Test your basic knowledge |

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. Similar Triangles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
A=S^2 - P=4S - Diagonal is root2 times side
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(area of base)*height

2. Weighted Average
A=1/2bh
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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

3. Same Distance
2 equal sides - 2 equal angles
T(up)=D/R1 T(down)=D/R2 - Add and solve for D
360
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

4. Rational Number
Part/whole = %/100
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
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

5. Volume of Pyramid
(1/3)LW*H
S=180(n-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
360

6. Volume of Sphere
A=[(B1+B2)*H]/2
D/W= (R1+R2)*T
Volume=(4/3)pir^3
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side

7. Combinations

8. Fundamental Counting Principle
= (x degree / 360) pi*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
A=L*W - P=2L+2W - Diagonals equal length
Multiply number of choices available in each option to get total number of options

9. Intersection
(area of base)*height
Consists of all the elements that appear in both sets
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
Volume=(4/3)pir^3

10. Parallelograms
D/W=R1T1 + R2T2
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

11. Sum of Interior Angles
A=L*W - P=2L+2W - Diagonals equal length
#successful events / total# possible outcomes
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=180(n-2)

12. Area of a Triangle
A=1/2bh
x1y1 = x2y2
(area of base)*height
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given

13. Area of a Sector
D/W=R1T1 + R2T2
= (x degree / 360) pi*r^2
Consists of all the elements that appear in both sets
1 - 3 - 5 - ...

14. Isosceles Triangle
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
An=A1(r)^n-1
Positive and negative whole numbers
2 equal sides - 2 equal angles

15. Average Rate
Middle number (or average of 2) of set from smallest to largest
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
1 - 3 - 5 - ...
(distance between opposite vertices) - square root(L^2+W^2+H^2)

16. Exponent Rules
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 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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

17. Integer
(1/3)pir^2*h
A=S^2 - P=4S - Diagonal is root2 times side
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
Positive and negative whole numbers

18. Extension of the Pythagorean Theorem
Consists of all of the elements that appear in either set without repeating elements
(distance between opposite vertices) - square root(L^2+W^2+H^2)
x1/y1 = x2/y2
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

19. Percents
= (x degree / 360) C
Part/whole = %/100
x1y1 = x2y2
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

20. Percentage Change
(area of base)*height
([old-new]/old)*100%
Order doesn't matter - nCr=n! / r!(n-r)!
Positive and negative whole numbers

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

22. Combined Rates
D=R*T - W=R*T
Part/whole = %/100
(1/3)LW*H
D/W=R1T1 + R2T2

23. Union
Consists of all of the elements that appear in either set without repeating elements
Consists of all the elements that appear in both sets
Part/whole = %/100
([old-new]/old)*100%

24. Median
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
(1/3)LW*H
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
Middle number (or average of 2) of set from smallest to largest

25. Same Time
S=180(n-2)
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T
A=L*W - P=2L+2W - Diagonals equal length

26. Triangle Inequality
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
A=1/2bh
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

27. Odd Numbers
A=S^2 - P=4S - Diagonal is root2 times side
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
1 - 3 - 5 - ...
S-S-S - S-A-S - A-S-A

28. Adding/Subtracting Exponents
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
Volume=(4/3)pir^3
Multiply number of choices available in each option to get total number of options

29. Arithmetic Sequence
A=[(B1+B2)*H]/2
An=A1+(n-1)d
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
(1/3)pir^2*h

30. Distance/Work Formula
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=R*T - W=R*T
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Middle number (or average of 2) of set from smallest to largest

31. Sum of Exterior Angles
D/W= (R1+R2)*T
Consists of all of the elements that appear in either set without repeating elements
Middle number (or average of 2) of set from smallest to largest
360

32. Cylinders
Volume=(4/3)pir^3
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
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

33. Mixture Formula
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
Order doesn't matter - nCr=n! / r!(n-r)!
= (x degree / 360) pi*r^2
(area of base)*height

34. Area Trapezoid
A=[(B1+B2)*H]/2
2 equal sides - 2 equal angles
An=A1(r)^n-1
= (x degree / 360) C

35. Real Wheel Formula
2 equal sides - 2 equal angles
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
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

36. Rectangles
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
A=L*W - P=2L+2W - Diagonals equal length
Middle number (or average of 2) of set from smallest to largest

37. Indirect Variation
x1y1 = x2y2
Square root[(x2-x1)^2 + (y2-y1)^2]
A=[(B1+B2)*H]/2
Middle number (or average of 2) of set from smallest to largest

38. Volume of Cone
0 - -2 - -4 - ...
(1/3)pir^2*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
S=180(n-2)

39. Square
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%
= (x degree / 360) C
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

40. Even/Odd Results
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
An=A1+(n-1)d
D/W=R1T1 + R2T2

41. Equilateral Triangle
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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
1 - 3 - 5 - ...

42. Weighted Averages
= (x degree / 360) C
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
An=A1+(n-1)d

43. Probability
D/W= (R1+R2)*T
= (x degree / 360) pi*r^2
#successful events / total# possible outcomes
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

44. Direct Variation
x1/y1 = x2/y2
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Part/whole = %/100
Order matters - nPr=n! / (n-r)!

45. Same Work
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
D/W= (R1+R2)*T

46. Length on an Arc
Middle number (or average of 2) of set from smallest to largest
= (x degree / 360) C
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

47. Area Hexagon
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
Multiply number of choices available in each option to get total number of options
A=(3root3/2)r^2
Volume=(4/3)pir^3

48. Mode
The most frequently occurring number in a set
Consists of all the elements that appear in both sets
= (x degree / 360) C
Order doesn't matter - nCr=n! / r!(n-r)!

49. Permutations
Order matters - nPr=n! / (n-r)!
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
0 - -2 - -4 - ...
(area of base)*height

50. Even Numbers
Square root[(x2-x1)^2 + (y2-y1)^2]
A=L*W - P=2L+2W - Diagonals equal length
Part/whole = %/100
0 - -2 - -4 - ...