ordintes of. Find the co-ordintes of P. c Find P s column vector. TSK Write ech vector s column vector, eg. CD = H J F C E D G d I e c. Clculte the length (modulus) of,, c, d, nd e in Question 1, leving your nswers in surd form. 3. Drw nd lel ech vector elow on squred pper. f = 4 g = h = 3 PQ = 0 5 XY = 4. Write down the modulus (in surd form) of the vector with the longest length in Question 3.

4 Sets, vectors nd functions 4 TSK L = p nd L = q. S is the midpoint of L nd T cuts in the rtio : 1. Express the following vectors in terms of p nd q. ƒ S c T d ST e S f TL. ƒ O = O; OC = 4O Express the following vectors in terms of nd. C c Explin why, nd C re colliner (lie on the sme stright line) d Find the rtio : C. O 4 3 T S L 3. X cuts in the rtio : 1. 6 Y cuts DC in the rtio 1 :. Express the following vectors in terms of nd. XY D c Explin why XYD is prllelogrm. 1 C D 4. KL is prllelogrm. P is the midpoint of. PQ = +5 Express the following vectors in terms of nd. K LP c LQ d KQ e Explin why K, nd Q re colliner (lie on the sme stright line) f Find the rtio K : KQ. K Q 4 P L TSK If f(x) =3x + 6, find the vlue of: f(z) f(4) c f(1) d f(00). If g(x) =x 3, find the vlue of: g(3) g(1) c g(4) d g 1

5 Sets, vectors nd functions 5 3. If h(x) =(x +3), find the vlue of: h(4) h(0) c h() d h(p) 4. If fðxþ = x +3x 1, find the vlue of: x +4 f(0) f(1) c f(1) d f(w) 5. If f(x) =x + 7, find the vlue of x when f(x) = If g(x) =4x 18, find the vlue of x when g(x) = x If hðxþ =, find the vlue of x when h(x) = If g(x) =x 3x, find the vlues of x when g(x) = If f(x) =x + 8, find the vlues of w when f(w) =6w. 10. If f(x) = 14, find the vlue(s) of x when f(x) =0 x f(x) =x 5x c f(x) =x 8x If g(x) =3x +, write down ech function elow: g(x) 6 4g(x) +1 c 5 g(x) d 6g(x) 1. If f(x) =5x 3 nd g(x) =x + 9, solve f(x) +4=3 g(x) 13. If f(x) =4x + 5 then f(x 3) = 4(x 3) + 5 = 4x 7 Write down the function f(x + 1). 14. If g(x) =3x 6, write down ech function elow: g(x +4) g(x) c g(x) TSK 8.6 For questions 1 nd, the functions f, g nd h re s follows: fðxþ ¼x þ 3 gðhþ ¼x 1 hðxþ ¼x 4 1. Find the following: gf hf c fg d fh e gh f fgh. Evlute: fgð4þ hgðþ c ghðþ d gfð Þ e fghð3þ f gfhð0þ

6 Sets, vectors nd functions 6 In questions 3 to 8, find the inverse of ech function: 3. fðxþ ¼x 4 4. fðxþ ¼ ðx þ 1Þ 5. fðxþ ¼x 3 6. fðxþ ¼ðx þ Þ 7. fðxþ ¼ x 3 8. fðxþ ¼ x 4 þ