Practice Mathematics III questions with answers and explanations.
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The sum is n(n+1)/2=21, so the mean is 21/6.
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Use the circle-area formula A = πr². Substituting r = 2 gives A = π × 2² = 4π.
An antiderivative is 1/2 x²+5x. At x=2, the value is 12.0.
The dot product is 1×3+6×5=33.
Rewrite the value using base 2: 4 = 2^2. Matching exponents gives x = 2.
aₙ=a₁+(n−1)d=3+(9−1)×5=43.
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The sum is n(n+1)/2=15, so the mean is 15/5.
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There are 6 favourable outcomes out of 13 equally likely outcomes, so P(red)=6/13.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=15x²+6x. Substituting x=1 gives 21.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=12x²+4x. Substituting x=4 gives 208.
