Digital SAT Math

Nickle

1/20 of a dollar

Pint

1/8 of a gallon of 3.7854 litres or 1/2 of quart

Infinite solutions

same slope, same y-intercept, same equations

No solution

same slope, different y-intercept

One solution

perpendicular slope, (x=a)

Negative slope

falls from left to right

Positive Slope

rises from left to right

Bigger fraction

inclined line

Smaller slope

flatter line

Substitution

For isolated variables

Elimination

Easier when equations have identical, opposite, or integer multiple terms

Two same equations

Infinite solutions

Two different constants

No solution (i.e 0 = 1)

One Intersection Point

One solution

Looses

Subtract from the equation

at least c, no less than

= c

at most c, no more than

<= c

y > mx+b / y >= mx+b

Shade above the line (From left to right)

y < mx+b / y <= mx+b

Shade below the line (From left to right)

Proportions

Must have the same units in both numerators or both denominators or in both numerator and denominator of both sides

quart

1/4 of a gallon

Linear Units

Divided with the conversion factor

Non-Linear Units

Multiplied with the conversion factor^n

Percent

"what" means x "is" means = "of" means multiplied by "percent" means divided by 100

Digital SAT Percentage Answer

must be without % sign

Percentage Change %

= (difference / initial) * 100

Answer to nearest tenth

If the hundredth decimal is 5 or more, round the tenth decimal up by one. Otherwise, leave the tenth decimal as it is.

Example:3.46 (hundredths is 6, which is more than 5) → 3.5 3.44 (hundredths is 4, which is less than 5) → 3.4

Answer to the nearest hundredth

If the thousandths decimal is 5 or more, round the hundredths decimal up by one. Otherwise, leave the hundredths decimal as it is.

Example:3.456 (thousandths is 6, which is more than 5) →3.46 3.453 (thousandths is 3, which is less than 5) → 3.45

Answer to the nearest thousandth

If the ten-thousandths decimal is 5 or more, round the thousandths decimal up by one. Otherwise, leave the thousandths decimal as it is.

Example:3.4567 (ten-thousandths is 7, which is more than 5) → 3.457 3.4563 (ten-thousandths is 3, which is less than 5) → 3.456

Mean

average (sum of values/number of values)

Median

The middle value in the least to greatest ordered data

For even → Average of Middle two values n/2 th For odd → Middle value via (n+1)/2

Mode

Most repeated numbers

Range

Max - Min

Standard Deviation (Definition For SAT)

How spread the data is

Centre

Mean: The average of all values. Median: The middle value; if even, the average of the two middle values. Mode: The most frequent value.

Spread

Variance: The average of squared differences from the mean. Standard Deviation: A measure of data spread. Range: Difference between maximum and minimum values.

Decrease Mean

Remove a larger number, Add a Smaller Number, Has decreasing frequency

Increase Mean

Remove a smaller number, Add a Larger Number, Has increasing frequency

Decrease Median or remain the same

Remove a larger number, Add a Smaller Number

Increase Median or remain the same

Remove a smaller number, Add a larger number

Symmetric Distribution

Mean = Median

The presence of large outliers

Mean > Median

Presence of small outliers

Median > Mean

Less Mean

Higher Left Density

More mean

Higher Right Density

Relationship Between mean and median

Large Outliers: If large outliers are present, the mean will increase more than the median. Small Outliers: If small outliers are present, the mean will decrease more than the median.

To find x with mean

1 Multiply the mean by the number of values 2 subtract total (i.e step 1) by sum of all values to find x

Increase Range

Adding a smaller value that is less than the current minimum Adding a larger value that is greater than the current maximum.

Average Adjustment Method

This method helps find the effect of removing or adding a specific value to a set. By recalculating the average after excluding or including that value, you can determine how much that value changes the total. For example, it shows how far someone drove on their longest day by adjusting the average distance driven when that day is removed

Dime

1/10th of a dollar

Bar graph

A bar graph compares different categories by showing the value of each with bars.

Frequency bar graph

A frequency bar graph shows how often each category occurs with bars.

Dot plots

Dot plots represent frequencies with dots (like frequency bar graphs use bars) and are ideal for small, easily countable values.

Histograms

Histograms represent frequencies with bars for ranges of values, useful for larger data sets because it is impractical to show each possible value

Upward Trend

"Increases", "rises", "grows"

Downward trend

"Decreases", "drops", "declines"

Flat trend

"Remains constant", "stops", "stays the same"

Shallow slope

"Slowly", "gradually"

Steep slope

"Rapidly", "quickly"

Scatterplots

Scatterplots display data points on an xy-plane, showing the relationship between two variables and often use a line of best fit to indicate trends.

Negative Linear Relationship

When one variable increases, the other decreases.

Positive Linear Relationship

When both variables increase together.

Non-Linear Relationship

When the relationship doesn't fit a straight line

(Upward Parabola) Parabola Opening Upwards

Indicates a positive quadratic relationship, where the function is f(x)= ax^2 + bx + c with a>0

(Downward Parabola) Parabola Opening Downwards

Indicates a negative quadratic relationship, where the function is f(x)= ax^2 + bx + c with a<0

Y-intercept of Parabolic Equation

"c"

Linear Relationship

Additional Continuity

Exponential Relationship

Multiplicative, Exponential Continuity y=a(b)^x Where, a = y-intercept, b=common factor

Exponential Function Types

halved, double, percentage... etc

Linear

Changes (i.e., increases or decreases) at a constant rate

Changes by per unit of time

Changes by of the initial value per unit of time

Exponential

Changes by (of the current value) per unit of time

Changes by a factor of (e.g., halves, doubles) per unit of time

Increasing Exponential

b>0

Decreasing Exponential

b<0

Probability

The likelihood of an event occurring, expressed as a fraction or decimal between 0 and 1.

Relative Frequency

The likelihood of an event occurring within one subset relative to that or another subset.

Identifying Relative Frequency Question

Look for questions asking for the ratio of a subset to another group, not the whole sample. For example, "What fraction of classmates who do not own a skateboard also do not own a bike?" focuses on one subgroup's frequency relative to another subgroup

Data Inference Questions

Questions that involve making generalizations or predictions about a population based on sample data

Data Inference Formula

estimate = sample proportion*population range = estimate ± margin of error (error of estimate uncertainty)

Large sample size

More Precise, small margin of error

High Confidence Level (e.g., 95%): small margin of error, wider range.

Low Confidence Level (e.g., 90%): Smaller margin of error, narrower range.

Small sample size

A less precise, large margin of error

High Confidence Level (e.g., 95%): Very large margin of error, very wide range.

Low Confidence Level (e.g., 90%): Large margin of error, but narrower range compared to high confidence.

High Confidence

Large margin of error, wider range

Less Confidence

Small Margin of Error, Narrower range

Convenience Sampling

Samples are chosen because they are easy to access or convenient

Voluntary Response Sampling

People choose to respond on their own.

Response Bias

Respondents give inaccurate answers, often due to sensitive questions.

Undercoverage

Some population members are not well represented in the sample.

Nonresponse

Some selected participants do not respond or complete the survey.

Control Group

Group that does not receive the experimental treatment.

Sample Study

A part of the population is studied to make inferences about the whole population.