AM Last Recap 2

Vectors & Geometry

100

Magnitude of v = 3i + 4j

5

200

Multiply v = i + j by scalar 3

3i + 3j

300

Midpoint of A(1,2) and B(5,6)

(3,4)

400

Length of line segment AB with A(0,0) and B(3,4)

5

500

Equation of perpendicular bisector of AB with A(0,0), B(2,4)

y = -x + 2

Straight Lines & Circles

100

Equation of a straight line through points (0,0) and (2,3)

y = 3/2 x

200

Condition for two lines to be parallel

Gradient/Slopes are equal

300

Equation of circle with center (2, -3) and radius 5

(x-2)^2 + (y+3)^2 = 25

400

Find intersection points of x^2 + y^2 = 5 and y = x + 1

(1,2), (-2,-1)

500

Find tangent to circle x^2 + y^2 = 4 at point (2,0)

x = 2

Exponentials & Logarithms

100

Solve e^x = 5

x = ln(5)

200

Solve 2^x = 8

x = 3

300

Simplify log_a (xy)

log_a x + log_a y

400

Change of base formula for log_b x

log_b x = log x / log b

Calculus & Kinematics 1

100

Derivative of x^3

3x^2

200

Derivative of e^x

e^x

300

Find stationary points of f(x) = x^3 - 3x^2 + 2

f'(x) = 3x^2 - 6x = 3x(x-2), stationary points at x = 0, 2

400

Integrate x^2 dx

x^3 / 3 + C

500

Find displacement s if v = ds/dt = 3t^2, initial s=0

s = t^3

Calculus & Kinematics 2

100

Derivative of sin x

cos x

200

Find dy/dx if y = x^2 + 3x + 1

dy/dx = 2x + 3

300

Use first derivative test to determine max/min of f(x) = -x^2 + 4x + 1

Maximum at x = 2

400

Integrate e^(2x) dx

(1/2) e^(2x) + C

500

Solve dx/dt = 5, x(0) = 2

x = 5t + 2