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SAT Math 2

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. Volume of a sphere
Adding or subtracting 180 to ? and reversing the sign of r.
C² = a² + b² - 2abcos(C)
V = (4/3)pr³
V = (1/3)bh

2. Standard form of the equation of a parabola.
Final amount = original amount x (1+growth rate)^number of changes
Hypotenuse is xv2 - and the sides are x.
y = a(x-h)² + k - where the vertex is (h -k)
An = a1rn?¹

3. Difference between 2 Angles formulas
The greatest common factor is 1 - but the numbers are not necessarily prime.
D= sv3
x=rcos?(theta) y=rsin? (theta)
Sin(a-b) = sin(a)cos(b) - sin(b)cos(a) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)]

4. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y-y1 = m(x-x1)
An = a1 + (n-1)d

5. Sum of finite geometric series
V = (1/3)bh
x=rcos?(theta) y=rsin? (theta)
(1-r/1-r)
N!

6. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
90°
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

7. Scalene triangle
D= sv3
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes

8. Standard form for a hyperbola that opens vertically
(y-k)²/a² - (x-h)²/b² = 1
x=rcos?(theta) y=rsin? (theta)
(n/2)(a1 + an)
(1-r/1-r)

9. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
NPr = n! / (n-r)!
Final amount = original amount x (1+growth rate)^number of changes
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)

10. Pythagorean Identities
SA = pr² +prl
N!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
a1 / 1-r

11. Formula for the area of a sector
(n/2)(a1 + an)
V = (1/3)bh
(x-h)²/a² + (y-k)²/b² = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.
A = (degree of the arc / 360)(area of a circle)

12. 30-60-90 triangle
Two sides and two angle are equal
Hypotenuse is 2x - short side is x - long side is xv3
V= (1/3)(pr²h)
NCr = nPr / r! = n! / (n-r)!r!

13. Combination formula
(y-k)²/a² - (x-h)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
An = a1 + (n-1)d

14. Formula for calculation exponential growth
NPr = n! / (n-r)!
V = (1/3)bh
Final amount = original amount x (1+growth rate)^number of changes
Between the vertex and the minor axis on the major axis

15. 45-45-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
Hypotenuse is xv2 - and the sides are x.
SA = 4pr²
Parentheses - exponents - multiplication - division - addition - subtraction

16. Formula for the volume of a cone
Two sides and two angle are equal
a1 / 1-r
F(x) = f(-x)
V= (1/3)(pr²h)

17. Supplementary angles add up to
180°
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(x-h)²/a² - (y-k)²/b² = 1
NPr = n! / (n-r)!

18. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
90°
D = v(l²+w²+h²)
Hypotenuse is 2x - short side is x - long side is xv3

19. Isosceles Triangles
(n-2)180
SA = 4pr²
No equal sides and no equal angles
Two sides and two angle are equal

20. Formula for the diagonal length of a cube
N-1
SA = 4pr²
D= sv3
An = a1rn?¹

21. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
a1 / 1-r
(x-h)²/a² - (y-k)²/b² = 1
x=rcos?(theta) y=rsin? (theta)

22. Two vectors are perpendicular if
NCr = nPr / r! = n! / (n-r)!r!
Their dot product = 0
C² = a² + b² - 2abcos(C)
(n-2)180

23. Sum of 2 Angles Formulas
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]
V = (4/3)pr³
Arc length equals = (degree of the arc / 360)(circumference)
F(x) = f(-x)

24. What is the triangle inequality rule?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Final amount = original amount x (1+growth rate)^number of changes
The greatest common factor is 1 - but the numbers are not necessarily prime.

25. Permutation formula (ordering)
A = ((s1 + s2)h) / 2
NPr = n! / (n-r)!
(y-k)²/a² - (x-h)²/b² = 1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

26. Surface area of a cone
(1-r/1-r)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(n-2)180
SA = pr² +prl

27. Volume of a pyramid
V = (1/3)bh
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
C² = a² + b² - 2abcos(C)
D = v(l²+w²+h²)

28. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]
(x-h)²/a² - (y-k)²/b² = 1
(n-2)180

29. Sum of infinite geometric series
(y-k)²/a² - (x-h)²/b² = 1
a1 / 1-r
F(x) = f(-x)
SA = 4pr²

30. Formula for the area of a trapezoid
180°
x = -b/2a y= c - (b²/4a)
Hypotenuse is xv2 - and the sides are x.
A = ((s1 + s2)h) / 2

31. What are the conversion equations for polar coordinates to normal coordinates?
C² = a² + b² - 2abcos(C)
Hypotenuse is xv2 - and the sides are x.
Parentheses - exponents - multiplication - division - addition - subtraction
x=rcos?(theta) y=rsin? (theta)

32. Surface area of a sphere
F(x) = f(-x)
Between the vertex and the minor axis on the major axis
x=rcos?(theta) y=rsin? (theta)
SA = 4pr²

33. How to determine if a number is prime
V = (4/3)pr³
(1-r/1-r)
N!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

34. Define an odd function.
F(x) = -f(-x)
SA = pr² +prl
Two sides and two angle are equal
V = (1/3)bh

35. Complimentary angles add up to
D= sv3
V = (4/3)pr³
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
90°

36. What is the form of a polar coordinate?
Two sides and two angle are equal
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Arc length equals = (degree of the arc / 360)(circumference)
SA = 4pr²

37. How many ways can n elements be ordered?
C² = a² + b² - 2abcos(C)
(x-h)²/a² + (y-k)²/b² = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.
a1 / 1-r
N!

38. What is the sum of the interior angles for a polygon with n sides?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Two sides and two angle are equal
(n-2)180
Hypotenuse is xv2 - and the sides are x.

39. What are natural numbers?
All whole numbers except for 0
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
C² = a² + b² - 2abcos(C)
(1-r/1-r)

40. Formula for geometric sequence
Between the vertex and the minor axis on the major axis
An = a1rn?¹
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Hypotenuse is xv2 - and the sides are x.

41. How can you determine the arc degree or central angle of an inscribed angle?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(x-h)²/a² + (y-k)²/b² = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.
Multiply the inscribed angle by 2
Hypotenuse is 2x - short side is x - long side is xv3

42. Standard form for a hyperbola that opens to the sides
Final amount = original amount x (1+growth rate)^number of changes
(y-k)²/a² - (x-h)²/b² = 1
(n/2)(a1 + an)
(x-h)²/a² - (y-k)²/b² = 1

43. Formula for the diagonal length of a rectangular prism
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]
y-y1 = m(x-x1)
D = v(l²+w²+h²)
SA = 4pr²

44. Define an even function.
Two sides and two angle are equal
(n-2)180
F(x) = f(-x)
A = ((s1 + s2)h) / 2

45. Standard form equation for circle
V= (1/3)(pr²h)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Arc length equals = (degree of the arc / 360)(circumference)
(y-k)²/a² - (x-h)²/b² = 1

46. Formula for arithmetic sequence
180°
An = a1 + (n-1)d
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
x=rcos?(theta) y=rsin? (theta)

47. Standard form equation for an ellipse
(x-h)²/a² + (y-k)²/b² = 1 - where (h -k) is the center of the ellipse - the length of the horizontal axis is 2a - the length of the vertical axis is 2b - if a>b - the horizontal axis is the major axis.
Two sides and two angle are equal
V = (1/3)bh
a1 / 1-r

48. In an ellipse - where are the foci?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Square the differences between each coordinate - then square root the sum
Arc length equals = (degree of the arc / 360)(circumference)
Between the vertex and the minor axis on the major axis

49. Law of Cosines
SA = 4pr²
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
a1 / 1-r
C² = a² + b² - 2abcos(C)

50. Sum of n terms of an arithmetic sequence
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
A = ((s1 + s2)h) / 2
(n/2)(a1 + an)
Sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)]