Practice Mathematics II questions with answers and explanations.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
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Use the circle-area formula A = πr². Substituting r = 3 gives A = π × 3² = 9π.
aₙ=a₁+(n−1)d=7+(10−1)×6=61.
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The sum is n(n+1)/2=55, so the mean is 55/10.
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There are 3 favourable outcomes out of 11 equally likely outcomes, so P(red)=3/11.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=6x²+16x. Substituting x=2 gives 56.
An antiderivative is 2/2 x²+2x. At x=3, the value is 15.0.
The dot product is 2×4+3×6=26.
Rewrite the value using base 3: 27 = 3^3. Matching exponents gives x = 3.
Percentage=(5/30)×100=16.67.
Subtract 8 from both sides and divide by 8: x = (80-8)/8 = 9.
