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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.
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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. Area of a Sector
(1/3)LW*H
x1/y1 = x2/y2
= (x degree / 360) pi*r^2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

2. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Part/whole = %/100
S-S-S - S-A-S - A-S-A
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

3. Mixture Formula
360
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

4. Cylinders
A=L*W - P=2L+2W - Diagonals equal length
([old-new]/old)*100%
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!

5. Permutations
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Order matters - nPr=n! / (n-r)!
x1y1 = x2y2
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

6. Isosceles Triangle
= (x degree / 360) C
2 equal sides - 2 equal angles
0 - -2 - -4 - ...
A=1/2bh

7. Sum of Exterior Angles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
#successful events / total# possible outcomes
360
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

8. Percents
A=[(B1+B2)*H]/2
Part/whole = %/100
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
#successful events / total# possible outcomes

9. Median
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest

10. Rational Number
#successful events / total# possible outcomes
An=A1+(n-1)d
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
An=A1(r)^n-1

11. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=1/2bh
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

12. Arithmetic Sequence
An=A1+(n-1)d
1 - 3 - 5 - ...
Order doesn't matter - nCr=n! / r!(n-r)!
An=A1(r)^n-1

13. Even Numbers
Middle number (or average of 2) of set from smallest to largest
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
0 - -2 - -4 - ...

14. Odd Numbers
1 - 3 - 5 - ...
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

15. Volume of Prism
S=180(n-2)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(area of base)*height
Volume=(4/3)pir^3

16. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
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
D/W= (R1+R2)*T

17. Integer
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Positive and negative whole numbers
An=A1(r)^n-1
1 - 3 - 5 - ...

18. Union
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
x1y1 = x2y2
Consists of all of the elements that appear in either set without repeating elements

19. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
D=R*T - W=R*T
Square root[(x2-x1)^2 + (y2-y1)^2]
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

20. Distance Formula
Multiply number of choices available in each option to get total number of options
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

21. Equilateral Triangle
2 equal sides - 2 equal angles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=(3root3/2)r^2

22. Even/Odd Results
A=(3root3/2)r^2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Positive and negative whole numbers

23. Area of a Triangle
Multiply number of choices available in each option to get total number of options
D/W=R1T1 + R2T2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=1/2bh

24. Combined Rates
D/W=R1T1 + R2T2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Order matters - nPr=n! / (n-r)!

25. Area Hexagon
Volume=(4/3)pir^3
Order doesn't matter - nCr=n! / r!(n-r)!
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=(3root3/2)r^2

26. Combinations

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27. Length on an Arc
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
An=A1(r)^n-1
= (x degree / 360) C

28. Volume of Cone
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
(1/3)pir^2*h
2 equal sides - 2 equal angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

29. Right Triangle
(distance between opposite vertices) - square root(L^2+W^2+H^2)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Middle number (or average of 2) of set from smallest to largest
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

30. Triangle Inequality
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=S^2 - P=4S - Diagonal is root2 times side
Order matters - nPr=n! / (n-r)!
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

31. Exponent Rules
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

32. Geometric Sequences
Middle number (or average of 2) of set from smallest to largest
D/W=R1T1 + R2T2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
An=A1(r)^n-1

33. Adding/Subtracting Exponents
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
360
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
([old-new]/old)*100%

34. Intersection
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
= (x degree / 360) C
Consists of all the elements that appear in both sets

35. Extension of the Pythagorean Theorem
1 - 3 - 5 - ...
Order doesn't matter - nCr=n! / r!(n-r)!
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(distance between opposite vertices) - square root(L^2+W^2+H^2)

36. Fundamental Counting Principle
Middle number (or average of 2) of set from smallest to largest
Multiply number of choices available in each option to get total number of options
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

37. Distance/Work Formula
Volume=(4/3)pir^3
Order doesn't matter - nCr=n! / r!(n-r)!
D=R*T - W=R*T
Part/whole = %/100

38. Parallelograms
D/W= (R1+R2)*T
Volume=(4/3)pir^3
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
([old-new]/old)*100%

39. Sum of Interior Angles
(1/3)pir^2*h
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
S=180(n-2)
x1y1 = x2y2

40. Volume of Sphere
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=S^2 - P=4S - Diagonal is root2 times side
Order matters - nPr=n! / (n-r)!
Volume=(4/3)pir^3

41. Average Rate
A=[(B1+B2)*H]/2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

42. Square
Order matters - nPr=n! / (n-r)!
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=S^2 - P=4S - Diagonal is root2 times side
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

43. Congruent Triangles
2 equal sides - 2 equal angles
Middle number (or average of 2) of set from smallest to largest
S-S-S - S-A-S - A-S-A
S=180(n-2)

44. Similar Triangles
(distance between opposite vertices) - square root(L^2+W^2+H^2)
D/W= (R1+R2)*T
1 - 3 - 5 - ...
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

45. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
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

46. Direct Variation
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Multiply number of choices available in each option to get total number of options
x1/y1 = x2/y2

47. Percentage Change
Middle number (or average of 2) of set from smallest to largest
x1y1 = x2y2
([old-new]/old)*100%
A=1/2bh

48. Real Wheel Formula
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
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers

49. Weighted Average
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
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
A=S^2 - P=4S - Diagonal is root2 times side
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

50. Area Trapezoid
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
0 - -2 - -4 - ...
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
A=[(B1+B2)*H]/2