A&A Review

Quadratics

100

Factor x² - 196

(x - 14)(x + 14)

200

Factor 6x² + 11x - 10

(3x - 2)(2x + 5)

300

Complete the square 3x² - 4x + 5

3(x - 2/3)² + 11/3

400

Find, in the form y = ax² + bx + c, the equation of the quadratic whose graph touches the x-axis at 4 and passes through (2, 12)

y = 3(x - 4)² 

500

(IB QUESTION) Given (k - 1)x² + 2x + (2k - 3), where k is a real number, has real distinct roots, find k

What is 1/2 < k < 2?

Functions

100

Define domain. 

The set of all possible x values, inputs

200

Given f(x) = x² - 7, state the domain and range.

Domain is all reals, range is all y values greater OR equal to -7

300

Graph x - 4 / x + 2. State all asymptotes and intercepts. 

Graph. Vertical asymptote at x = -2, Horizontal asymptote at y = 1, x - intercept at (4, 0) and y - intercept at (0, -2)

400

What is the range of 4sin(x)?

-4 <= y <= 4

500

(IB QUESTION) f(x) = x - 2 and g(x) = ax + b. Given that f(g(2)) = -3 and g(f(1)) = 5, find a and b. 

a = -2, b = 3

Exponentials and Logs

100

Calculate log₃9 + log₂16

6

200

State the domain of the function y = 3^x + 1

All real numbers

300

In 1985, there were 285 cellphone subscribers in a small town. The number of subscribers increased by 75% per year after 1985. How many cellphone subscribers were there in 1994?

43, 872 subscribers

400

Write log₉t as a log base 3 and simplify.

log₃t / log₃9 = log₃t / 2 = 1/2log₃t = log₃(radt)

500

(IB QUESTION) Let f(x) = 6 - ln(x² + 2). The graph of f passes through the point (p, 4), where p > 0. Find the value of p. 

sqrt(e² - 2) = 2.32

Unit Circle

100

Find sin(270 degrees) 

-1

200

Name an angle that is co-terminal with 45 degrees.

Teacher approves. ie; 405 degrees

300

tan^-1(1)=x. Find the value(s) of x in radians.

pi/4, 5pi/4

400

Find two angles (in RADIANS) on the unit circle, with x between 0 and 2pi, such that cos(x)= -2/3 (CALCULATOR ON)

x = 2.3 or 3.98

500

(IB QUESTION) Find the least POSITIVE value of x for which

 cos(x/2 + pi/3) = sqrt2 / 2

17pi/6

Non-Right Angle Trig

100

State the pythagorean identity.

sin²x + cos²x = 1

200

You are given two sides and an included angle. Which rule should you use?

Cosine rule.

300

Find the possible values of the included angle of a triangle with sides of length 8 and 5, and area 15 cm²

sin^-1(15/20) = 48.6 degrees or 131.4 degrees.

400

Find the measure of angle Q in triangle PQR given that angle QPR = 47 degrees, side QR = 11 m, and 

side PR = 9.6 m

Angle Q = 39.7 degrees.

500

(IB Question) Draw a triangle. Label ABC, with 

side AB = 5, angle A = 50 degrees, and angle C = 112 

degrees. Find side BC and the area of the triangle.

sine rule -- BC = 4.13 cm, area formula plug in = (1/2)(5)(4.13)sin18 = 3.19 cm²