CSU Math Placement Exam with verified solutions 2024

slope-intercept form y = mx + b slope formula m = (y₂- y₁) / (x₂- x₁) point slope form y - y₁ = m(x - x₁) standard form Ax + By = C distance formula d = √[( x₂ - x₁)² + (y₂ - y₁)²] equation of a circle (x - h)² + (y - k)² = r² where (h,k) is the center and r is the radius absolute value piece wise function |x| = { x if x or= 0 { -x if x 0 FOIL First, Outer, Inner, Last what does i equal? square root of -1 i^2 - 1 i^3 - i i^4 1 quadratic formula x = -b ± √(b² - 4ac)/2a vertex form y = a(x - h)² + k vertex (-b/2a , -b² - 4ac/4a) basic laws for working w/ exponents i) (A^N)(A^M) = A^N+M ii) (A^N)^M = A^NM iii) (AB)^N = (A^N)(B^N) iv) A^0 = 1 v) A^-N = 1/A^N vi)(A/B)^N = (A^N) / (B^N) rational exponents and radicals ^n√a = a^(1/n) ^n√a^m = a^(m/n) square root reminder after finding the square root: √64 = x ± 8 = x - NOT just 8 |ax - b| c ax - b c OR ax - b c graphing on a plane **make a table of values ANGLES clockwise = negative counterclockwise = positive degrees to radians degrees x π/180 = RAD (in π) radians to degrees radians x 180/π = DEG (in °) arc length formula s = r0 (arc length) = (radius)(angle) sector area formula A = r^20/2 (Area) = (radius^2)(angle)/2 Law of Sines a/sinA = b/sinB = c/sinC Law of Cosines c²=a²+b²-2abcosC a²=b²+c²-2bcCosA b²=a²+c²-2acCosB TRIG FUNCTIONS check page 13, study graphs Basic Trig Functions csc0 = 1/sin0 sec0 = 1/cos0 cot 0 = 1/tan0 tan0 = sin0/cos0 cot0 = cos0/sin0 More Basic Trig Functions cos²0 + sin²0 = 1 1 + tan²0 = sec²0 cot²0 + 1 = csc²0 Cofunction Identities sin(-0) = -sin0 cos(-0) = cos0 tab(-0) = -tan0 Negative Angle Identities cos(0-の) = cos0cosの + sin0sinの cos(0+の) = cos0cosの - sin0sinの sin(0-の) = sin0cosの - cos0sinの sin(0+の) = sin0cosの + cos0sinの tan(0+の) = tan0 + tanの/1 - tan0tanの tan(0-の) = tan0 - tanの/1 + tan0tanの Trig Functions sin(π/2 - 0) = cos0 cos(π/2 - 0) = sin0 tan(π/2 - 0) = cot0 cot(π/2 -0) = tan0 Cofunction Identities sin(90° - 0) = cos0 cos(90° - 0) = sin0 tan(90° - 0) = cot0 cot(90° - 0) = tan0 Double Angle Identities sin(2A) = 2sin(A)cos(A) cos(2A) = cos^2(A)- sin^2(A) tan(2A) = 2tan(A)/1 - tan^2(A) Half Angle Identifies sin(A/2) = ± √1 - cosA / 2 cos(A/2) = ± √1 + cosA / 2 tan(A/2) = ± √1 - cosA / 1 + cosA inverse function A function in which two variables are inversely proportional. (4,6) (6,4)