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DSAT

Math

Given

Arithmetic and Algebra

  • Linear - Slope-Intercept Form of a Line: y=mx+b

    • m is the slope

    • b is the y-intercept

    • same slope, different y-intercept = no solutions (lines are parallel)

    • different slope, y-intercept is irrelevant = 1 solution (lines intersect)

    • same slope, same y-intercept = infinitely many solutions (same line)

  • Slope: m=y2-y2/x2-x1

  • Midpoint: (x₁ + x₂/2, y₁ + y₂/2)

  • Vertex Form of a Parabola/ Quadratic: y=a(x-h)²+k

  • Standard Form: y=ax²+bx+c

    • a>0 opens upwards

    • a<0 opens downwards

    • (h,k) is the vertex

    • c is the y-intercept

  • Distance: d=√(x2 - x1)²+(y2 - y1)²

  • Difference of Squares: a²-b²=(a+b)(a-b)

  • Quadratic Equation: x = -b ± √b^2 - 4ac / 2a

    • Discriminant is b²-4ac

      • b²-4ac>0 = 2 real solutions

      • b²-4ac = 1 = 1 real solution

      • b²-4ac<0 = no real solutions

  • Sum of Solutions: -b/2a

    • also the x-value at the vertex

    • also the axis of symmetry

  • Product of Solutions: c/a

  • Exponents

    • Multiplying: (a^n)(a^m)=a^n+m

    • Dividing: a^n/a^m=a^n-m

    • To a Power: (a^n)^m=a^n*m

  • Binomial Product

    • Difference of Squares: (x-y)(x+y)=x²-y²

    • Perfect Squares Trinomial

      • Positive: (x+y)²=x²+2xy+y²

      • Negative: (x-y)²=x²-2xy-y²

Ratios, Percentages, and Statistics

  • Simple Interest: A=Prt

    • P is the principle amount

    • r is the interest rate

    • t is time (usually in years)

  • Average/ Mean: average = sum of terms/ number of terms

  • Median: middle number

  • Range: max/min

  • Standard Deviation: the measure of spread in the data set

    • higher standard deviation = greater spread

    • lower standard deviation = smaller spread

Geometry and Trigonometry

  • Equation of a Circle: (x-h)²+(y-k)²=r²

    • (h,k) is the center of the circle

    • r is the radius

  • Radians:

    • radians=degrees*(n/180)

    • degrees=radians*(180/n)

  • Arc Length: s=r/theta

    • theta is the radians

  • Degrees in a Polygon: (n-2)*180

  • Regular Polygon Interior Angle: (n-2)180/n

  • SOHCAHTOA:

    • sin=opp/hyp

    • cos=adj/hyp

    • tan=opp/adj

  • Sine/Cosine Relationship:

    • sin(x)=cos(90-x)

    • cos(x)=sin(90-x)

  • Pythagorean Theorem: a²+b²=c²

    • c is the hypotenuse

Statistics & Science

  • Percent: part/100

  • Percentage Change: (new-old)/old

  • Probability: desired possibilities/total possibilities

  • Speed: S=d/T

  • Density: mass/volume

English

  • Period = semicolon

    • Used to separate 2 complete sentences

  • Comma + it, this, s/he, they (sometimes) = comma splice = WRONG

  • Colon = single dash = explanation/ list

  • 2 Commas = 2 dashes = 2 parentheses = non-essential clause

  • Semicolon = period = comma + FANBOYS

  • Coordinating Conjunctions: FANBOYS - joins 2 independent clauses

    • For, and, nor, but, or, yet, so

    • Comma + coordinating conjunctions

  • Subordinating Conjunctions: joins an independent and a dependent clause

    • After, although, before, because, since, until, when…

  • Continuers: words that indicate an idea is continuing where it began

    • ex. Also, and, likewise, moreover…

  • Cause-and Effect:

    • ex. Because, consequently, thus, colons, dashes…

  • Contradictors: words that indicate a sentence is shifting directions/ contrasting

    • ex. But, in contrast, despite, however…

  • Comma splices are ALWAYS INCORRECT: caused by 2 constructions

    • pronoun as subject

    • adverb at the start of a clause

DSAT

Math

Given

Arithmetic and Algebra

  • Linear - Slope-Intercept Form of a Line: y=mx+b

    • m is the slope

    • b is the y-intercept

    • same slope, different y-intercept = no solutions (lines are parallel)

    • different slope, y-intercept is irrelevant = 1 solution (lines intersect)

    • same slope, same y-intercept = infinitely many solutions (same line)

  • Slope: m=y2-y2/x2-x1

  • Midpoint: (x₁ + x₂/2, y₁ + y₂/2)

  • Vertex Form of a Parabola/ Quadratic: y=a(x-h)²+k

  • Standard Form: y=ax²+bx+c

    • a>0 opens upwards

    • a<0 opens downwards

    • (h,k) is the vertex

    • c is the y-intercept

  • Distance: d=√(x2 - x1)²+(y2 - y1)²

  • Difference of Squares: a²-b²=(a+b)(a-b)

  • Quadratic Equation: x = -b ± √b^2 - 4ac / 2a

    • Discriminant is b²-4ac

      • b²-4ac>0 = 2 real solutions

      • b²-4ac = 1 = 1 real solution

      • b²-4ac<0 = no real solutions

  • Sum of Solutions: -b/2a

    • also the x-value at the vertex

    • also the axis of symmetry

  • Product of Solutions: c/a

  • Exponents

    • Multiplying: (a^n)(a^m)=a^n+m

    • Dividing: a^n/a^m=a^n-m

    • To a Power: (a^n)^m=a^n*m

  • Binomial Product

    • Difference of Squares: (x-y)(x+y)=x²-y²

    • Perfect Squares Trinomial

      • Positive: (x+y)²=x²+2xy+y²

      • Negative: (x-y)²=x²-2xy-y²

Ratios, Percentages, and Statistics

  • Simple Interest: A=Prt

    • P is the principle amount

    • r is the interest rate

    • t is time (usually in years)

  • Average/ Mean: average = sum of terms/ number of terms

  • Median: middle number

  • Range: max/min

  • Standard Deviation: the measure of spread in the data set

    • higher standard deviation = greater spread

    • lower standard deviation = smaller spread

Geometry and Trigonometry

  • Equation of a Circle: (x-h)²+(y-k)²=r²

    • (h,k) is the center of the circle

    • r is the radius

  • Radians:

    • radians=degrees*(n/180)

    • degrees=radians*(180/n)

  • Arc Length: s=r/theta

    • theta is the radians

  • Degrees in a Polygon: (n-2)*180

  • Regular Polygon Interior Angle: (n-2)180/n

  • SOHCAHTOA:

    • sin=opp/hyp

    • cos=adj/hyp

    • tan=opp/adj

  • Sine/Cosine Relationship:

    • sin(x)=cos(90-x)

    • cos(x)=sin(90-x)

  • Pythagorean Theorem: a²+b²=c²

    • c is the hypotenuse

Statistics & Science

  • Percent: part/100

  • Percentage Change: (new-old)/old

  • Probability: desired possibilities/total possibilities

  • Speed: S=d/T

  • Density: mass/volume

English

  • Period = semicolon

    • Used to separate 2 complete sentences

  • Comma + it, this, s/he, they (sometimes) = comma splice = WRONG

  • Colon = single dash = explanation/ list

  • 2 Commas = 2 dashes = 2 parentheses = non-essential clause

  • Semicolon = period = comma + FANBOYS

  • Coordinating Conjunctions: FANBOYS - joins 2 independent clauses

    • For, and, nor, but, or, yet, so

    • Comma + coordinating conjunctions

  • Subordinating Conjunctions: joins an independent and a dependent clause

    • After, although, before, because, since, until, when…

  • Continuers: words that indicate an idea is continuing where it began

    • ex. Also, and, likewise, moreover…

  • Cause-and Effect:

    • ex. Because, consequently, thus, colons, dashes…

  • Contradictors: words that indicate a sentence is shifting directions/ contrasting

    • ex. But, in contrast, despite, however…

  • Comma splices are ALWAYS INCORRECT: caused by 2 constructions

    • pronoun as subject

    • adverb at the start of a clause

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