Practice Mathematics I questions with answers and explanations.
The dot product is 1×2+6×1=8.
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.
Percentage=(9/44)×100=20.45.
Subtract 10 from both sides and divide by 6: x = (34-10)/6 = 4.
By Vieta’s formula, the sum of the roots equals the coefficient 11.
Percentage=(8/43)×100=18.60.
Subtract 9 from both sides and divide by 5: x = (24-9)/5 = 3.
By Vieta’s formula, the sum of the roots equals the coefficient 8.
aₙ=a₁+(n−1)d=8+(5−1)×1=12.
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The sum is n(n+1)/2=28, so the mean is 28/7.
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There are 6 favourable outcomes out of 9 equally likely outcomes, so P(red)=6/9.
