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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. Distance Formula
(area of base)*height
Square root[(x2-x1)^2 + (y2-y1)^2]
A=1/2bh
Consists of all the elements that appear in both sets

2. Length on an Arc
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
= (x degree / 360) C
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

3. Percentage Change
D/W=R1T1 + R2T2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
The most frequently occurring number in a set
([old-new]/old)*100%

4. Same Work
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
D=R*T - W=R*T
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

5. Congruent Triangles
S-S-S - S-A-S - A-S-A
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
Square root[(x2-x1)^2 + (y2-y1)^2]
A=L*W - P=2L+2W - Diagonals equal length

6. Arithmetic Sequence
An=A1+(n-1)d
A=(3root3/2)r^2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
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

7. Parallelograms
0 - -2 - -4 - ...
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

8. Combined Rates
An=A1+(n-1)d
D/W=R1T1 + R2T2
A=1/2bh
1 - 3 - 5 - ...

9. Square
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=1/2bh
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=S^2 - P=4S - Diagonal is root2 times side

10. Same Rate
D/W= (R1+R2)*T
= (x degree / 360) pi*r^2
D/W=R1T1 + R2T2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

11. Odd Numbers
(1/3)LW*H
Consists of all of the elements that appear in either set without repeating elements
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
1 - 3 - 5 - ...

12. Weighted Average
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
The most frequently occurring number in a set
Order matters - nPr=n! / (n-r)!
([old-new]/old)*100%

13. Rational Number
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(1/3)pir^2*h
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

14. Sum of Interior Angles
A=[(B1+B2)*H]/2
Square root[(x2-x1)^2 + (y2-y1)^2]
(area of base)*height
S=180(n-2)

15. Extension of the Pythagorean Theorem
An=A1+(n-1)d
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Consists of all the elements that appear in both sets

16. Distance/Work Formula
A=[(B1+B2)*H]/2
D=R*T - W=R*T
([old-new]/old)*100%
A=(3root3/2)r^2

17. Right Triangle
A=S^2 - P=4S - Diagonal is root2 times side
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)LW*H
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

18. Similar Triangles
Middle number (or average of 2) of set from smallest to largest
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
Consists of all of the elements that appear in either set without repeating elements

19. Percents
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Part/whole = %/100
2 equal sides - 2 equal angles
D=R*T - W=R*T

20. Isosceles Triangle
A=(3root3/2)r^2
2 equal sides - 2 equal angles
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(N1) + AVG2(N2) = AVGtotal(Ntotal)

21. Integer
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Consists of all of the elements that appear in either set without repeating elements
Positive and negative whole numbers
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

22. Probability
Volume=(4/3)pir^3
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
#successful events / total# possible outcomes
Positive and negative whole numbers

23. Direct Variation
= (x degree / 360) pi*r^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
1 - 3 - 5 - ...
x1/y1 = x2/y2

24. Exponent Rules
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
S-S-S - S-A-S - A-S-A
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Positive and negative whole numbers

25. Fundamental Counting Principle
A=S^2 - P=4S - Diagonal is root2 times side
The most frequently occurring number in a set
D=R*T - W=R*T
Multiply number of choices available in each option to get total number of options

26. Area of a Triangle
Part/whole = %/100
x1/y1 = x2/y2
A=1/2bh
2 equal sides - 2 equal angles

27. Volume of Pyramid
#successful events / total# possible outcomes
Order doesn't matter - nCr=n! / r!(n-r)!
Middle number (or average of 2) of set from smallest to largest
(1/3)LW*H

28. Special Right Triangles
A=(3root3/2)r^2
x1y1 = x2y2
= (x degree / 360) pi*r^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

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

30. Equilateral Triangle
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
2 equal sides - 2 equal angles
A=1/2bh

31. Same Distance
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
1 - 3 - 5 - ...
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D=R*T - W=R*T

32. Even Numbers
D/W= (R1+R2)*T
An=A1+(n-1)d
A=(3root3/2)r^2
0 - -2 - -4 - ...

33. Volume of Cone
An=A1+(n-1)d
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
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)pir^2*h

34. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest
D/W=R1T1 + R2T2
1 - 3 - 5 - ...

35. Median
Middle number (or average of 2) of set from smallest to largest
0 - -2 - -4 - ...
An=A1(r)^n-1
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

36. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
An=A1+(n-1)d
360
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

37. Union
Consists of all of the elements that appear in either set without repeating elements
An=A1(r)^n-1
#successful events / total# possible outcomes
A=1/2bh

38. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
An=A1+(n-1)d
([old-new]/old)*100%
Volume=(4/3)pir^3

39. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
S=180(n-2)
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A

40. Adding/Subtracting Exponents
x1y1 = x2y2
A=1/2bh
A=[(B1+B2)*H]/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

41. Sum of Exterior Angles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
360
A=[(B1+B2)*H]/2
Order matters - nPr=n! / (n-r)!

42. Area Trapezoid
A=[(B1+B2)*H]/2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
360
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

43. Rectangles
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=L*W - P=2L+2W - Diagonals equal length
Part/whole = %/100

44. Volume of Prism
(area of base)*height
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
D/W= (R1+R2)*T

45. Area of a Sector
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
2 equal sides - 2 equal angles
= (x degree / 360) pi*r^2
Volume=(4/3)pir^3

46. Intersection
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
S-S-S - S-A-S - A-S-A
Consists of all the elements that appear in both sets
x1y1 = x2y2

47. Permutations
Positive and negative whole numbers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Order matters - nPr=n! / (n-r)!
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

48. Indirect Variation
A=1/2bh
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
x1y1 = x2y2
= (x degree / 360) pi*r^2

49. Area Hexagon
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
A=(3root3/2)r^2
Multiply number of choices available in each option to get total number of options
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

50. Cylinders
(1/3)LW*H
1 - 3 - 5 - ...
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Middle number (or average of 2) of set from smallest to largest