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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. Geometric Sequences
An=A1+(n-1)d
Consists of all the elements that appear in both sets
An=A1(r)^n-1
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

2. Same Time
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
D/W= (R1+R2)*T
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
= (x degree / 360) pi*r^2

3. Rectangles
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
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
A=L*W - P=2L+2W - Diagonals equal length

4. Percentage Change
An=A1(r)^n-1
([old-new]/old)*100%
Consists of all of the elements that appear in either set without repeating elements
A=1/2bh

5. Direct Variation
x1/y1 = x2/y2
(area of base)*height
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

6. Area Trapezoid
([old-new]/old)*100%
(area of base)*height
A=[(B1+B2)*H]/2
A=1/2bh

7. Exponent Rules
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
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
Part/whole = %/100
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

8. Cylinders
Part/whole = %/100
D/W=R1T1 + R2T2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
x1/y1 = x2/y2

9. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
D/W= (R1+R2)*T
D/W=R1T1 + R2T2
= (x degree / 360) pi*r^2

10. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Square root[(x2-x1)^2 + (y2-y1)^2]
A=1/2bh
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

11. Probability
(1/3)pir^2*h
#successful events / total# possible outcomes
x1/y1 = x2/y2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

12. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Square root[(x2-x1)^2 + (y2-y1)^2]
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

13. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
= (x degree / 360) C
Volume=(4/3)pir^3
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

14. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
([old-new]/old)*100%
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
= (x degree / 360) C

15. Distance Formula
S-S-S - S-A-S - A-S-A
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Positive and negative whole numbers
Square root[(x2-x1)^2 + (y2-y1)^2]

16. Combinations

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17. Volume of Cone
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)pir^2*h
x1/y1 = x2/y2

18. Union
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Middle number (or average of 2) of set from smallest to largest
x1/y1 = x2/y2
Consists of all of the elements that appear in either set without repeating elements

19. Integer
D/W= (R1+R2)*T
Positive and negative whole numbers
0 - -2 - -4 - ...
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

20. Real Wheel Formula
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
0 - -2 - -4 - ...
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

21. Congruent Triangles
S-S-S - S-A-S - A-S-A
x1y1 = x2y2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

22. Mode
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Volume=(4/3)pir^3
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
The most frequently occurring number in a set

23. Similar Triangles
Positive and negative whole numbers
D/W= (R1+R2)*T
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

24. Sum of Interior Angles
D=R*T - W=R*T
The most frequently occurring number in a set
S=180(n-2)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

25. Triangle Inequality
A=L*W - P=2L+2W - Diagonals equal length
0 - -2 - -4 - ...
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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

26. Distance/Work Formula
D=R*T - W=R*T
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Consists of all the elements that appear in both sets
An=A1(r)^n-1

27. Combined Rates
S-S-S - S-A-S - A-S-A
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D/W=R1T1 + R2T2
Order matters - nPr=n! / (n-r)!

28. Same Work
An=A1+(n-1)d
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
D/W= (R1+R2)*T
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

29. Even/Odd Results
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=[(B1+B2)*H]/2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
D/W=R1T1 + R2T2

30. Right Triangle
A=(3root3/2)r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
([old-new]/old)*100%

31. Intersection
x1/y1 = x2/y2
Consists of all the elements that appear in both sets
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

32. Even Numbers
Positive and negative whole numbers
= (x degree / 360) C
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements

33. Weighted Average
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
#successful events / total# possible outcomes
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

34. Arithmetic Sequence
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
360
Order matters - nPr=n! / (n-r)!
An=A1+(n-1)d

35. Volume of Pyramid
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)LW*H
The most frequently occurring number in a set
([old-new]/old)*100%

36. Isosceles Triangle
A=(3root3/2)r^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
Order doesn't matter - nCr=n! / r!(n-r)!
2 equal sides - 2 equal angles

37. Indirect Variation
S=180(n-2)
Order doesn't matter - nCr=n! / r!(n-r)!
x1y1 = x2y2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

38. Area of a Triangle
([old-new]/old)*100%
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
D/W= (R1+R2)*T

39. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
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=1/2bh

40. Same Distance
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)
S=180(n-2)
An=A1+(n-1)d

41. Percents
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Part/whole = %/100
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
2 equal sides - 2 equal angles

42. Permutations
Order matters - nPr=n! / (n-r)!
1 - 3 - 5 - ...
A=(3root3/2)r^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

43. Average Rate
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Order doesn't matter - nCr=n! / r!(n-r)!
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

44. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Multiply number of choices available in each option to get total number of options

45. Odd Numbers
Consists of all the elements that appear in both sets
D/W= (R1+R2)*T
1 - 3 - 5 - ...
Multiply number of choices available in each option to get total number of options

46. Parallelograms
S-S-S - S-A-S - A-S-A
The most frequently occurring number in a set
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

47. Area of a Sector
Consists of all of the elements that appear in either set without repeating elements
An=A1(r)^n-1
= (x degree / 360) pi*r^2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

48. Square
([old-new]/old)*100%
A=S^2 - P=4S - Diagonal is root2 times side
2 equal sides - 2 equal angles
Order doesn't matter - nCr=n! / r!(n-r)!

49. Median
#successful events / total# possible outcomes
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Middle number (or average of 2) of set from smallest to largest
(distance between opposite vertices) - square root(L^2+W^2+H^2)

50. Adding/Subtracting Exponents
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
= (x degree / 360) C
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
The most frequently occurring number in a set