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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. Square
360
Positive and negative whole numbers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side

2. Union
Order doesn't matter - nCr=n! / r!(n-r)!
D/W= (R1+R2)*T
Consists of all of the elements that appear in either set without repeating elements
An=A1(r)^n-1

3. Adding/Subtracting Exponents
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
x1y1 = x2y2
(distance between opposite vertices) - square root(L^2+W^2+H^2)

4. Distance/Work Formula
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Multiply number of choices available in each option to get total number of options
D=R*T - W=R*T
The most frequently occurring number in a set

5. Volume of Cone
A=(3root3/2)r^2
(1/3)pir^2*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

6. Parallelograms
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Positive and negative whole numbers
(1/3)LW*H
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

7. Sum of Exterior Angles
An=A1+(n-1)d
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
D=R*T - W=R*T
360

8. Same Rate
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Order matters - nPr=n! / (n-r)!
An=A1+(n-1)d
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

9. Average Rate
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Multiply number of choices available in each option to get total number of options
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Positive and negative whole numbers

10. Rational Number
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
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

11. Volume of Prism
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(area of base)*height
A=S^2 - P=4S - Diagonal is root2 times side

12. Mode
The most frequently occurring number in a set
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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)

13. Area of a Sector
= (x degree / 360) pi*r^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
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

14. Even Numbers
A=S^2 - P=4S - Diagonal is root2 times side
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
0 - -2 - -4 - ...

15. Same Distance
Square root[(x2-x1)^2 + (y2-y1)^2]
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Positive and negative whole numbers
Multiply number of choices available in each option to get total number of options

16. Indirect Variation
S-S-S - S-A-S - A-S-A
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
x1y1 = x2y2
Square root[(x2-x1)^2 + (y2-y1)^2]

17. Right Triangle
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
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

18. Isosceles Triangle
2 equal sides - 2 equal angles
S-S-S - S-A-S - A-S-A
(1/3)LW*H
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

19. Permutations
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
An=A1+(n-1)d
= (x degree / 360) C

20. Combined Rates
([old-new]/old)*100%
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
D/W=R1T1 + R2T2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

21. Area Hexagon
D/W= (R1+R2)*T
D=R*T - W=R*T
A=(3root3/2)r^2
Positive and negative whole numbers

22. Geometric Sequences
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
An=A1(r)^n-1
Square root[(x2-x1)^2 + (y2-y1)^2]
= (x degree / 360) pi*r^2

23. Weighted Averages
2 equal sides - 2 equal angles
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

24. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D=R*T - W=R*T
x1/y1 = x2/y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

25. Area Trapezoid
D/W= (R1+R2)*T
Multiply number of choices available in each option to get total number of options
A=[(B1+B2)*H]/2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

26. Similar Triangles
S=180(n-2)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
A=(3root3/2)r^2
(area of base)*height

27. Volume of Sphere
Volume=(4/3)pir^3
Order matters - nPr=n! / (n-r)!
An=A1(r)^n-1
Multiply number of choices available in each option to get total number of options

28. Median
2 equal sides - 2 equal angles
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)LW*H
Middle number (or average of 2) of set from smallest to largest

29. Equilateral Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

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

31. Combinations

32. Percents
0 - -2 - -4 - ...
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
Part/whole = %/100

33. Special Right Triangles
Order matters - nPr=n! / (n-r)!
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T
360

34. Integer
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Positive and negative whole numbers
D/W=R1T1 + R2T2
#successful events / total# possible outcomes

35. Direct Variation
An=A1+(n-1)d
x1/y1 = x2/y2
A=L*W - P=2L+2W - Diagonals equal length
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

36. Distance Formula
Square root[(x2-x1)^2 + (y2-y1)^2]
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
([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

37. Intersection
Consists of all the elements that appear in both sets
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
360

38. Percentage Change
x1/y1 = x2/y2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
([old-new]/old)*100%
= (x degree / 360) C

39. Arithmetic Sequence
An=A1+(n-1)d
Volume=(4/3)pir^3
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

40. Odd Numbers
Consists of all of the elements that appear in either set without repeating elements
Order matters - nPr=n! / (n-r)!
#successful events / total# possible outcomes
1 - 3 - 5 - ...

41. Triangle Inequality
Consists of all of the elements that appear in either set without repeating elements
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Part/whole = %/100
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

42. Same Work
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
D=R*T - W=R*T
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

43. Extension of the Pythagorean Theorem
A=L*W - P=2L+2W - Diagonals equal length
(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
S=180(n-2)

44. Area of a Triangle
A=1/2bh
A=[(B1+B2)*H]/2
A=S^2 - P=4S - Diagonal is root2 times side
(distance between opposite vertices) - square root(L^2+W^2+H^2)

45. Volume of Pyramid
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
(1/3)LW*H

46. Rectangles
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
D=R*T - W=R*T
A=L*W - P=2L+2W - Diagonals equal length

47. Congruent Triangles
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=S^2 - P=4S - Diagonal is root2 times side
S-S-S - S-A-S - A-S-A
A=[(B1+B2)*H]/2

48. Fundamental Counting Principle
(area of base)*height
Positive and negative whole numbers
Multiply number of choices available in each option to get total number of options
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2

49. Cylinders
Part/whole = %/100
(area of base)*height
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

50. Length on an Arc
Consists of all the elements that appear in both sets
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
2 equal sides - 2 equal angles
= (x degree / 360) C