Choose a course and topic, attempt each question and open its complete worked solution when you are ready.
Find the slope of y=x²+3x at x=2.
Differentiate and then substitute x=2.
Evaluate lim(x→π) sin(π−x)/[π(π−x)].
Simplify the expression before substitution and preserve one-sided information.
Substitution into the original expression verifies the stated domain and final value.
Find the circle passing through (0,0), (4,0) and (0,6).
Use x²+y²+Dx+Ey+F=0 and substitute the three points.
Find the equation of the perpendicular bisector of the segment joining (1,2) and (5,6).
The midpoint is (3,4). The segment slope is 1, so the perpendicular slope is −1.
Find the sum 7+77+777+⋯ to n terms.
Write each term as 7(10ᵏ−1)/9 and sum the geometric series.
For the geometric progression \(\frac{5}{2}\), \(\frac{5}{4}\), \(\frac{5}{8}\), …, find its twentieth term and its nth term.
Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.
The displayed substitutions cover every requested part and verify the result against the original data.
For distinct integers a and b, prove that a−b divides aⁿ−bⁿ for every positive integer n.
Write a=(a−b)+b and expand aⁿ.
Using digits 1,2,3,4,5 without repetition, count (i) all four-digit numbers(ii) the even ones.
For part (ii), first choose the last digit as 2 or 4.
Evaluate [i¹⁸+(\(\frac{1}{i}\))²⁵]³.
Reduce each power using the four-term cycle of i.
Evaluate tan(19π/3).
Tangent has period π.