Practice Mathematics I questions with answers and explanations.
Subtract 5 from both sides and divide by 3: x = (29-5)/3 = 8.
By Vieta’s formula, the sum of the roots equals the coefficient 14.
aₙ=a₁+(n−1)d=4+(10−1)×6=58.
The dot product is 1×3+5×5=28.
Percentage=(12/47)×100=25.53.
Subtract 4 from both sides and divide by 2: x = (18-4)/2 = 7.
By Vieta’s formula, the sum of the roots equals the coefficient 11.
aₙ=a₁+(n−1)d=3+(9−1)×5=43.
Choose an option to check your answer.
The sum is n(n+1)/2=10, so the mean is 10/4.
Choose an option to check your answer.
There are 5 favourable outcomes out of 12 equally likely outcomes, so P(red)=5/12.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=12x²+4x. Substituting x=1 gives 16.
