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 circler 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 clausesFor, and, nor, but, or, yet, so

Comma + coordinating conjunctions

**Subordinating Conjunctions:**joins an independent and a dependent clauseAfter, 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**: caused by 2 constructions__ALWAYS INCORRECT__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 circler 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 clausesFor, and, nor, but, or, yet, so

Comma + coordinating conjunctions

**Subordinating Conjunctions:**joins an independent and a dependent clauseAfter, 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**: caused by 2 constructions__ALWAYS INCORRECT__pronoun as subject

adverb at the start of a clause