Simplify: 11011\(_2\) - 1101\(_2\)
101000\(_2\)
1100\(_2\)
1110\(_2\)
1011\(_2\)
Correct answer is C
11011\(_2\) - 1101\(_2\) = 1110\(_2\)
Evaluate (0.13)\(^3\)correct to three significant figures
0.00219
0.00220
0.00300
0.00390
Correct answer is B
(0.13)\(^3\) = 0.13 x 0.13 x 0.13 = 0.002197
= 0.00220 (3 s.f)
\(P = \frac{Q}{12R}\)
\(P = \frac{12Q}{R}\)
\(P = 12QR\)
\(P = \frac{12}{QR}\)
Correct answer is B
\(P \propto \frac{Q}{R}\)
\(P = K \frac{Q}{R}\)
When Q = 36, R = 16, P = 27
Then substitute into the equation
\(27 = K \frac{36}{16}\)
\(K = \frac{27 \times 16}{36}\)
\(K = 12\)
So the equation connecting P, Q and R is
\(P = \frac{12Q}{R}\)
y varies directly as w2. When y = 8, w = 2. Find y when w = 3
18
12
9
6
Correct answer is A
\(y \propto w^2\)
y = kw2
8 = k(2)2
8 = k(4)
k = 8/4
k = 2
Thus y = 2w2
When w = 3, y = 2(3)2
y = 2 x 9 = 18
Find the value of k if y - 1 is a factor of y3 + 4y2 + ky - 6
-6
-4
0
1
Correct answer is D
if y - 1 is a factor of y3 + 4y2 + ky - 6, then
f(1) = (1)3 + 4(1)2 + k(1) - 6 = 0 (factor theorem)
1 + 4 + k - 6 = 0
5 - 6 + k = 0
-1 + k = 0
k = 1