Mathematics Higher Level. 38. Given that. 12x. 3(4x 1) 12(4x 1) 39. Find. (3 x 2) 40. What is the value of. sin 2 x dx? A 1
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1 8. Given that f x find f ( x). ( ) (x ), x ( x ) (x ) (x ) 9. Find (x ) dx. 9 ( x ) c ( x ) c ( x ) c ( x ) c. What is the value of 6 sin x dx?. P and Q have coordinates (,, ) and (,, ). What is the length of PQ? units 9 units units units Objective Question Item ank 9/ Page
2 . line has equation xy7. Find the gradient and the coordinates of the y-intercept of this line. and, 7 7 and, and, 7 and, 7. What is the equation of the line which passes through the point (6, ) and is parallel to the line with equation y x? xy x y x y x y. The equation of a line L is xy. What is the gradient of any line perpendicular to L?. line, with gradient, passes through the mid-point of (, ) and ( 7, ). What is the equation of this line? y8 ( x ) y ( x ) y ( x ) y( x ) Objective Question Item ank 9/ Page 6
3 6. P(, ), Q(, ) and R(, ) are the vertices of a triangle. What is the gradient of the altitude from R? 7 7. The circle with equation Find the value of p. 6 has radius 7 units. x y x y p 8. The point with coordinates (6, 9) lies on the circle with centre (, 6). What is the equation of the circle? ( x) ( y6) ( x) ( y6) ( x) ( y6) ( x) ( y6) 9. The point P(6, ) lies on the circle with centre (, ). What is the equation of the tangent to the circle at P? x x 6 y y 6 Objective Question Item ank 9/ Page 7
4 . The circle with equation x What are the x-coordinates of P and Q? and and 7 and 7 and ( y) intersects the x-axis at the points P and Q.. Vectors f and g are given by f ik and g i j. Find f g. units units units 7 units. If PQ, P is the point (,, ) and R is the point (7,, 6), find QR in component form. 9 7 Objective Question Item ank 9/ Page 8
5 . If p, what is the x-component of a unit vector parallel to p? 8. Given that u t and v are parallel vectors, what is the value of t? Given that vectors u, v and w are component form?, and 6 respectively, what is uvw in Objective Question Item ank 9/ Page 9
6 6. The diagram shows a trapezium EFGH where GH is parallel to FE and GH FE. G H p F q E FG represents vector p and FE represents vector q. Find an expression for EH in terms of p and q. p p p p q q q 7. The diagram shows a square based pyramid, PQRST. ST, TQ and TP represent vectors f, g and h respectively. P S R f h T g Q Express RP in terms of f, g and h. f gh f gh f gh f gh Objective Question Item ank 9/ Page
7 8. S(,, ), T( 6,, 6) and U(,, 6) are collinear. alculate the ratio that T divides SU. : : : : 9. Given that of PQ? PQ and P is the point (,, ), what are the coordinates of the midpoint (,, ) (,, ) (,, ) (,, ) 6. Vectors u and v are given by uijk and v ipjpk. If u. v 8, what is the value of p? 6. If the vectors r and are perpendicular, what is the value of r? 6 Objective Question Item ank 9/ Page
8 6. Vectors p and q are given by and respectively. Given that p units and q unit, find the angle between p and q. 6. Vectors u and v are such that What is the value of u. v? u and u. ( u v ) t what value of x does cosx have a minimum value for 6 x? Objective Question Item ank 9/ Page
9 6. If k cos tan, what is the value of k? The graph shown in the diagram has equation of the form y cos( qx) r where x y 6 What are the values of q and r? q r 6 x If y sin x, find the value of x, in the interval x, for which y is a maximum. Objective Question Item ank 9/ Page
10 68. If cos x(cosx), how many solutions does this equation have in the interval x? 69. What is the exact value of cos? 7. The diagram shows a right angled triangle with sides of length, and and an angle x. x What is the exact value of sin x? Objective Question Item ank 9/ Page
11 7. If ksin a 6 and kcos a, where k, what is the value of ktan a? 6 7. If cosx sinx is written in the form ksin xcos a kcos xsin a, what is the value of tan a? Objective Question Item ank 9/ Page
12 Question Information and nswer Question nswer urricular rea Level of ifficulty / t bottom of page and on next page / / / / / / / Objective Question Item ank 9/ Page
13 Question nswers Key urricular rea Level of ifficulty G G G G G G G G G... / G G G G G G G G G G G G G G9... / T... / T T... / T T7... / T8... / T T... / T... / Objective Question Item ank 9/ Page
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