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SAT Math Formulas

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Volume of Prism
Multiply number of choices available in each option to get total number of options
(area of base)*height
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
#successful events / total# possible outcomes

2. Integer
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
x1y1 = x2y2
Positive and negative whole numbers
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

3. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D/W=R1T1 + R2T2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

4. Mode
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Middle number (or average of 2) of set from smallest to largest
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
The most frequently occurring number in a set

5. Odd Numbers
Multiply number of choices available in each option to get total number of options
1 - 3 - 5 - ...
A=S^2 - P=4S - Diagonal is root2 times side
A=(3root3/2)r^2

6. Weighted Averages
An=A1(r)^n-1
(1/3)LW*H
Positive and negative whole numbers
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

7. Triangle Inequality
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(distance between opposite vertices) - square root(L^2+W^2+H^2)

8. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1y1 = x2y2
Consists of all of the elements that appear in either set without repeating elements
(distance between opposite vertices) - square root(L^2+W^2+H^2)

9. Isosceles Triangle
Order matters - nPr=n! / (n-r)!
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
An=A1(r)^n-1
2 equal sides - 2 equal angles

10. Percents
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Part/whole = %/100
An=A1+(n-1)d

11. Parallelograms
D/W= (R1+R2)*T
An=A1(r)^n-1
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

12. Area Trapezoid
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=L*W - P=2L+2W - Diagonals equal length
A=[(B1+B2)*H]/2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

13. Direct Variation
Order matters - nPr=n! / (n-r)!
([old-new]/old)*100%
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
x1/y1 = x2/y2

14. Rectangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Part/whole = %/100
A=L*W - P=2L+2W - Diagonals equal length
(area of base)*height

15. Permutations
Consists of all the elements that appear in both sets
Order matters - nPr=n! / (n-r)!
Multiply number of choices available in each option to get total number of options
Positive and negative whole numbers

16. Area Hexagon
A=(3root3/2)r^2
x1/y1 = x2/y2
Part/whole = %/100
A=1/2bh

17. Right Triangle
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=L*W - P=2L+2W - Diagonals equal length
2 equal sides - 2 equal angles
S-S-S - S-A-S - A-S-A

18. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
An=A1(r)^n-1
D=R*T - W=R*T

19. Intersection
S=180(n-2)
Consists of all the elements that appear in both sets
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

20. Exponent Rules
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Order doesn't matter - nCr=n! / r!(n-r)!
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

21. Weighted Average
Order doesn't matter - nCr=n! / r!(n-r)!
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
The most frequently occurring number in a set

22. Rational Number
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(1/3)LW*H
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
= (x degree / 360) C

23. Same Time
#successful events / total# possible outcomes
D/W=R1T1 + R2T2
D/W= (R1+R2)*T
Order matters - nPr=n! / (n-r)!

24. Combinations

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25. Area of a Sector
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Middle number (or average of 2) of set from smallest to largest
= (x degree / 360) pi*r^2
D/W=R1T1 + R2T2

26. Same Work
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
S-S-S - S-A-S - A-S-A
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

27. Even Numbers
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Order doesn't matter - nCr=n! / r!(n-r)!

28. Sum of Exterior Angles
360
D/W= (R1+R2)*T
(1/3)pir^2*h
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

29. Union
2 equal sides - 2 equal angles
([old-new]/old)*100%
Consists of all of the elements that appear in either set without repeating elements
= (x degree / 360) C

30. Equilateral Triangle
S=180(n-2)
A=[(B1+B2)*H]/2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Part/whole = %/100

31. Sum of Interior Angles
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
S=180(n-2)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(1/3)LW*H

32. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
S=180(n-2)
2 equal sides - 2 equal angles
A=[(B1+B2)*H]/2

33. Average Rate
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Volume=(4/3)pir^3

34. Real Wheel Formula
D/W=R1T1 + R2T2
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
1 - 3 - 5 - ...

35. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Part/whole = %/100
The most frequently occurring number in a set
([old-new]/old)*100%

36. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
x1/y1 = x2/y2
S=180(n-2)
Square root[(x2-x1)^2 + (y2-y1)^2]

37. Square
#successful events / total# possible outcomes
Square root[(x2-x1)^2 + (y2-y1)^2]
A=S^2 - P=4S - Diagonal is root2 times side
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised

38. Volume of Pyramid
#successful events / total# possible outcomes
(1/3)LW*H
The most frequently occurring number in a set
An=A1(r)^n-1

39. Median
Middle number (or average of 2) of set from smallest to largest
Consists of all the elements that appear in both sets
S=180(n-2)
= (x degree / 360) C

40. Area of a Triangle
An=A1(r)^n-1
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=1/2bh

41. Arithmetic Sequence
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
An=A1+(n-1)d
0 - -2 - -4 - ...
= (x degree / 360) C

42. Geometric Sequences
An=A1(r)^n-1
A=[(B1+B2)*H]/2
Multiply number of choices available in each option to get total number of options
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

43. Same Distance
Negative number raised to even power will be positive - negative number raised to odd power will be negative - numbers with absolute values between 0 and 1 will be a smaller distance from 0 the higher the power to which they are raised
= (x degree / 360) C
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

44. Volume of Sphere
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Volume=(4/3)pir^3
(1/3)pir^2*h

45. Combined Rates
D/W=R1T1 + R2T2
The sum of the lengths of any two sides is greater than the length of the third side - AB + AC > BC - [AB - AC] < BC < AB + AC
Middle number (or average of 2) of set from smallest to largest
An=A1(r)^n-1

46. Distance/Work Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D=R*T - W=R*T
(1/3)LW*H
#successful events / total# possible outcomes

47. Mixture Formula
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
An=A1+(n-1)d
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)LW*H

48. Length on an Arc
= (x degree / 360) C
A=S^2 - P=4S - Diagonal is root2 times side
Volume=(4/3)pir^3
A=[(B1+B2)*H]/2

49. Adding/Subtracting Exponents
Square root[(x2-x1)^2 + (y2-y1)^2]
Factor out the common value - 4^a + 4^a + 4^a + 4^a - 4^a (1+1+1+1) - 4^a * 4^1 - 4^a+1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
2 equal sides - 2 equal angles

50. Congruent Triangles
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Volume=(4/3)pir^3
(1/3)pir^2*h
S-S-S - S-A-S - A-S-A