The diagram is a circle centre O. Find the value of x
30o
50o
61o
78o
65.5\(^{\circ}\)
Correct answer is E
∠PQR (Reflex) = 360° – 68° = 292°
∠PQR = 2∠PQR
292° = 4x + 30°
4x = 292 – 30 = 262
\(x = \frac{262}{4}=65.5°\)
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
\(\frac{3}{a+b}\)
\(\frac{a-3b}{a^2-b^2}\)
\(\frac{3a-b}{a^2 – b^2}\)
\(\frac{a-3b}{a^2+b^2}\)
Correct answer is B
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\)
= \(\frac{2a-2b-a-b}{(a+b)(a-b)}\)
= \(\frac{a-3b}{a^2 - ab + ab - b^2}\)
= \(\frac{a-3b}{a^2-b^2}\)
A boy walks 800m in 20 minutes. Calculate his average speed in km per hour
2.4
4
16
24
Correct answer is A
\(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\\
Distance = 800m = \frac{800}{1000}km = 0.8km\\
Time\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}hr=\frac{1}{3}hr\\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)km/hr = (0.8\times3)km/hr\\=2.4km/hr\)
Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
x > 4
x > -4
x < 4
x < -4
Correct answer is D
\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\\
\frac{3(x+2)-4(x+1)>6}{12}; 3x + 6 – 4x – 4 > 6\
-x +2>6; -x > 4; x < -4\)
\(\frac{1}{11}\)
\(\frac{5}{22}\)
\(\frac{7}{22}\)
\(\frac{6}{11}\)
Correct answer is D
Prob (2 or 3) = prob(2) + prob(3)
Prob (mark 2) \(=\frac{7}{22}\) + Prob(mark 3) = \(\frac{5}{22}\)
Prob(2 or 3) \(=\frac{7}{22}+\frac{5}{22}=\frac{12}{22}=\frac{6}{11}\)
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