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PCAT Math Study Guide With Solution
Typology: Exams
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Formula between Fahrenheit/Celsius - ANSWER F= 1.8C + 32 Formula between Kelvin/Celsius - ANSWER K= C + 273 Unit Conversions: - ANSWER King Henry danced merrily down central main Kilo (1000) Deci (10^-1) Centi (10^-2) Milli (10^-3) Micro (10^-6) Nano (10^-9) Sin = Cos = Tan = - ANSWER Sin = csc Cos = sec Tan = cot Tan also equals - ANSWER sin/cos Cot also equals - ANSWER 1/tan or cos/sin
Sec also equals - ANSWER 1/cos Cos also equals - ANSWER 1/sin Circle trig identities - ANSWER cos^2 + sin^2 = 1 1 + tan^2 = sec^ 1 + cot^2 = csc^ Converting radians to degrees - ANSWER radians x 180/pi Converting degrees to radians - ANSWER degrees x pi/ Derivative of: e^x - ANSWER e^x Derivative of: ln x - ANSWER 1/x Derivative of: sin x - ANSWER cos x Derivative of: cos x - ANSWER -sin x Integral of: sin x - ANSWER -cos x Integral of: cos x - ANSWER sin x Standard deviation - ANSWER measures the spread of the data. A small standard deviation means the data is tightly packed, a large standard deviation means it is spread out. Denoted by either "omega or s."
"Normal" bell shaped curve - ANSWER a. The means is in the middle, and the curve is symmetric about the mean b. 68% of the data falls within +/- 1 standard deviation from the mean c. 95% of the data falls within +/- 2 standard deviation from the mean
Non-removable discontinuity - ANSWER 2 separate pieces (vertical asymptote)
Formula for finding median given set of numbers - ANSWER (n+1)/
Removable discontinuity - ANSWER 1 piece and can fix with one point (empty spot). Numerator and denominator cancel
How do you find where an equation of a line is discontinuous? - ANSWER Make denominator equal to 0 and solve for "x"
How do you find where an equation of a line is removable/non-removable? - ANSWER Factor both the numerator and denominator. Removable is where you cross out both the numerator and denominator.
Conditions for rejecting the null hypothesis (<0.05 means reject) - ANSWER -Larger |t| value -"s" should be small -"n" should be large -"x" furthest from the claim made
Trig graphing of a "sin" graph - ANSWER y = asin (bx + c)
"a" is the amplitude, "b" is the period, and "c" is the phase shift
How to find the max value given an equation for a curve? - ANSWER First, find derivative of equation and equal it to 0 to solve for "x" (remember, the slope of the max has a slop of 0). This "x" is the critical value.
Second, plug in the critical value to the ORIGINAL equation to solve for the max.
Formula for rate: - ANSWER Rate = Distance/time
Common Pythagorean triangles - ANSWER 3,4, 5,12,13 (10,24,26)... etc
Square root of -1 - ANSWER i
1 mile= - ANSWER 5280 feet
1 lb= - ANSWER 16 oz
and then flip "x" and "y" variables
Where is a function discontinuous? - ANSWER When denominator equals 0
"Constant" - ANSWER Straight line
What fraction is equivalent to 0.025%? - ANSWER First turn into decimal!
Second turn into fraction! 25/
One hose can fill a pool in 6 hours, another can fill it in 8 hours, how long will it take to fill the pool if they are both filling the pool. - ANSWER Rate! 1/ +1/8= 1/x
How to solve absolute value equations? Example: |2x-5| = 11 - ANSWER 2x- =11 and 2x-5= -11 (solve for both x)
How many nanograms are in a kilogram? - ANSWER 10^
Find K if the slope of the line through the points (3,k), (k,1) is 2 - ANSWER (y2-y1)/(x2-X1)
Equation and finding the b term for period - ANSWER 2pi/ b = period given in graph (now solve for b)
Given 15 consecutive integers the relationship between the mean and median.... - ANSWER Mean=median
Integral of e^x - ANSWER e^x
Indefinite integral of dx - ANSWER X+c
For integral equations... - ANSWER Either two on the outside or the center. Check and see which conditions are true
What's not a function? - ANSWER X^2 + y^2 = 1
How many real zeros does the derivative of a third degree function have? - ANSWER 0, 1, or 2
Can you take the log of a negative number? - ANSWER No (make sure to check this if solving a log equation!!)
Relationship of variables if curved line - ANSWER Variable
Relationship of variables if straight line - ANSWER Constant
What is i^17? - ANSWER 17/4= 16+ Take remainder and solve from there
Find the vertical asymptote - ANSWER Set denominator equal to zero
