PSAT NMSQT LATEST 2026 QUESTIONS AND SOLUTIONS
RATED A+
✔✔Measures of center - ✔✔
✔✔Mean - ✔✔Sum of items/number of items = mean
AVERAGE
✔✔Median - ✔✔Middle term of a set when set up smallest to larges.
✔✔What happens when the set us even? - ✔✔Take mean of two middle numbers
✔✔Mode - ✔✔Most common number, can have multiple modes
✔✔If each appears once? - ✔✔No mode
✔✔Range - ✔✔The difference between the smallest and largest values in a set of data
✔✔Standard deviation - ✔✔How spread out or varied the data points are in a set.
✔✔Standard deviation equation - ✔✔= √average of squared differences of data points
from their mean
✔✔Normal distribution - ✔✔The typical distribution of a large sampling in a bell-curve
✔✔Confidence intervals - ✔✔A range of values defined so that there is a pre-
determined probability that the value of an unknown parameter that is under
investigation will fall within the range
✔✔The higher the level.... - ✔✔The more likely the parameter will fall within the interval.
✔✔Suppose a stockbroker has research indicating a 95% confidence interval that a
company's stock will have a return between -7.8% and +9.5% during the next year.
What does this mean? - ✔✔Unknown parameter = average stock for the year
95% chance the average return will be in this interval
✔✔Margin of error - ✔✔The maximum expected difference between the actual
(unknown) parameter and the estimate for that parameter obtained through a sample
✔✔The smaller a margin of error... - ✔✔The more accurate the survey results
✔✔Function solutions - ✔✔
✔✔Root/zero of a function - ✔✔The value for which the function has a value of zero
, ✔✔Can it have more than one? - ✔✔Yes
✔✔How do you find? - ✔✔Determine the equation or look at the graph
✔✔How to find? - ✔✔Put into foils, set equal to zero to find them
✔✔Or - ✔✔Use the quadratic formula
✔✔Imaginary numbers - ✔✔A complex number involves the square root of a negative
number, and will be expressed using i
✔✔i - ✔✔√-1
✔✔√-64 - ✔✔8i
✔✔i¹ - ✔✔i
✔✔i² - ✔✔-1
✔✔i³ - ✔✔-i
✔✔i⁴ - ✔✔1
✔✔i⁵ - ✔✔i
✔✔i⁶ - ✔✔-1
✔✔Hypotenuse - ✔✔The longest side, across from the 90 degree angle
✔✔Opposite - ✔✔Directly opposite the angle
✔✔Adjacent - ✔✔Next to the angle being used
✔✔sine = - ✔✔opposite/hypotenuse
✔✔cos = - ✔✔adjacent/hypotenuse
✔✔tan = opposite/adjacent - ✔✔
✔✔Trigonomic identities - ✔✔sin²x + cos²x = 1
tan x = sin x /cos x
RATED A+
✔✔Measures of center - ✔✔
✔✔Mean - ✔✔Sum of items/number of items = mean
AVERAGE
✔✔Median - ✔✔Middle term of a set when set up smallest to larges.
✔✔What happens when the set us even? - ✔✔Take mean of two middle numbers
✔✔Mode - ✔✔Most common number, can have multiple modes
✔✔If each appears once? - ✔✔No mode
✔✔Range - ✔✔The difference between the smallest and largest values in a set of data
✔✔Standard deviation - ✔✔How spread out or varied the data points are in a set.
✔✔Standard deviation equation - ✔✔= √average of squared differences of data points
from their mean
✔✔Normal distribution - ✔✔The typical distribution of a large sampling in a bell-curve
✔✔Confidence intervals - ✔✔A range of values defined so that there is a pre-
determined probability that the value of an unknown parameter that is under
investigation will fall within the range
✔✔The higher the level.... - ✔✔The more likely the parameter will fall within the interval.
✔✔Suppose a stockbroker has research indicating a 95% confidence interval that a
company's stock will have a return between -7.8% and +9.5% during the next year.
What does this mean? - ✔✔Unknown parameter = average stock for the year
95% chance the average return will be in this interval
✔✔Margin of error - ✔✔The maximum expected difference between the actual
(unknown) parameter and the estimate for that parameter obtained through a sample
✔✔The smaller a margin of error... - ✔✔The more accurate the survey results
✔✔Function solutions - ✔✔
✔✔Root/zero of a function - ✔✔The value for which the function has a value of zero
, ✔✔Can it have more than one? - ✔✔Yes
✔✔How do you find? - ✔✔Determine the equation or look at the graph
✔✔How to find? - ✔✔Put into foils, set equal to zero to find them
✔✔Or - ✔✔Use the quadratic formula
✔✔Imaginary numbers - ✔✔A complex number involves the square root of a negative
number, and will be expressed using i
✔✔i - ✔✔√-1
✔✔√-64 - ✔✔8i
✔✔i¹ - ✔✔i
✔✔i² - ✔✔-1
✔✔i³ - ✔✔-i
✔✔i⁴ - ✔✔1
✔✔i⁵ - ✔✔i
✔✔i⁶ - ✔✔-1
✔✔Hypotenuse - ✔✔The longest side, across from the 90 degree angle
✔✔Opposite - ✔✔Directly opposite the angle
✔✔Adjacent - ✔✔Next to the angle being used
✔✔sine = - ✔✔opposite/hypotenuse
✔✔cos = - ✔✔adjacent/hypotenuse
✔✔tan = opposite/adjacent - ✔✔
✔✔Trigonomic identities - ✔✔sin²x + cos²x = 1
tan x = sin x /cos x
