Practice Mathematics III questions with answers and explanations.
f′(x)=6x²+6x. Substituting x=4 gives 120.
An antiderivative is 4/2 x²+2x. At x=5, the value is 60.0.
The dot product is 4×4+3×6=34.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 9 gives A = π × 9² = 81π.
Percentage=(6/31)×100=19.35.
Choose an option to check your answer.
The sum is n(n+1)/2=15, so the mean is 15/5.
Choose an option to check your answer.
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.
Rewrite the value using base 4: 256 = 4^4. Matching exponents gives x = 4.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 8 gives A = π × 8² = 64π.
Percentage=(5/30)×100=16.67.
