3 questions. Try each one, then open the answer to check yourself and read the explanation.
The sum of the progression 1 + x + x2 + x3 + . . . =
Answer: A (1/(1 − x))
This is a G.P. with first term 1 and common ratio x. Its sum to infinity is a/(1 − r) = 1/(1 − x) (for −1 < x < 1).
In the diagram below PQ is parallel to RS calculate the value of x
Answer: B (40°)
The angle at the crossing next to 100° is 180° − 100° = 80° (angles on a straight line). In the top triangle, ∠Q = 180° − 60° − 80° = 40°. x is alternate to ∠Q because PQ∥RS, so x = 40°.
Find the matrix T if ST = I where S = (−1 1 / 1 −2) and I is the identity matrix.
(S has rows −1, 1 and 1, −2; each option lists the rows of T)
Answer: B ((−2 −1 / −1 −1))
T = S−1. det S = (−1)(−2) − (1)(1) = 1. Swap the leading diagonal and change the signs of the other two entries: T = (−2 −1 / −1 −1). Check: ST gives the identity matrix.