6 questions. Try each one, then open the answer to check yourself and read the explanation.
If A = [−1 −1 −1; 3 1 −1; 1 2 1] (rows separated by semicolons), find |A|
Answer: C (−4)
Expanding along the first row: −1(1×1 − (−1)×2) + 1(3×1 − (−1)×1) − 1(3×2 − 1×1) = −3 + 4 − 5 = −4.
In how many ways can a committee of two boys and one girl be selected from a group of five boys and three girls
Answer: B (30)
Choose 2 of 5 boys (5C2 = 10) and 1 of 3 girls (3 ways): 10 × 3 = 30.
A father is now three times as old as his son, twelve years ago, he was six times as old as his son. Calculate the present age of the father
Answer: A (60)
Let the son be y, so the father is 3y. Then 3y − 12 = 6(y − 12), so 3y = 60 and y = 20. The father is 60.
The common ratio of the g.p log y, log y2, log y4 is
Answer: A (2)
log y2 = 2 log y, so the ratio is 2 log y ÷ log y = 2 (and log y4 ÷ log y2 = 2 too).
Find the integral of f(x) = 3x2
Answer: A (x3 + c)
∫3x2 dx = 3x3/3 + c = x3 + c.
What is the value of (2 + 3i)(2 − 3i), where i is the imaginary unit?
Answer: A (13)
(2 + 3i)(2 − 3i) = 4 − 9i2 = 4 + 9 = 13, since i2 = −1.