Prepare for your Precalculus final exam with these practice questions and answers. This covers functions, trigonometry, logarithms, sequences, and introductory limits.
Q: Complete the Square
Answer: x^2+bx = (x+(b/2))^2 – (b/2)^2
Q: Quadratic Formula
Answer: (-b +/- sqrt(b^2 – 4ac))/(2a)
Q: Slope of a Line
Answer: (y2-y1)/(x2-x1)
Q: Equation of a Line
Answer: y = mx+b
Q: Equation of a Line with 1 point and Slop
Answer: y2-y1 = m(x2-x1)
Q: Equation of a Line with 2 points
Answer: y2-y1 = ((y2-y1)/(x2-x1))(x2-x1)
Q: Vertical Shift Down
Answer: f(x) = x^2 – 2 Shift down 2
Q: Vertical Shift Up
Answer: f(x) = x^2 + 3 Shift up 3
Q: Horizontal Shift Right
Answer: f(x) = (x-3)^2
Q: Horizontal Shift Left
Answer: f(x) = (x+2)^2 Shift left 2
Q: Vertical Stretch
Answer: f(x) = 2x^2 Stretch by 2
Q: Vertical Shrink
Answer: f(x) = (1/2)x^2 Shrink by 2
Q: Horizontal Stretch
Answer: f(x) = (x/2)^2 Stretch by 2
Q: Horizontal Shrink
Answer: f(x) = (4x)^2 shrink by 1/4
Q: Rules of Exponents
Answer: x^m + x^n = x^(m+n)x^m * y^m = (xy)^m(x^m)^n = x^nmx^0 = 1x^-m = 1/x^m(x^m)/(x^n) = x^(m-n)(x^m)/(y^m) = (x/y)^m
Q: Exponential Growth
Answer: f(x) = cb^(kx)
Q: Population Growth
Answer: P(x) = P(0)*r^(t/d)
Q: Exponential Growth and Doubling
Answer: P(t) = P(0) * 2^((t-t0)/d)
Q: Simple Interest
Answer: P(1+rm)
Q: Compound Interest (once)
Answer: P(1+r)^m
Q: Compound Interest (n times)
Answer: P(1+r/n)^(nm)
Q: Laws of Logs
Answer: b^(log(b)y) = ylog(b)y^t = t*log(b)^ylog(b)xy = log(b)x + log(b)yb^x * b^y = b^(x+y)b^x / b^y = b^(x-y)logb(b)(x/y) = log(b)x – log(b)ylog(b)(1/y) = -log(b)y
Q: Laws of Natural Logs
Answer: e^0 = 1e^1 = ee^x + e^y = e(x+y)e^(-x) = 1/e^x(e^x)/(e^y) = e^(xy)ln1 = 0lne = 1ln(xy) = lnx + lnyln(1/x) = -lnxln(x/y) = lnx – lnylnx^t = t * lnx
Q: Unit Circle
Answer: 0,1(sqrt(3)/2), 1/2)(sqrt(2)/2,sqrt(2)/2)(1/2, sqrt(3)/2)1,0
Q: Change of Base formula
Answer: log(b)(y) = (log(a)(y) / log(a)(b))
Q: SohCahToa
Answer: Sine (Opp/Hyp)Cos (Adj/Hyp)Tan (Opp/Adj)
Q: Trigonometric Identities
Answer: Cos^(2)x + sin^(2)x = 1cos(-x) = cosxsin(-x) = -sinxtan(-x) = -tanxcos((pi/2) – x) = sinxsin((pi/2) – x) = cosxtan((pi/2) – x) = 1/tanxcos(x+pi) = -cosxsin(x+pi) = -sinxtan(x+pi) = tanx