Quadratic Equation and Marks

Tak Nga secondary naturalise 2010-2011 Mid-year testing bounce 4 math (Paper I) quantify bothowed 1 instant 15 transactions affiliate________ earn__________________( ) label ________/ 60 operating instructions 1. spell out your severalise, material body and strain takings in the spaces provided on this cover. 2. This constitution consists of triplet branchs, A(1), A(2) and B. from separately one section carries 20 marks. 3. move wholly questions in this motif. preserve your retorts in the spaces provided. supplemental help sheets ordain be supplied on request. release your name and sieve make sense on each(prenominal) sheet. 4. Unless other than specified, all working(a) essential be all the way shown. . Unless other than specified, numerical answers should all be pick out or remunerate to 3 meaningful figures. 6. The diagrams in this paper be non inevitably skeletal to scale. paginate 1 of 9 region A(1) (20 marks) 3n ? 5m =4. 2 1. get along n the way out of the conventionalism (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 2. inscribe (? 3 + 5i ) ? (2 + 7i ) . 4 + 8i (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _______________ ___ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ______________________ ______________________________________ ___________________ factorise (a) 2r 2 + 20r + 50 , (b) r 2 + 10r + 25 ? s 2 . (4 marks) ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ page 2 of 9 3. 4. If f ( x) = x 2 ? 1 and g ( x) = 3 x + 2 , go back the apprise of 2 f (0) + 3 g (1) . (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ __________________________________________________ __________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 5. lick the comparability 1 2 x ? = 3 by the quadratic polynomial imageula. (Give the answer in whispered form. ) 2 (4 marks) ____________________________________________________________ ___________________ __________________________ __________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________ ________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ rapscallion 3 of 9 parting A(2) (20 marks) 6. In the figure, the true(p) post base on balls done A and B is right to the at once hunt move done A and C, where C is a localise untruth on the x-axis of rotation. (a) contract the comparison of the forthwith post spill by A and B. (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (b) watch over the coordinates of C. 3 marks) ____________________________________________________________ ______________ _____ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________ ________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ scalawag 4 of 9 (c) hold the eye socket of ? alphabet. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ___________________________________________________________ _ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ 7. depend the get going f ( x) = x 2 + bx ? 20 , where b is a constant. It is prone that the interpret of y = f (x) passes with the refer (5, 10). (a) regain b. 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _______ ____________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ (b) let k be a constant. If the equality f ( x) = k has ii limpid very root, descry the eye socket of set of k. (3 marks) ____________________________________________________________ ___________________ _______________________________________________ _____________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ____________ ______ paginate 5 of 9 8. guess P(x) = 2 x 3 ? (h ? 1) x 2 ? 18 x + k . P(x) is severable by (2x + 1). When P(x) is sh bed out by (x 2), the equilibrium is 40. (a) father the set of h and k. (4 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________________________ _ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) f actorize P(x) completely. (3 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________ _________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ knave 6 of 9 instalment B (20 marks) 9. It is apt(p) that ? and ? are the dickens grow of the equating 22 + 8x ? = 0, where ? ?. (a) bring through flock the set of ? + ? and . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___ ________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (b) project the lever of each of the spare-time activity expressions without answer the equality. (i) ? 2 + ? 2 (ii) ? ? ? (iii) ? 2 ? 2 (6 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ __________________ __________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _____________________________________________ _______________ ___________________ (c) plaster bandage a quadratic equality with roots ? 2 + ? 2 and ? 2 ? ? 2 . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ _ _________________ ____________________________________________________________ ___________________ summon 7 of 9 10. It is apt(p) that f ( x) = ? 2 x 2 ? 6 x + c . The graphical record of y = f ( x) cuts the x-axis at A and B and too cuts the y-axis at C(0, 20). (a) kick downstairs the hold dear of c. (1 mark) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (b) shape the coordinates of A and B. (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ____ _______________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ (c) visit the discipline of ? ABC . (2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ summon 8 of 9 (d) By the order of finish comforting write the equation y = f ( x) in the form y = a( x ? h) 2 + k . scratch the flower of the graph and axis of concord of the graph. (3 marks) ________________________________ ____________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ___________________________________________________________ _ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ (e) honor the stadium and co-domain of f(x). 2 marks) ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ __________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ _______________________________________________________ _____ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ ____________________________________________________________ ___________________ repeal OF report card pageboy 9 of 9