If M = {x : 3 ≤ x < 8} and N = {x : 8 < x ≤ 12}, which of the following is true?
i. 8 ∈ M ∩ N
ii. 8 ∈ M ∪ N
iii. M ∩ N = ∅
iii only
i and ii
ii and iii only
i, ii and iii
Correct answer is A
M = {3, 4, 5, 6, 7,}, N = {9, 10, 11, 12}
1415
1315
45
1115
Correct answer is B
314×1351113−513 = 265183 = 265÷183
= 1315
If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
x α z
x α 1z
a α z2
x α 1z2
Correct answer is B
x∝1y, y ∝ z
x = ky
y = mz
Since y = mz,
x = kmz, where k and m are constants. Hence,
x ∝ 1z
Express 0.0000407, correct to 2 significant figures
0.0
0.00004
0.000041
0.0000407
Correct answer is C
0.0000407 to 2 s.f 0.000041 (2 s.f)