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SAT Math 2

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. What is the form of a polar coordinate?
The greatest common factor is 1 - but the numbers are not necessarily prime.
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)]
NPr = n! / (n-r)!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

2. Volume of a pyramid
V = (1/3)bh
SA = pr +prl
D = v(l+w+h)
x=rcos?(theta) y=rsin? (theta)

3. 45-45-90 triangle
N-1
Hypotenuse is xv2 - and the sides are x.
y-y1 = m(x-x1)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

4. How to determine if a number is prime
(1-r/1-r)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Their dot product = 0
(x-h) + (y-k) = r - where (h -k) is the center of the circle

5. What is the triangle inequality rule?
SA = pr +prl
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
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.

6. Formula for arc length
Two sides and two angle are equal
Arc length equals = (degree of the arc / 360)(circumference)
Their dot product = 0
90

7. Scalene triangle
A = ((s1 + s2)h) / 2
(x-h)/a - (y-k)/b = 1
No equal sides and no equal angles
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

8. What are relatively prime numbers?
V= (1/3)(prh)
The greatest common factor is 1 - but the numbers are not necessarily prime.
D= sv3
V = (1/3)bh

9. Sum of infinite geometric series
a1 / 1-r
(y-k)/a - (x-h)/b = 1
N!
Two sides and two angle are equal

10. How many ways can n elements be ordered?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
N!
A = ((s1 + s2)h) / 2
y = a(x-h) + k - where the vertex is (h -k)

11. How can multiple polar coordinates be made?
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Adding or subtracting 180 to ? and reversing the sign of r.
V = (1/3)bh
D = v(l+w+h)

12. Double Angle Formulas
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Square the differences between each coordinate - then square root the sum
An = a1rn?
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

13. Where is tangent positive/negative?
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
D= sv3

14. Isosceles Triangles
Two sides and two angle are equal
N!
An = a1 + (n-1)d
D= sv3

15. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
V= (1/3)(prh)
y = a(x-h) + k - where the vertex is (h -k)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

16. How to find the distance between two points in 3d plane?
(x-h)/a - (y-k)/b = 1
NCr = nPr / r! = n! / (n-r)!r!
The greatest common factor is 1 - but the numbers are not necessarily prime.
Square the differences between each coordinate - then square root the sum

17. What is the order of operations?
Square the differences between each coordinate - then square root the sum
Parentheses - exponents - multiplication - division - addition - subtraction
(x-h)/a + (y-k)/b = 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.
NPr = n! / (n-r)!

18. Standard form equation for an ellipse
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)/a + (y-k)/b = 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.

19. What is the sum of the interior angles for a polygon with n sides?
Their dot product = 0
(n-2)180
(1-r/1-r)
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

20. Formula for calculation exponential growth
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)]
Two sides and two angle are equal
Final amount = original amount x (1+growth rate)^number of changes
F(x) = f(-x)

21. What are natural numbers?
All whole numbers except for 0
Final amount = original amount x (1+growth rate)^number of changes
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Their dot product = 0

22. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
180
Two sides and two angle are equal
Hypotenuse is xv2 - and the sides are x.

23. Formula for the volume of a cone
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 = (degree of the arc / 360)(area of a circle)
V= (1/3)(prh)
NCr = nPr / r! = n! / (n-r)!r!

24. Standard form for a hyperbola that opens vertically
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-k)/a - (x-h)/b = 1
x = -b/2a y= c - (b/4a)
V = (4/3)pr

25. Formula for the diagonal length of a cube
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
D= sv3
(x-h) + (y-k) = r - where (h -k) is the center of the circle
y = a(x-h) + k - where the vertex is (h -k)

26. Define an even function.
F(x) = f(-x)
NCr = nPr / r! = n! / (n-r)!r!
Two sides and two angle are equal
(y-k)/a - (x-h)/b = 1

27. Permutation formula (ordering)
V = (4/3)pr
An = a1rn?
No equal sides and no equal angles
NPr = n! / (n-r)!

28. Standard form of the equation of a parabola.
Their dot product = 0
y = a(x-h) + k - where the vertex is (h -k)
C = a + b - 2abcos(C)
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

29. Two vectors are perpendicular if
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Square the differences between each coordinate - then square root the sum
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Their dot product = 0

30. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(x-h) + (y-k) = r - where (h -k) is the center of the circle
x = -b/2a y= c - (b/4a)
N-1

31. Volume of a sphere
F(x) = f(-x)
Multiply the inscribed angle by 2
y-y1 = m(x-x1)
V = (4/3)pr

32. Sum of finite geometric series
(y-k)/a - (x-h)/b = 1
(1-r/1-r)
D= sv3
NPr = n! / (n-r)!

33. Supplementary angles add up to
SA = 4pr
(x-h)/a + (y-k)/b = 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.
(n/2)(a1 + an)
180

34. Standard form equation for circle
(x-h) + (y-k) = r - where (h -k) is the center of the circle
Arc length equals = (degree of the arc / 360)(circumference)
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)]
(n/2)(a1 + an)

35. Sum of 2 Angles Formulas
(x-h)/a + (y-k)/b = 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.
The greatest common factor is 1 - but the numbers are not necessarily prime.
Multiply the inscribed angle by 2
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)]

36. In an ellipse - where are the foci?
V = (4/3)pr
Between the vertex and the minor axis on the major axis
A = (degree of the arc / 360)(area of a circle)
(x-h)/a - (y-k)/b = 1

37. How can you determine the arc degree or central angle of an inscribed angle?
90
x = -b/2a y= c - (b/4a)
V = (4/3)pr
Multiply the inscribed angle by 2

38. Define an odd function.
x=rcos?(theta) y=rsin? (theta)
(x-h) + (y-k) = r - where (h -k) is the center of the circle
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
F(x) = -f(-x)

39. Surface area of a sphere
D = v(l+w+h)
SA = 4pr
(1-r/1-r)
Arc length equals = (degree of the arc / 360)(circumference)

40. What are the conversion equations for polar coordinates to normal coordinates?
SA = 4pr
F(x) = f(-x)
Their dot product = 0
x=rcos?(theta) y=rsin? (theta)

41. Difference between 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)]
Multiply the inscribed angle by 2
NPr = n! / (n-r)!
(n/2)(a1 + an)

42. Pythagorean Identities
D = v(l+w+h)
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = pr +prl

43. Formula for arithmetic sequence
An = a1rn?
An = a1 + (n-1)d
a1 / 1-r
Between the vertex and the minor axis on the major axis

44. Law of Cosines
C = a + b - 2abcos(C)
Between the vertex and the minor axis on the major axis
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
(n-2)180

45. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
Two sides and two angle are equal
Hypotenuse is xv2 - and the sides are x.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

46. Complimentary angles add up to
Square the differences between each coordinate - then square root the sum
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1 + (n-1)d
90

47. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
V= (1/3)(prh)
x = -b/2a y= c - (b/4a)
Hypotenuse is 2x - short side is x - long side is xv3
N!

48. Surface area of a cone
Square the differences between each coordinate - then square root the sum
Hypotenuse is 2x - short side is x - long side is xv3
SA = pr +prl
Multiply the inscribed angle by 2

49. Standard form for a hyperbola that opens to the sides
(x-h)/a - (y-k)/b = 1
y-y1 = m(x-x1)
90
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)]

50. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
y-y1 = m(x-x1)
Between the vertex and the minor axis on the major axis
F(x) = f(-x)
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx

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