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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. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Multiply number of choices available in each option to get total number of options
S-S-S - S-A-S - A-S-A
Positive and negative whole numbers

2. Length on an Arc
= (x degree / 360) C
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Volume=(4/3)pir^3
Order doesn't matter - nCr=n! / r!(n-r)!

3. Even Numbers
0 - -2 - -4 - ...
360
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

4. Area of a Triangle
([old-new]/old)*100%
An=A1+(n-1)d
A=1/2bh
x1/y1 = x2/y2

5. Isosceles Triangle
2 equal sides - 2 equal angles
S=180(n-2)
The most frequently occurring number in a set
x1/y1 = x2/y2

6. Area Hexagon
A=(3root3/2)r^2
(1/3)LW*H
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A

7. Area Trapezoid
A=S^2 - P=4S - Diagonal is root2 times side
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(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=[(B1+B2)*H]/2

8. Special Right Triangles
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Positive and negative whole numbers
= (x degree / 360) C
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

9. Arithmetic Sequence
An=A1+(n-1)d
The most frequently occurring number in a set
An=A1(r)^n-1
Consists of all of the elements that appear in either set without repeating elements

10. Square
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=S^2 - P=4S - Diagonal is root2 times side
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Multiply number of choices available in each option to get total number of options

11. Odd Numbers
1 - 3 - 5 - ...
(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
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

12. 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
x1/y1 = x2/y2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)LW*H

13. Mixture Formula
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Middle number (or average of 2) of set from smallest to largest

14. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
([old-new]/old)*100%
0 - -2 - -4 - ...
D=R*T - W=R*T

15. Indirect Variation
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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
x1y1 = x2y2

16. Equilateral Triangle
Multiply number of choices available in each option to get total number of options
Order matters - nPr=n! / (n-r)!
The most frequently occurring number in a set
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

17. Probability
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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
0 - -2 - -4 - ...
#successful events / total# possible outcomes

18. Percentage Change
= (x degree / 360) C
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
([old-new]/old)*100%
An=A1(r)^n-1

19. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
#successful events / total# possible outcomes
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Multiply number of choices available in each option to get total number of options

20. Volume of Cone
= (x degree / 360) pi*r^2
D/W= (R1+R2)*T
2 equal sides - 2 equal angles
(1/3)pir^2*h

21. Same Time
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
D/W=R1T1 + R2T2
S=180(n-2)
D/W= (R1+R2)*T

22. Weighted Average
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(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A
A=(3root3/2)r^2

23. Volume of Pyramid
A=S^2 - P=4S - Diagonal is root2 times side
(1/3)LW*H
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Consists of all of the elements that appear in either set without repeating elements

24. Percents
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Part/whole = %/100
#successful events / total# possible outcomes
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

25. Integer
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Order doesn't matter - nCr=n! / r!(n-r)!
#successful events / total# possible outcomes
Positive and negative whole numbers

26. Geometric Sequences
Order doesn't matter - nCr=n! / r!(n-r)!
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
An=A1(r)^n-1
A=[(B1+B2)*H]/2

27. 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
Order doesn't matter - nCr=n! / r!(n-r)!
A=(3root3/2)r^2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

28. Mode
x1y1 = x2y2
(1/3)pir^2*h
The most frequently occurring number in a set
S-S-S - S-A-S - A-S-A

29. Sum of Interior Angles
(1/3)LW*H
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
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=180(n-2)

30. Fundamental Counting Principle
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
Multiply number of choices available in each option to get total number of options
Consists of all of the elements that appear in either set without repeating elements
= (x degree / 360) C

31. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=S^2 - P=4S - Diagonal is root2 times side
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

32. Extension of the Pythagorean Theorem
x1/y1 = x2/y2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
An=A1+(n-1)d
Part/whole = %/100

33. Volume of Prism
#successful events / total# possible outcomes
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
x1/y1 = x2/y2
(area of base)*height

34. Parallelograms
x1/y1 = x2/y2
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
A=S^2 - P=4S - Diagonal is root2 times side

35. Same Work
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)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
x1y1 = x2y2

36. Rectangles
A=L*W - P=2L+2W - Diagonals equal length
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
Square root[(x2-x1)^2 + (y2-y1)^2]
x1y1 = x2y2

37. Same Rate
360
Consists of all the elements that appear in both sets
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Middle number (or average of 2) of set from smallest to largest

38. Area of a Sector
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
0 - -2 - -4 - ...
= (x degree / 360) pi*r^2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

39. Median
S=180(n-2)
Middle number (or average of 2) of set from smallest to largest
D=R*T - W=R*T
A=L*W - P=2L+2W - Diagonals equal length

40. Even/Odd Results
(1/3)LW*H
A=(3root3/2)r^2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
x1/y1 = x2/y2

41. Combined Rates
0 - -2 - -4 - ...
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D/W=R1T1 + R2T2
(1/3)LW*H

42. Combinations

43. Congruent Triangles
S-S-S - S-A-S - A-S-A
1 - 3 - 5 - ...
Volume=(4/3)pir^3
D/W= (R1+R2)*T

44. Union
Consists of all of the elements that appear in either set without repeating elements
A=(3root3/2)r^2
= (x degree / 360) pi*r^2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

45. Real Wheel Formula
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Square root[(x2-x1)^2 + (y2-y1)^2]
D/W= (R1+R2)*T
R=rotations - L=circumference - radii - diameters - R1L1=R2L2

46. Right Triangle
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
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^2 + b^2 = c^2 - 3-4-5 - 5-12-13

47. Similar Triangles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

48. Volume of Sphere
Volume=(4/3)pir^3
= (x degree / 360) pi*r^2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Multiply number of choices available in each option to get total number of options

49. Same Distance
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
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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

50. Triangle Inequality
= (x degree / 360) pi*r^2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
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