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SAT Math Formulas

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Even Numbers
Middle number (or average of 2) of set from smallest to largest
0 - -2 - -4 - ...
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
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

2. Average Rate
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=[(B1+B2)*H]/2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

3. Equilateral Triangle
D/W= (R1+R2)*T
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
= (x degree / 360) pi*r^2
A=1/2bh

4. Isosceles Triangle
2 equal sides - 2 equal angles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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

5. Direct Variation
x1/y1 = x2/y2
(area of base)*height
#successful events / total# possible outcomes
Multiply number of choices available in each option to get total number of options

6. Right Triangle
(1/3)pir^2*h
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
(1/3)LW*H

7. Percentage Change
A=(3root3/2)r^2
= (x degree / 360) pi*r^2
([old-new]/old)*100%
Part/whole = %/100

8. Geometric Sequences
2 equal sides - 2 equal angles
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
1 - 3 - 5 - ...

9. Weighted Averages
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
1 - 3 - 5 - ...
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
([old-new]/old)*100%

10. Same Distance
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
x1/y1 = x2/y2
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
#successful events / total# possible outcomes

11. Permutations
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
360
x1/y1 = x2/y2
Order matters - nPr=n! / (n-r)!

12. Congruent Triangles
Volume=(4/3)pir^3
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D/W=R1T1 + R2T2
S-S-S - S-A-S - A-S-A

13. Cylinders
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
x1y1 = x2y2
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
T(up)=D/R1 T(down)=D/R2 - Add and solve for D

14. Union
A=(3root3/2)r^2
Volume=(4/3)pir^3
The most frequently occurring number in a set
Consists of all of the elements that appear in either set without repeating elements

15. Volume of Sphere
Middle number (or average of 2) of set from smallest to largest
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Volume=(4/3)pir^3

16. Special Right Triangles
Volume=(4/3)pir^3
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(1/3)pir^2*h
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h

17. Odd Numbers
= (x degree / 360) C
1 - 3 - 5 - ...
Consists of all of the elements that appear in either set without repeating elements
A=1/2bh

18. Probability
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(1/3)pir^2*h
#successful events / total# possible outcomes

19. Volume of Pyramid
(1/3)LW*H
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
Part/whole = %/100
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

20. Similar Triangles
(area of base)*height
An=A1+(n-1)d
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
An=A1(r)^n-1

21. Square
A=S^2 - P=4S - Diagonal is root2 times side
Positive and negative whole numbers
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Part/whole = %/100

22. Triangle Inequality
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
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
(area of base)*height
A=[(B1+B2)*H]/2

23. Same Work
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
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=(3root3/2)r^2
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

24. Distance Formula
(1/3)LW*H
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Square root[(x2-x1)^2 + (y2-y1)^2]
Part/whole = %/100

25. Combined Rates
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
0 - -2 - -4 - ...
A=1/2bh
D/W=R1T1 + R2T2

26. Rational Number
D/W=R1T1 + R2T2
x1y1 = x2y2
(area of base)*height
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

27. Sum of Exterior Angles
360
A=1/2bh
Consists of all the elements that appear in both sets
(1/3)LW*H

28. Same Rate
(area of base)*height
0 - -2 - -4 - ...
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Part/whole = %/100

29. Area Hexagon
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
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
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=(3root3/2)r^2

30. Even/Odd Results
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
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
D/W=R1T1 + R2T2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

31. Same Time
D/W= (R1+R2)*T
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
1 - 3 - 5 - ...
Square root[(x2-x1)^2 + (y2-y1)^2]

32. Adding/Subtracting Exponents
Positive and negative whole numbers
x1y1 = x2y2
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

33. Arithmetic Sequence
An=A1+(n-1)d
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
Multiply number of choices available in each option to get total number of options

34. Distance/Work Formula
S-S-S - S-A-S - A-S-A
= (x degree / 360) pi*r^2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T

35. Fundamental Counting Principle
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
S-S-S - S-A-S - A-S-A
Multiply number of choices available in each option to get total number of options

36. Combinations

37. Indirect Variation
Volume=(4/3)pir^3
A=(3root3/2)r^2
S-S-S - S-A-S - A-S-A
x1y1 = x2y2

38. Integer
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
0 - -2 - -4 - ...
Positive and negative whole numbers
D/W=R1T1 + R2T2

39. Rectangles
Order matters - nPr=n! / (n-r)!
= (x degree / 360) C
A=L*W - P=2L+2W - Diagonals equal length
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

40. Volume of Cone
Positive and negative whole numbers
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T
(1/3)pir^2*h

41. Exponent Rules
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
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
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

42. Length on an Arc
An=A1(r)^n-1
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
= (x degree / 360) C
A=1/2bh

43. Sum of Interior Angles
1 - 3 - 5 - ...
S=180(n-2)
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

44. Percents
Part/whole = %/100
1 - 3 - 5 - ...
A=[(B1+B2)*H]/2
([old-new]/old)*100%

45. Area of a Sector
= (x degree / 360) pi*r^2
An=A1+(n-1)d
Consists of all the elements that appear in both sets
A=S^2 - P=4S - Diagonal is root2 times side

46. Mixture Formula
D/W=R1T1 + R2T2
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
Positive and negative whole numbers

47. Mode
D=R*T - W=R*T
A=1/2bh
The most frequently occurring number in a set
Part/whole = %/100

48. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
Order matters - nPr=n! / (n-r)!
= (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

49. Median
Consists of all of the elements that appear in either set without repeating elements
A=1/2bh
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

50. Area Trapezoid
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
= (x degree / 360) pi*r^2
A=[(B1+B2)*H]/2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given