Practice Mathematics II questions with answers and explanations.
Percentage=(10/35)×100=28.57.
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The sum is n(n+1)/2=28, so the mean is 28/7.
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There are 2 favourable outcomes out of 8 equally likely outcomes, so P(red)=2/8.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=3x²+10x. Substituting x=2 gives 32.
An antiderivative is 2/2 x²+1x. At x=3, the value is 12.0.
The dot product is 2×2+2×4=12.
Rewrite the value using base 3: 27 = 3^3. Matching exponents gives x = 3.
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Use the circle-area formula A = πr². Substituting r = 7 gives A = π × 7² = 49π.
An antiderivative is 1/2 x²+5x. At x=2, the value is 12.0.
The dot product is 1×4+6×3=22.
Rewrite the value using base 2: 4 = 2^2. Matching exponents gives x = 2.
