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Algebra
22A rectangle is enlarged by scale factor 1.5. How does its perimeter change?→A regular polygon has interior angle 165^\circ. Find the number of sides.→Find the arc length of a circle with radius 7 cm and angle 120 degree.→Find the coordinates of the point dividing the line segment joining (1,2) and (9,10) in the ratio 1:3.→Find the distance between (2,-3) and (8,9)→Find the equation of the circle with centre (3,-2) and radius 5.→Find the equation of the perpendicular bisector of the line joining (2,4) and (6,8).→Find the midpoint of the line joining (-4,6) and (10,-2).→If f of x equals x squared minus 3 x plus 4, find f of 2 and f of negative 1.→1/(x+4) - 1/(x-7) = 11/30→Find k for 2x^2 + kx + 3 = 0 equal roots→Find k for kx(x-2) + 6 = 0 equal roots→Find the value of $k$ such that $x^2 + kx + 9$ has exactly one real root.→If one root of the equation x squared minus 2 m x minus m minus 3 equals 0 is negative 1, what is the other root?→The roots of x squared minus p x plus 12 equals 0 differ by 2. Find p.→Train travels 480 km if speed had been 8 km/h less it takes 3 hours more→Line AB passes through points A(-6,6) and B(12,3). If the equation of the line is written in slope-intercept form, y equals m x plus b , then m equals negative 1 divided by 6 . What is the value of b?→Find the point of intersection of y equals 2 x minus 5 and y equals negative x plus 7.→Find the value of k such that the system has no solutions: 2x+ky equals 6 and 4x+10y equals 12→Solve the system: 3x - 2y equals 7 and 5x + y equals 19→Two numbers differ by 14 and their sum is 68. Find the numbers.→A phone plan charges a fixed fee plus £0.12 per minute. If 250 minutes cost £41, find the fixed fee.→
Calculus
7Approximate the area under the curve f(x) = 3x + 1 on [0, 2] using Riemann sums, then find the exact area using a definite integral.→Calculate the area between y equals x and y equals x squared.→Find the area enclosed by the curves y = sin(x) and y = cos(x) on the interval [π/4, 5π/4]→Find the area of the region bounded by the graph of y equals the absolute value of x squared minus 1 and the x-axis from x = −2 to x = 2.→Find the area of the region bounded by x equals negative 3 y squared and y equals negative 2 x by integrating with respect to y.→Find the area under $y=x^2$ from $x=0$ to $x=3$.→Use a double integral to find the area of the region bounded by y equals 1 minus x squared and y equals x squared minus 3.→