8 questions. Try each one, then open the answer to check yourself and read the explanation.
If dy/dx = 6x − 3 and y(−1) = 8, find y(x)
Answer: D (3x2 − 3x + 2)
Integrating gives y = 3x² − 3x + k; y(−1) = 3 + 3 + k = 8, so k = 2.
Simplify log108/log104
Answer: B (3/2)
log 8/log 4 = 3 log 2/(2 log 2) = 3/2.
Simplify (√147 − √75)/√48
Answer: B (1/2)
(7√3 − 5√3)/(4√3) = 2√3/(4√3) = 1/2.
In how many ways can 7 directors sit round a table?
Answer: A (720)
n people round a table can be arranged in (n − 1)! ways: 6! = 720.
The third term of a G.P is 4 while the sixth term is 32. Find its common ratio
Answer: D (2)
ar⁵ ÷ ar² = r³ = 32/4 = 8, so r = 2.
Evaluate log28 + log216 − log24
Answer: C (5)
3 + 4 − 2 = 5.
If the angles of a quadrilateral are (3y + 10)°, (2y + 30)°, (y + 20)° and 4y°, find the value of y
Answer: C (30°)
10y + 60 = 360, so y = 30.
Simplify 2 log(2/5) − log(72/125) + log 9
Answer: D (1 − 2log2)
log(4/25 × 125/72 × 9) = log(5/2) = log 10 − log 4 = 1 − 2 log 2.