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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. Even/Odd Results
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
= (x degree / 360) C
A=(3root3/2)r^2

2. Mode
2 equal sides - 2 equal angles
The most frequently occurring number in a set
(distance between opposite vertices) - square root(L^2+W^2+H^2)
([old-new]/old)*100%

3. Arithmetic Sequence
Consists of all the elements that appear in both sets
360
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

4. Integer
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Positive and negative whole numbers
A=[(B1+B2)*H]/2
1 - 3 - 5 - ...

5. Same Time
D/W= (R1+R2)*T
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
x1/y1 = x2/y2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

6. Weighted Average
360
S-S-S - S-A-S - A-S-A
(1/3)LW*H
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

7. Congruent Triangles
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
Square root[(x2-x1)^2 + (y2-y1)^2]
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

8. Special Right Triangles
(1/3)pir^2*h
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Part/whole = %/100
Middle number (or average of 2) of set from smallest to largest

9. Extension of the Pythagorean Theorem
(1/3)LW*H
(distance between opposite vertices) - square root(L^2+W^2+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
Middle number (or average of 2) of set from smallest to largest

10. Similar Triangles
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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

11. Same Rate
= (x degree / 360) C
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
Part/whole = %/100
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

12. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
An=A1(r)^n-1
Volume=(4/3)pir^3

13. Right Triangle
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
Multiply number of choices available in each option to get total number of options
An=A1(r)^n-1
2 equal sides - 2 equal angles

14. Triangle Inequality
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
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
Multiply number of choices available in each option to get total number of options

15. Sum of Exterior Angles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
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
Positive and negative whole numbers
360

16. Average Rate
A=[(B1+B2)*H]/2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)pir^2*h
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

17. Combinations
Volume=(4/3)pir^3
Order doesn't matter - nCr=n! / r!(n-r)!
Consists of all the elements that appear in both sets
0 - -2 - -4 - ...

18. Fundamental Counting Principle
Multiply number of choices available in each option to get total number of options
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

19. Parallelograms
A=[(B1+B2)*H]/2
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
(1/3)LW*H

20. Even Numbers
The most frequently occurring number in a set
A=(3root3/2)r^2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
0 - -2 - -4 - ...

21. Area of a Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
A=1/2bh
= (x degree / 360) C
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

22. Rational Number
Consists of all of the elements that appear in either set without repeating elements
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
360

23. Volume of Cone
Multiply number of choices available in each option to get total number of options
x1/y1 = x2/y2
(1/3)pir^2*h
A=S^2 - P=4S - Diagonal is root2 times side

24. Volume of Prism
D/W= (R1+R2)*T
A=1/2bh
(area of base)*height
A=[(B1+B2)*H]/2

25. Probability
D/W=R1T1 + R2T2
#successful events / total# possible outcomes
S=180(n-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

26. Volume of Sphere
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D/W= (R1+R2)*T
Volume=(4/3)pir^3
S-S-S - S-A-S - A-S-A

27. Distance Formula
(1/3)LW*H
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Square root[(x2-x1)^2 + (y2-y1)^2]
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

28. Sum of Interior Angles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(area of base)*height
Volume=(4/3)pir^3
S=180(n-2)

29. Area of a Sector
= (x degree / 360) pi*r^2
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= (R1+R2)*T
0 - -2 - -4 - ...

30. 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)
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

31. Cylinders
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
Order matters - nPr=n! / (n-r)!
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

32. Mixture Formula
([old-new]/old)*100%
x1/y1 = x2/y2
2 equal sides - 2 equal angles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

33. Volume of Pyramid
(1/3)LW*H
Order doesn't matter - nCr=n! / r!(n-r)!
Consists of all the elements that appear in both sets
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

34. Area Trapezoid
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=[(B1+B2)*H]/2
Multiply number of choices available in each option to get total number of options
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

35. Percents
Part/whole = %/100
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)LW*H
Consists of all of the elements that appear in either set without repeating elements

36. Area Hexagon
A=(3root3/2)r^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
#successful events / total# possible outcomes
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

37. Indirect Variation
S=180(n-2)
A=1/2bh
x1y1 = x2y2
A=S^2 - P=4S - Diagonal is root2 times side

38. Combined Rates
Consists of all of the elements that appear in either set without repeating elements
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
D/W=R1T1 + R2T2
A=[(B1+B2)*H]/2

39. Direct Variation
Volume=(4/3)pir^3
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D/W= (R1+R2)*T
x1/y1 = x2/y2

40. Geometric Sequences
An=A1(r)^n-1
D/W= (R1+R2)*T
(1/3)LW*H
A=(3root3/2)r^2

41. Equilateral Triangle
(1/3)LW*H
Volume=(4/3)pir^3
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

42. Rectangles
= (x degree / 360) pi*r^2
A=L*W - P=2L+2W - Diagonals equal length
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

43. Median
Multiply number of choices available in each option to get total number of options
(1/3)pir^2*h
0 - -2 - -4 - ...
Middle number (or average of 2) of set from smallest to largest

44. Exponent Rules
An=A1(r)^n-1
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
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

45. Real Wheel Formula
D/W=R1T1 + R2T2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Volume=(4/3)pir^3

46. Adding/Subtracting Exponents
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
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-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

47. Square
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
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(area of base)*height

48. Permutations
= (x degree / 360) pi*r^2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Order matters - nPr=n! / (n-r)!
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

49. Weighted Averages
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Part/whole = %/100
(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

50. Isosceles Triangle
2 equal sides - 2 equal angles
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
Consists of all of the elements that appear in either set without repeating elements
x1/y1 = x2/y2

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