OCR GCE AS Level Further Maths B (MEI) Core Pure June 2018 question paper Y410

Find real numbers a and b such that (a - 3 i)(5 - i) = b - 17 i.

Find a cubic equation with real coefficients, two of whose roots are 2 - i and 3.

Write down the image of the point (2, 3) under this transformation.

You are given that this image is the point (a, 0). Find the value of a.

Find how many terms of the series

are needed for the sum to exceed 0.999 999.

Fig. 9 shows a sketch of the region OPQ of the Argand diagram defined by

Find, in modulus-argument form, the complex number represented by the point P.

Find, in the form a + i b, where a and b are exact real numbers, the complex number represented by the

point Q.

In this question you must show detailed reasoning.

Determine whether the points representing the complex numbers

• 3 + 5i

• 5.5 (cos 0.8 + i sin 0.8)

lie within this region.

Three planes have equations

- x + 2 y + z = 0 2 x - y - z = 0 x + y = a

where a is a constant.

Chris claims that the position vectors - i + 2 j + k, 2 i - j - k and i + j lie in a plane. Determine whether

or not Chris is correct.