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. Fundamental Counting Principle
1 - 3 - 5 - ...
#successful events / total# possible outcomes
Multiply number of choices available in each option to get total number of options
A=(3root3/2)r^2

2. Equilateral Triangle
An=A1(r)^n-1
Order matters - nPr=n! / (n-r)!
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

3. Weighted Averages
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
D=R*T - W=R*T
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)
Consists of all of the elements that appear in either set without repeating elements

4. Exponent Rules
(distance between opposite vertices) - square root(L^2+W^2+H^2)
2 equal sides - 2 equal angles
A=1/2bh
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

5. Rational Number
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=S^2 - P=4S - Diagonal is root2 times side
(1/3)LW*H

6. Distance Formula
S=180(n-2)
360
Square root[(x2-x1)^2 + (y2-y1)^2]
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

7. Union
Order doesn't matter - nCr=n! / r!(n-r)!
(distance between opposite vertices) - square root(L^2+W^2+H^2)
Consists of all of the elements that appear in either set without repeating elements
A number that can be represented by a fraction where both the numerator and the denominator are integers and the denominator is not zero

8. Congruent 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
S-S-S - S-A-S - A-S-A
(area of base)*height
Order matters - nPr=n! / (n-r)!

9. Area Trapezoid
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
#successful events / total# possible outcomes
A=[(B1+B2)*H]/2
(area of base)*height

10. Percents
Part/whole = %/100
S=180(n-2)
(1/3)LW*H
Consists of all the elements that appear in both sets

11. Average Rate
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)
A=[(B1+B2)*H]/2
A=(3root3/2)r^2

12. Percentage Change
A=(3root3/2)r^2
([old-new]/old)*100%
D/W= (R1+R2)*T
(avg1)(number1) + (avg2)(number2) = (avgT)(numberT)

13. Triangle Inequality
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)
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

14. Mode
The most frequently occurring number in a set
Volume=(4/3)pir^3
An=A1(r)^n-1
Consists of all the elements that appear in both sets

15. Even Numbers
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd
D=R*T - W=R*T
0 - -2 - -4 - ...
([old-new]/old)*100%

16. Rectangles
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
Part/whole = %/100
A=L*W - P=2L+2W - Diagonals equal length
Positive and negative whole numbers

17. Adding/Subtracting Exponents
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
S=180(n-2)
(distance between opposite vertices) - square root(L^2+W^2+H^2)

18. Median
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
Middle number (or average of 2) of set from smallest to largest
x1/y1 = x2/y2
(area of base)*height

19. Area Hexagon
A=1/2bh
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
A=(3root3/2)r^2
A=L*W - P=2L+2W - Diagonals equal length

20. Right Triangle
Square root[(x2-x1)^2 + (y2-y1)^2]
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles
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

21. Probability
Order matters - nPr=n! / (n-r)!
Multiply number of choices available in each option to get total number of options
#successful events / total# possible outcomes
Order doesn't matter - nCr=n! / r!(n-r)!

22. Same Work
D=R*T - W=R*T
S=180(n-2)
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

23. Volume of Sphere
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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
0 - -2 - -4 - ...

24. Extension of the Pythagorean Theorem
(distance between opposite vertices) - square root(L^2+W^2+H^2)
A=(3root3/2)r^2
D/W=R1T1 + R2T2
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2

25. Combined Rates
D/W=R1T1 + R2T2
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
(distance between opposite vertices) - square root(L^2+W^2+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

26. Same Distance
D/W=R1T1 + R2T2
An=A1+(n-1)d
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

27. Integer
Positive and negative whole numbers
Consists of all the elements that appear in both sets
(distance between opposite vertices) - square root(L^2+W^2+H^2)
D=R*T - W=R*T

28. Similar Triangles
Consists of all the elements that appear in both sets
D=R*T - W=R*T
(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

29. Special Right Triangles
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution
D=R*T - W=R*T
S=180(n-2)

30. Same Rate
([old-new]/old)*100%
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
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
T(total)= (T1*T2)/(T1+T2) - (same as finding combined rate of two workiers working on 1 thing)

31. Mixture Formula
Middle number (or average of 2) of set from smallest to largest
S-S-S - S-A-S - A-S-A
Part/whole = %/100
P1(N1) + P2(N2) = Pfinal(Nfinal) - P=percentage of acid - N=amount of the solution

32. Parallelograms
#successful events / total# possible outcomes
Opposite sides congruent - opposite angles congruent - diagonals bisect each other - Area=altitude*side
Positive and negative whole numbers
360

33. Same Time
Order matters - nPr=n! / (n-r)!
A=S^2 - P=4S - Diagonal is root2 times side
D/W= (R1+R2)*T
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

34. Intersection
Consists of all the elements that appear in both sets
Multiply number of choices available in each option to get total number of options
(1/3)LW*H
360

35. Permutations
A=L*W - P=2L+2W - Diagonals equal length
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
S=180(n-2)

36. Volume of Pyramid
A-A - 2 Sides in same proportion and Angle in between is the same - A1:A2=L1^2:L2^2
(1/3)LW*H
(area of base)*height
Part/whole = %/100

37. Isosceles Triangle
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
A=L*W - P=2L+2W - Diagonals equal length
2 equal sides - 2 equal angles
S=180(n-2)

38. Volume of Cone
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
x1/y1 = x2/y2
(1/3)pir^2*h
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)

39. Distance/Work Formula
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
D=R*T - W=R*T
A=L*W - P=2L+2W - Diagonals equal length
(N1T1)/W1 = (N2T2)/W2 - N=number of workers

40. Even/Odd Results
360
#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
Even+/-even=even even*even=even - odd+-odd=even even*odd=even - even+odd=odd odd*odd=odd

41. Weighted Average
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
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)
S-S-S - S-A-S - A-S-A

42. Area of a Sector
Consists of all the elements that appear in both sets
A^2 + b^2 = c^2 - 3-4-5 - 5-12-13
(area of base)*height
= (x degree / 360) pi*r^2

43. Sum of Exterior Angles
Multiply number of choices available in each option to get total number of options
360
(1/3)pir^2*h
3 equal sides - 3 60-degree angles - split into 2 30-60-90 triangles

44. Square
(N1T1)/W1 = (N2T2)/W2 - N=number of workers
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
A=S^2 - P=4S - Diagonal is root2 times side
([old-new]/old)*100%

45. Volume of Prism
The most frequently occurring number in a set
30-60-90 = 1:root3:2 - 45-45-90 = 1:1:root2
(area of base)*height
Multiply number of choices available in each option to get total number of options

46. Odd Numbers
Square root[(x2-x1)^2 + (y2-y1)^2]
Positive and negative whole numbers
1 - 3 - 5 - ...
A=1/2bh

47. Area of a Triangle
A=1/2bh
A=[(B1+B2)*H]/2
Part/whole = %/100
Square root[(x2-x1)^2 + (y2-y1)^2]

48. Real Wheel Formula
R=rotations - L=circumference - radii - diameters - R1L1=R2L2
(1/3)LW*H
Part/whole = %/100
1 - 3 - 5 - ...

49. Cylinders
A=L*W - P=2L+2W - Diagonals equal length
Volume=pir^2h - Surface Area=2pir^2 + 2pir*h
A=1/2bh
Order doesn't matter - nCr=n! / r!(n-r)!

50. Length on an Arc
= (x degree / 360) C
x1y1 = x2y2
(D1+D2) / (T1+T2) or use weighted average formula subsituting D and T with whatever 2 given
AVG1(N1) + AVG2(N2) = AVGtotal(Ntotal)