1. (a)

1. (b)

is parallel to

, where is a scalar.

2. Using partial fractions, we find that

Using method of differences (DIY), we have that

3. differs from by less than 1

Plot the graph of and in the GC, sketch it out. * You can key in modulus by pressing (alpha)(window)(1).

Observe that the -coordinates of the intersections points between the graphs are .

.

4.

Replace with .

5. (i) .

5. (ii) Let , then .

5. (iii)

6. (a)

Sum of first 40 even-numbered terms

We have

6. (b)

years of extraction

7.

8. We substitute the given points and into . We have

—(1)

—(2)

—(3)

Using GC,

We have .

We observe we have a circle with centre and radius

9. (i) Equations of asymptotes: .

9. (ii) Max and Min . Axial intercepts: and .

9. (iii)

(a) From the sketch, the line does not cut the curve when .

(b) From the sketch, two real roots when

.

10.