Page 05 MARKS 5. The picture shows a model of a water molecule. H H O Relative to suitable coordinate axes, the oxygen atom is positioned at point ( ) 2 2 5 − A , , . The two hydrogen atoms are positioned at points ( ) 10 18 7 − B , , and ( ) 4 6 21 − − C , , as shown in the diagram below. ( ) 10 18 7 − B , , ( ) 2 2 5 − A , , ( ) 4 6 21 − − C , , (a) Express AB and AC in component form. (b) Hence, or otherwise, find the size of angle BAC. 6. Scientists are studying the growth of a strain of bacteria. The number of bacteria present is given by the formula ( ) 0 107 200 t B t e =  , where t represents the number of hours since the study began. (a) State the number of bacteria present at the start of the study. (b) Calculate the time taken for the number of bacteria to double. [Turn over 2 4 1 4