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
\(|PR|^2=|PO|^2+|OR|^2\\
|PR|^2=5^2+12^2\\
|PR|=\sqrt{25+144}=\sqrt{169}=13km\)
A man bought 220 mangoes at N5x. He sold each for 3x kobo and made a gain of N8. Find the value of x
2
5
6
10
Correct answer is B
The cost price of the whole mangoes = N5x
The sold amount of the mangoes = 3x * 220 = N6.60x
The gain made on mangoes = N6.60x - N5x = N8.00 => N1.60x = N8 => \(x=\frac{8}{1.60}=\frac{1}{0.2}=\frac{10}{2}=5\)
Find the equation whose roots are 2 and \(-3\frac{1}{2}\)
2x2 + 3x + 14 = 0
2x2 + 5x + 7 = 0
2x2 + 5x - 7 = 0
2x2 + 3x - 14 = 0
Correct answer is D
x2 (sum of roots)x + (product of roots) = 0
Sum of roots \(2+-3\frac{1}{2} = -1\frac{1}{2}=-\frac{1}{2}\)
Product of roots \(=2 \times -3\frac{1}{2}=-7\\
x^2-\left(\frac{-3}{2}\right)x+(-7)=0\Rightarrow 2x^2 + 3x - 14 = 0\)
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