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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. Percentage Change
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
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
([old-new]/old)*100%
D/W=R1T1 + R2T2

2. Exponent Rules
A=1/2bh
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
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

3. Even/Odd Results
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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

4. Distance Formula
D/W= (R1+R2)*T
Square root[(x2-x1)^2 + (y2-y1)^2]
Order doesn't matter - nCr=n! / r!(n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)

5. Congruent Triangles
S-S-S - S-A-S - A-S-A
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

6. Right Triangle
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
S-S-S - S-A-S - A-S-A
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13

7. Volume of Sphere
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
A=S^2 - P=4S - Diagonal is root2 times side
Volume=(4/3)pir^3
Order matters - nPr=n! / (n-r)!

8. Volume of Pyramid
A=[(B1+B2)*H]/2
x1/y1 = x2/y2
(area of base)*height
(1/3)LW*H

9. Average Rate
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
D/W= (R1+R2)*T
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
A=[(B1+B2)*H]/2

10. Even Numbers
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Volume=(4/3)pir^3
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
0 - -2 - -4 - ...

11. Triangle Inequality
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
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
Order doesn't matter - nCr=n! / r!(n-r)!

12. Cylinders
Volume=pir^2h - Surface Area=2pir^2 + 2pir*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
Order matters - nPr=n! / (n-r)!
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

13. Probability
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
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
1 - 3 - 5 - ...

14. Indirect Variation
Part/whole = %/100
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
x1y1 = x2y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

15. Isosceles Triangle
x1y1 = x2y2
Order matters - nPr=n! / (n-r)!
2 equal sides - 2 equal angles
The most frequently occurring number in a set

16. Area of a Sector
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
The most frequently occurring number in a set
An=A1(r)^n-1
= (x degree / 360) pi*r^2

17. Weighted Averages
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
S=180(n-2)
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
A=L*W - P=2L+2W - Diagonals equal length

18. Same Time
D/W= (R1+R2)*T
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
x1y1 = x2y2
360

19. Similar Triangles
Volume=(4/3)pir^3
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
(distance between opposite vertices) - square root(L^2+W^2+H^2)

20. Sum of Exterior Angles
360
D/W=R1T1 + R2T2
x1y1 = x2y2
D/W= (R1+R2)*T

21. Same Rate
(1/3)LW*H
(1/3)pir^2*h
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
= (x degree / 360) pi*r^2

22. Square
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1/y1 = x2/y2
A=S^2 - P=4S - Diagonal is root2 times side
S=180(n-2)

23. Mode
The most frequently occurring number in a set
Volume=(4/3)pir^3
A=1/2bh
A=(3root3/2)r^2

24. Union
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
A=[(B1+B2)*H]/2
Consists of all of the elements that appear in either set without repeating elements
S-S-S - S-A-S - A-S-A

25. Area of a Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Order doesn't matter - nCr=n! / r!(n-r)!
A=1/2bh
An=A1+(n-1)d

26. Sum of Interior Angles
360
S=180(n-2)
0 - -2 - -4 - ...
2 equal sides - 2 equal angles

27. Odd Numbers
D/W=R1T1 + R2T2
A=(3root3/2)r^2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
1 - 3 - 5 - ...

28. Geometric Sequences
= (x degree / 360) C
([old-new]/old)*100%
A=L*W - P=2L+2W - Diagonals equal length
An=A1(r)^n-1

29. Rectangles
(1/3)LW*H
A=L*W - P=2L+2W - Diagonals equal length
Positive and negative whole numbers
1 - 3 - 5 - ...

30. Area Trapezoid
x1y1 = x2y2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=[(B1+B2)*H]/2
Multiply number of choices available in each option to get total number of options

31. Fundamental Counting Principle
Positive and negative whole numbers
D/W=R1T1 + R2T2
Multiply number of choices available in each option to get total number of options
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

32. Length on an Arc
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
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
= (x degree / 360) C

33. Same Work
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
2 equal sides - 2 equal angles
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

34. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
x1/y1 = x2/y2
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
Consists of all of the elements that appear in either set without repeating elements

35. Mixture Formula
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Positive and negative whole numbers
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

36. Area Hexagon
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
Order matters - nPr=n! / (n-r)!
D/W= (R1+R2)*T
A=(3root3/2)r^2

37. Arithmetic Sequence
A=(3root3/2)r^2
An=A1+(n-1)d
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

38. Volume of Prism
(area of base)*height
= (x degree / 360) C
Order doesn't matter - nCr=n! / r!(n-r)!
A=[(B1+B2)*H]/2

39. Permutations
Order matters - nPr=n! / (n-r)!
A=1/2bh
Consists of all of the elements that appear in either set without repeating elements
(1/3)LW*H

40. Rational Number
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
Consists of all the elements that appear in both sets
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

41. Parallelograms
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
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

42. Real Wheel Formula
A=1/2bh
Order doesn't matter - nCr=n! / r!(n-r)!
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

43. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
0 - -2 - -4 - ...
2 equal sides - 2 equal angles
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

44. Equilateral Triangle
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 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
(1/3)LW*H

45. Integer
= (x degree / 360) pi*r^2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
x1/y1 = x2/y2
Positive and negative whole numbers

46. Combinations

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47. Distance/Work Formula
D=R*T - W=R*T
Consists of all the elements that appear in both sets
S=180(n-2)
= (x degree / 360) pi*r^2

48. 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
D/W= (R1+R2)*T
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
#successful events / total# possible outcomes

49. Intersection
Consists of all the elements that appear in both sets
([old-new]/old)*100%
Square root[(x2-x1)^2 + (y2-y1)^2]
Consists of all of the elements that appear in either set without repeating elements

50. Median
Middle number (or average of 2) of set from smallest to largest
Multiply number of choices available in each option to get total number of options
The most frequently occurring number in a set
(distance between opposite vertices) - square root(L^2+W^2+H^2)