7 questions. Try each one, then open the answer to check yourself and read the explanation.
If P = [2 1; −3 0] and I is a 2×2 unit matrix, evaluate P2 − 2P + 4I (matrices written row by row, rows separated by ;)
Answer: C ([1 0; 0 1])
P2 = [1 2; −6 −3] and 2P = [4 2; −6 0]. So P2 − 2P + 4I = [1 − 4 + 4, 2 − 2; −6 + 6, −3 − 0 + 4] = [1 0; 0 1].
Calculate the mean deviation of the sets of numbers 7, 3, 14, 9, 7 and 8.
Answer: D (2 1/3)
Mean = 48/6 = 8. The distances from 8 are 1, 5, 6, 1, 1, 0, which add to 14. Mean deviation = 14/6 = 2⅓.
The shadow of a pole 5√3 cm high is 5.5cm. Find the angle of elevation of the sum.
Answer: C (60°)
tan θ = height ÷ shadow = 5√3/5 = √3, so the angle of elevation of the sun is 60°.
Evaluate (0.21 × 0.072 × 0.00054)/(0.006 × 1.68 × 0.063) correct to 4 s.f.
Answer: A (0.01286)
Top = 8.1648 × 10−6 and bottom = 6.3504 × 10−4. The quotient is 0.012857…, which is 0.01286 to 4 significant figures.
If N = [3 5 −4; 6 −3 −5; −2 2 1] find |N| (matrix written row by row, rows separated by ;)
Answer: A (17)
Expand along the first row: 3(−3 + 10) − 5(6 − 10) − 4(12 − 6) = 21 + 20 − 24 = 17.
A man invested ₦5,000 for 9 months at 4%. What is the simple interest?
Answer: A (₦150)
Simple interest = PRT/100 = 5000 × 4 × (9/12) ÷ 100 = ₦150.
In a class of 60 students, 30 offer Physics and 40 offer Chemistry. If a student is picked at random from the class, what is the probability that the student offers both Physics and Chemistry?
Answer: D (1/6)
30 + 40 = 70, which is 10 more than the 60 students, so 10 students offer both. Probability = 10/60 = 1/6.