Pure Mathematics 1

!!! REMAINDER !!!

There are indications of marks of the questions. Please make sure the points you get from each question are not the same.

Do you understand?

• YES

• NO

2.The graph of y = f(x) is transformed to the graph of y=f(2x)-3.

(a) Describe fully the two single transformations that have been combined to give the resulting transformation. [3]

• Stretch with scale factor of either 2 or 1/2;

• Scale factor 1/2 in the y-direction;

• Scale factor 1/2 in the x-direction;

• Translation of 3 units in negative y-direction.

• Translation of 3 units in negative x-direction.

2.The graph of y = f(x) is transformed to the graph of y=f(2x)-3.

(b) The point P(5, 6) lies on the transformed curve y = f(2x). State the coordinates of the corresponding point on the original curve y =f(x). [2]

• x=10

• y=10

• x=9

• y=9

• 7/4

• 12

• 5

• 7/2

6. The second term of a geometric progression is 54 and the sum to infinity of the progression is 243. The common ratio is greater than 1/2. Find the tenth term, giving your answer in exact form. [5]

7. In the diagram the lengths of AB and AC are both 15 cm. The point P is the foot of the perpendicular from C to AB. The length CP = 9 cm. An arc of a circle with center B passes through C and meets AB at Q. Calculate the area of the shaded region which is bounded by the arc CQ and the lines CP and PQ. [6]

• 70.4

• 51.8cm

• 42.7<Area(cm)<42.8

• 56.2<Area(cm)<56.3