Convert 101101two to a number in base ten
61
46
45
44
Correct answer is C
1011012 = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 32 + 0 + 8 + 4 + 0 + 1 = 4510
In the diagram, PR is a diameter, ∠PRQ = (3x-8)° and ∠RPQ = (2y-7)°. Find x in terms of y
\(x=\frac{75-2y}{3}\)
\(x=\frac{105-3y}{2}\)
\(x=\frac{105-2y}{3}\)
\(x=\frac{75-3y}{2}\)
Correct answer is C
180 = ∠RPQ + ∠PRQ + ∠PQR Since PQR = 90 (theorem: angle in a semi circle)
180 = ∠RPQ + ∠PRQ + 90 => 180° = (3x-8)°+(2y-7)°+90°; 90+8+7 = 3x+2y =>\(\frac{105-2y}{3}=x\)
In the diagram, KL//MN, ∠LKP = 30o and ∠NMP = 45o. Find the size of the reflex ∠KPM.
285o
255o
225o
210o
Correct answer is A
∠KPM = 360o - (30 + 45)o
= 360o - 75o = 285o
A fair die is tossed once, what is the probability of obtaining neither 5 or 2
\(\frac{5}{6}\)
\(\frac{2}{3}\)
\(\frac{1}{2}\)
\(\frac{1}{6}\)
Correct answer is B
Probability of obtaining a 5 is P(5)=\(\frac{1}{6}\)
Probability of obtaining a 2 is P(2)=\(\frac{1}{6}\)
Probability of obatining either 2 or 5 = P(2∪5) = \(\frac{2}{6}\)
Probability of obtaining neither 5 or 2 = \(1 - \frac{2}{6}=\frac{4}{6}=\frac{2}{3}\)
From a point P, R is 5km due west and 12km due south. Find the distance between P and R
5km
12km
13km
17km
Correct answer is C
Using Pythagoras theorem
\(|PR|^2=|PO|^2+|OR|^2\\
|PR|^2=5^2+12^2\\
|PR|=\sqrt{25+144}=\sqrt{169}=13km\)
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