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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. Standard form equation for circle
(x-h) + (y-k) = r - where (h -k) is the center of the circle
(y-k)/a - (x-h)/b = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
SA = 4pr

2. What is the sum of the interior angles for a polygon with n sides?
(n/2)(a1 + an)
(x-h)/a - (y-k)/b = 1
(n-2)180
The greatest common factor is 1 - but the numbers are not necessarily prime.

3. Formula for the volume of a cone
(n-2)180
x = -b/2a y= c - (b/4a)
Two sides and two angle are equal
V= (1/3)(prh)

4. Standard form for a hyperbola that opens to the sides
D= sv3
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
(x-h)/a - (y-k)/b = 1
Multiply the inscribed angle by 2

5. What are relatively prime numbers?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily prime.
(n-2)180

6. Formula for the diagonal length of a cube
Square the differences between each coordinate - then square root the sum
SA = pr +prl
D= sv3
x=rcos?(theta) y=rsin? (theta)

7. Supplementary angles add up to
No equal sides and no equal angles
180
N-1
Multiply the inscribed angle by 2

8. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
V = (4/3)pr
N-1
A = (degree of the arc / 360)(area of a circle)
a1 / 1-r

9. Pythagorean Identities
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)]
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
No equal sides and no equal angles
N-1

10. Two vectors are perpendicular if
Their dot product = 0
No equal sides and no equal angles
(y-k)/a - (x-h)/b = 1
SA = 4pr

11. Law of Cosines
C = a + b - 2abcos(C)
F(x) = f(-x)
(x-h)/a - (y-k)/b = 1
x=rcos?(theta) y=rsin? (theta)

12. Surface area of a sphere
C = a + b - 2abcos(C)
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes
SA = 4pr

13. What is the order of operations?
Between the vertex and the minor axis on the major axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
Parentheses - exponents - multiplication - division - addition - subtraction
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

14. Formula for the area of a trapezoid
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
A = ((s1 + s2)h) / 2
No equal sides and no equal angles
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

15. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
(y-k)/a - (x-h)/b = 1
All whole numbers except for 0
a1 / 1-r

16. Define an even function.
90
F(x) = f(-x)
V= (1/3)(prh)
Hypotenuse is xv2 - and the sides are x.

17. Sum of n terms of an arithmetic sequence
SA = pr +prl
180
(n/2)(a1 + an)
N-1

18. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
x = -b/2a y= c - (b/4a)
(y-k)/a - (x-h)/b = 1
F(x) = -f(-x)

19. Formula for arc length
(x-h)/a - (y-k)/b = 1
C = a + b - 2abcos(C)
A = (degree of the arc / 360)(area of a circle)
Arc length equals = (degree of the arc / 360)(circumference)

20. Isosceles Triangles
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Hypotenuse is xv2 - and the sides are x.
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

21. Sum of finite geometric series
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)
(x-h)/a - (y-k)/b = 1
(1-r/1-r)

22. Standard form of the equation of a parabola.
y = a(x-h) + k - where the vertex is (h -k)
V = (4/3)pr
Sinx+cosx = 1 secx = 1+tanx cscx = 1+cotx
Adding or subtracting 180 to ? and reversing the sign of r.

23. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
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)]
D= sv3
y-y1 = m(x-x1)
x=rcos?(theta) y=rsin? (theta)

24. How can you determine the arc degree or central angle of an inscribed angle?
Between the vertex and the minor axis on the major axis
180
(n/2)(a1 + an)
Multiply the inscribed angle by 2

25. Formula for arithmetic sequence
(x-h)/a - (y-k)/b = 1
An = a1 + (n-1)d
a1 / 1-r
SA = pr +prl

26. What are the conversion equations for polar coordinates to normal coordinates?
(y-k)/a - (x-h)/b = 1
x=rcos?(theta) y=rsin? (theta)
(n-2)180
Adding or subtracting 180 to ? and reversing the sign of r.

27. In an ellipse - where are the foci?
N-1
(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.
Between the vertex and the minor axis on the major axis
(x-h) + (y-k) = r - where (h -k) is the center of the circle

28. Standard form equation for an ellipse
Square the differences between each coordinate - then square root the sum
(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.
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

29. Sum of infinite geometric series
a1 / 1-r
A = ((s1 + s2)h) / 2
Their dot product = 0
F(x) = f(-x)

30. Formula for the area of a sector
No equal sides and no equal angles
F(x) = f(-x)
A = (degree of the arc / 360)(area of a circle)
Multiply the inscribed angle by 2

31. Where is tangent positive/negative?
D = v(l+w+h)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
F(x) = -f(-x)
A = ((s1 + s2)h) / 2

32. Formula for the diagonal length of a rectangular prism
Square the differences between each coordinate - then square root the sum
90
D = v(l+w+h)
180

33. Formula for geometric sequence
An = a1rn?
90
Final amount = original amount x (1+growth rate)^number of changes
No equal sides and no equal angles

34. What are natural numbers?
Final amount = original amount x (1+growth rate)^number of changes
No equal sides and no equal angles
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
All whole numbers except for 0

35. 45-45-90 triangle
V= (1/3)(prh)
(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!
Hypotenuse is xv2 - and the sides are x.

36. Standard form for a hyperbola that opens vertically
(y-k)/a - (x-h)/b = 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)]
Adding or subtracting 180 to ? and reversing the sign of r.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

37. What is the triangle inequality rule?
a1 / 1-r
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Between the vertex and the minor axis on the major axis
Hypotenuse is xv2 - and the sides are x.

38. Formula for calculation exponential growth
NPr = n! / (n-r)!
Final amount = original amount x (1+growth rate)^number of changes
a1 / 1-r
N-1

39. Double Angle 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)]
A = ((s1 + s2)h) / 2
Final amount = original amount x (1+growth rate)^number of changes
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

40. Difference between 2 Angles formulas
V = (1/3)bh
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx
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)]

41. Permutation formula (ordering)
Square the differences between each coordinate - then square root the sum
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
N-1
NPr = n! / (n-r)!

42. Sum of 2 Angles Formulas
D= sv3
(n-2)180
Square the differences between each coordinate - then square root the sum
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)]

43. What is the form of a polar coordinate?
Their dot product = 0
y = a(x-h) + k - where the vertex is (h -k)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
A = ((s1 + s2)h) / 2

44. Surface area of a cone
Their dot product = 0
Parentheses - exponents - multiplication - division - addition - subtraction
N-1
SA = pr +prl

45. Complimentary angles add up to
Hypotenuse is xv2 - and the sides are x.
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
90

46. If the general parabola equation is y = ax+bx+c - what is the vertex of the parabola
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 = -b/2a y= c - (b/4a)
(1-r/1-r)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

47. Volume of a pyramid
Adding or subtracting 180 to ? and reversing the sign of r.
Their dot product = 0
V = (1/3)bh
90

48. Scalene triangle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles
N!
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

49. How many ways can n elements be ordered?
SA = pr +prl
N!
NCr = nPr / r! = n! / (n-r)!r!
Sin2x= 2sinxcosx cos2x = cosx - sinx = 2cosx - 1 = 1 - sinx

50. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
(x-h)/a - (y-k)/b = 1
Arc length equals = (degree of the arc / 360)(circumference)
a1 / 1-r

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