Practice Mathematics II questions with answers and explanations.
By Vieta’s formula, the sum of the roots equals the coefficient 7.
Rewrite the value using base 2: 4 = 2^2. Matching exponents gives x = 2.
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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+1x. At x=2, the value is 4.0.
The dot product is 1×3+2×5=13.
By Vieta’s formula, the sum of the roots equals the coefficient 13.
aₙ=a₁+(n−1)d=6+(9−1)×5=46.
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The sum is n(n+1)/2=45, so the mean is 45/9.
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There are 2 favourable outcomes out of 9 equally likely outcomes, so P(red)=2/9.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=3x²+14x. Substituting x=1 gives 17.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
