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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. Odd Numbers
An=A1(r)^n-1
= (x degree / 360) pi*r^2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
1 - 3 - 5 - ...

2. Combinations

3. Mode
D/W=R1T1 + R2T2
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(1/3)LW*H
The most frequently occurring number in a set

4. Indirect Variation
x1y1 = x2y2
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=1/2bh

5. Congruent Triangles
A=[(B1+B2)*H]/2
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
= (x degree / 360) C

6. Same Work
= (x degree / 360) C
A=[(B1+B2)*H]/2
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)

7. Cylinders
1 - 3 - 5 - ...
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Consists of all the elements that appear in both sets

8. Parallelograms
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
360
D/W=R1T1 + R2T2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

9. Integer
x1/y1 = x2/y2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Positive and negative whole numbers
A=S^2 - P=4S - Diagonal is root2 times side

10. Intersection
Consists of all the elements that appear in both sets
An=A1(r)^n-1
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

11. Special Right Triangles
Multiply number of choices available in each option to get total number of options
= (x degree / 360) C
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Part/whole = %/100

12. Volume of Sphere
= (x degree / 360) pi*r^2
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
Volume=(4/3)pir^3

13. Isosceles Triangle
= (x degree / 360) pi*r^2
2 equal sides - 2 equal angles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
x1/y1 = x2/y2

14. Direct Variation
x1/y1 = x2/y2
A=[(B1+B2)*H]/2
(area of base)*height
S=180(n-2)

15. Area of a Sector
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
= (x degree / 360) C
= (x degree / 360) pi*r^2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

16. Permutations
(1/3)pir^2*h
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Order matters - nPr=n! / (n-r)!
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

17. Percentage Change
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
([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

18. Rectangles
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=L*W - P=2L+2W - Diagonals equal length
A=1/2bh
Consists of all of the elements that appear in either set without repeating elements

19. Volume of Pyramid
D=R*T - W=R*T
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(1/3)LW*H
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

20. Exponent Rules
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
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
The most frequently occurring number in a set
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

21. Sum of Interior Angles
S=180(n-2)
D=R*T - W=R*T
The most frequently occurring number in a set
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

22. Probability
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
#successful events / total# possible outcomes
An=A1(r)^n-1
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

23. Distance Formula
A=S^2 - P=4S - Diagonal is root2 times side
(1/3)pir^2*h
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
Square root[(x2-x1)^2 + (y2-y1)^2]

24. Even Numbers
(area of base)*height
0 - -2 - -4 - ...
Consists of all of the elements that appear in either set without repeating elements
x1y1 = x2y2

25. Extension of the Pythagorean Theorem
(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
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Multiply number of choices available in each option to get total number of options

26. Area Trapezoid
A=[(B1+B2)*H]/2
An=A1(r)^n-1
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=L*W - P=2L+2W - Diagonals equal length

27. Length on an Arc
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
(1/3)LW*H
= (x degree / 360) C
(area of base)*height

28. Fundamental Counting Principle
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

29. Square
Consists of all of the elements that appear in either set without repeating elements
S=180(n-2)
S-S-S - S-A-S - A-S-A
A=S^2 - P=4S - Diagonal is root2 times side

30. Combined Rates
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
x1y1 = x2y2
D/W=R1T1 + R2T2

31. Sum of Exterior Angles
(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
Order doesn't matter - nCr=n! / r!(n-r)!
360

32. Geometric Sequences
([old-new]/old)*100%
An=A1(r)^n-1
Order doesn't matter - nCr=n! / r!(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

33. Triangle Inequality
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Order matters - nPr=n! / (n-r)!
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
#successful events / total# possible outcomes

34. Arithmetic Sequence
An=A1+(n-1)d
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Consists of all of the elements that appear in either set without repeating elements
(1/3)pir^2*h

35. Similar 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
Volume=(4/3)pir^3
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

36. Area of a Triangle
#successful events / total# possible outcomes
A=1/2bh
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
A=(3root3/2)r^2

37. Average Rate
= (x degree / 360) pi*r^2
(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
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

38. Same Time
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
= (x degree / 360) C
D/W= (R1+R2)*T
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

39. Volume of Prism
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
Part/whole = %/100
(area of base)*height
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

40. Adding/Subtracting Exponents
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
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)

41. Rational Number
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
Square root[(x2-x1)^2 + (y2-y1)^2]
x1/y1 = x2/y2

42. Percents
Part/whole = %/100
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
0 - -2 - -4 - ...
([old-new]/old)*100%

43. Even/Odd Results
A=[(B1+B2)*H]/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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Volume=(4/3)pir^3

44. Same Rate
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
= (x degree / 360) pi*r^2

45. Volume of Cone
(distance between opposite vertices) - square root(L^2+W^2+H^2)
(1/3)pir^2*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Multiply number of choices available in each option to get total number of options

46. Weighted Averages
Middle number (or average of 2) of set from smallest to largest
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=(3root3/2)r^2
Consists of all the elements that appear in both sets

47. Area Hexagon
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Middle number (or average of 2) of set from smallest to largest
A=(3root3/2)r^2
x1y1 = x2y2

48. Same Distance
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
D=R*T - W=R*T
0 - -2 - -4 - ...
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

49. Real Wheel Formula
S=180(n-2)
Consists of all the elements that appear in both sets
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

50. Median
Middle number (or average of 2) of set from smallest to largest
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Square root[(x2-x1)^2 + (y2-y1)^2]
(1/3)pir^2*h