Given, that \(4P4_5 = 119_{10}\), find the value of P
1
2
3
4
Correct answer is C
\(4P4_5 = 119_{10}\)
\(4 \times 5^2 + P \times 5^1 + 4 \times 5^0 = 119\)
\(100 + 5P + 4 = 119\)
\(5P = 119 - 104 = 15\)
\(P = 3\)
3.4
4.3
5.9
6.2
Correct answer is B
Using the sine rule
\(\frac{|QR|}{sinP}=\frac{|PQ|}{sinR}\\
\frac{x}{sin43^o}=\frac{5}{sin53^o}\\
x = \frac{5\times sin43^o}{sin53^o}\\
=\frac{5\times 0.6820}{0.7986}\\
=4.3\)
Find the value of x in the equation 3x\(^2\) - 8x - 3 = 0
\(\frac{1}{3},-3\)
\(-\frac{1}{3},-3\)
\(-\frac{1}{3},3\)
\(\frac{1}{3},3\)
Correct answer is C
3x\(^2\) - 8x - 3 = 0
3x\(^2\) - 9x + x - 3 = 0
3x(x - 3) + 1(x - 3) = 0
(3x + 1)(x - 3) = 0
3x = -1 \(\implies\) x = \(-\frac{1}{3}\)
or x = 3.
In the diagram, ZM is a straight line. Calculate the value of x.
27o
30o
35o
37o
Correct answer is C
The sum of angles in a triangle is 180o
2xo + (2x -21)o + ∠ZYP = 180o
Also ∠ZYP = 180o - (3x+14)o
∴2xo + (2x-21)o + 180o - (3x+14)o = 180
x = 35o
PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?
180o
150o
105o
75o
Correct answer is C
< QPS = 75°
< QRS = 180° - 75° = 105° (opposite angles of a cyclic quadrilateral)
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