Practice Mathematics I questions with answers and explanations.
Subtract 6 from both sides and divide by 2: x = (28-6)/2 = 11.
By Vieta’s formula, the sum of the roots equals the coefficient 16.
aₙ=a₁+(n−1)d=5+(14−1)×4=57.
Subtract 5 from both sides and divide by 8: x = (85-5)/8 = 10.
By Vieta’s formula, the sum of the roots equals the coefficient 13.
aₙ=a₁+(n−1)d=4+(13−1)×3=40.
Choose an option to check your answer.
The sum is n(n+1)/2=55, so the mean is 55/10.
Choose an option to check your answer.
There are 2 favourable outcomes out of 7 equally likely outcomes, so P(red)=2/7.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=3x²+16x. Substituting x=1 gives 19.
An antiderivative is 1/2 x²+1x. At x=2, the value is 4.0.
The dot product is 1×4+2×3=10.
