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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. Permutations
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!
A=[(B1+B2)*H]/2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

2. Even Numbers
Consists of all the elements that appear in both sets
0 - -2 - -4 - ...
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

3. Indirect Variation
Order doesn't matter - nCr=n! / r!(n-r)!
x1y1 = x2y2
Positive and negative whole numbers
Order matters - nPr=n! / (n-r)!

4. Volume of Prism
Part/whole = %/100
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=1/2bh
(area of base)*height

5. Geometric Sequences
Middle number (or average of 2) of set from smallest to largest
An=A1(r)^n-1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=S^2 - P=4S - Diagonal is root2 times side

6. Isosceles Triangle
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
2 equal sides - 2 equal angles
Order doesn't matter - nCr=n! / r!(n-r)!
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

7. Percentage Change
An=A1+(n-1)d
x1y1 = x2y2
D/W= (R1+R2)*T
([old-new]/old)*100%

8. Same Rate
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
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

9. Exponent Rules
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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/W=R1T1 + R2T2

10. Direct Variation
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
D/W= (R1+R2)*T
x1/y1 = x2/y2
Middle number (or average of 2) of set from smallest to largest

11. Union
An=A1(r)^n-1
S=180(n-2)
A=L*W - P=2L+2W - Diagonals equal length
Consists of all of the elements that appear in either set without repeating elements

12. Same Work
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

13. Average Rate
The most frequently occurring number in a set
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
D=R*T - W=R*T
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

14. Rectangles
#successful events / total# possible outcomes
D/W=R1T1 + R2T2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=L*W - P=2L+2W - Diagonals equal length

15. Combinations

16. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for 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
1 - 3 - 5 - ...
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

17. Area Hexagon
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
The most frequently occurring number in a set
(1/3)LW*H
A=(3root3/2)r^2

18. Median
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(1/3)LW*H
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Middle number (or average of 2) of set from smallest to largest

19. Special Right Triangles
D/W=R1T1 + R2T2
= (x degree / 360) C
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Middle number (or average of 2) of set from smallest to largest

20. Area of a Sector
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
#successful events / total# possible outcomes
= (x degree / 360) pi*r^2
= (x degree / 360) C

21. Percents
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
Part/whole = %/100
A=(3root3/2)r^2
x1y1 = x2y2

22. Volume of Pyramid
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
S=180(n-2)
A=1/2bh
(1/3)LW*H

23. Volume of Sphere
Volume=(4/3)pir^3
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Consists of all of the elements that appear in either set without repeating elements

24. Combined Rates
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
D/W=R1T1 + R2T2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=1/2bh

25. Square
The most frequently occurring number in a set
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%

26. Probability
Consists of all of the elements that appear in either set without repeating elements
#successful events / total# possible outcomes
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A

27. Distance/Work Formula
D=R*T - W=R*T
(area of base)*height
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=1/2bh

28. Area Trapezoid
A=[(B1+B2)*H]/2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
D/W= (R1+R2)*T

29. Right Triangle
D/W= (R1+R2)*T
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=[(B1+B2)*H]/2
360

30. Even/Odd Results
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
The most frequently occurring number in a set
Part/whole = %/100
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

31. Extension of the Pythagorean Theorem
Square root[(x2-x1)^2 + (y2-y1)^2]
Part/whole = %/100
Consists of all the elements that appear in both sets
(distance between opposite vertices) - square root(L^2+W^2+H^2)

32. Intersection
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Consists of all the elements that appear in both sets
0 - -2 - -4 - ...
#successful events / total# possible outcomes

33. Parallelograms
A=L*W - P=2L+2W - Diagonals equal length
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Multiply number of choices available in each option to get total number of options
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

34. Weighted Average
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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
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

35. Fundamental Counting Principle
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Middle number (or average of 2) of set from smallest to largest
Part/whole = %/100
Multiply number of choices available in each option to get total number of options

36. Adding/Subtracting Exponents
1 - 3 - 5 - ...
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
x1/y1 = x2/y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

37. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
2 equal sides - 2 equal angles

38. Equilateral Triangle
D/W= (R1+R2)*T
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
2 equal sides - 2 equal angles
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

39. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2
S-S-S - S-A-S - A-S-A
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

40. Area of a Triangle
Multiply number of choices available in each option to get total number of options
A=1/2bh
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side

41. Mode
= (x degree / 360) C
Positive and negative whole numbers
The most frequently occurring number in a set
Part/whole = %/100

42. Same Time
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
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
D/W= (R1+R2)*T

43. Cylinders
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
D/W= (R1+R2)*T
= (x degree / 360) pi*r^2

44. Triangle Inequality
The most frequently occurring number in a set
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
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
Volume=(4/3)pir^3

45. Arithmetic Sequence
An=A1+(n-1)d
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
Part/whole = %/100

46. Integer
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=1/2bh
Positive and negative whole numbers

47. Similar Triangles
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)LW*H

48. Sum of Exterior Angles
(1/3)LW*H
An=A1(r)^n-1
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
360

49. Real Wheel Formula
A=1/2bh
x1y1 = x2y2
(1/3)LW*H
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

50. Length on an Arc
An=A1+(n-1)d
= (x degree / 360) C
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A