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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 for a hyperbola that opens vertically
x = -b/2a y= c - (b²/4a)
(1-r/1-r)
(y-k)²/a² - (x-h)²/b² = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

2. Sum of n terms of an arithmetic sequence
(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.
D= sv3
SA = pr² +prl
(n/2)(a1 + an)

3. Two vectors are perpendicular if
Hypotenuse is 2x - short side is x - long side is xv3
N-1
Two sides and two angle are equal
Their dot product = 0

4. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
All whole numbers except for 0
SA = pr² +prl
V = (1/3)bh

5. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
All whole numbers except for 0
y-y1 = m(x-x1)
Final amount = original amount x (1+growth rate)^number of changes
Two sides and two angle are equal

6. Scalene triangle
All whole numbers except for 0
No equal sides and no equal angles
An = a1 + (n-1)d
x=rcos?(theta) y=rsin? (theta)

7. 30-60-90 triangle
Multiply the inscribed angle by 2
Hypotenuse is 2x - short side is x - long side is xv3
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
C² = a² + b² - 2abcos(C)

8. What are the conversion equations for polar coordinates to normal coordinates?
Parentheses - exponents - multiplication - division - addition - subtraction
x=rcos?(theta) y=rsin? (theta)
(y-k)²/a² - (x-h)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!

9. Pythagorean Identities
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
V = (1/3)bh
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
NCr = nPr / r! = n! / (n-r)!r!

10. Formula for arithmetic sequence
An = a1rn?¹
An = a1 + (n-1)d
y = a(x-h)² + k - where the vertex is (h -k)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

11. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
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)]
All whole numbers except for 0
V= (1/3)(pr²h)

12. Define an odd function.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Adding or subtracting 180 to ? and reversing the sign of r.
F(x) = -f(-x)
NCr = nPr / r! = n! / (n-r)!r!

13. Sum of finite geometric series
NPr = n! / (n-r)!
(1-r/1-r)
Final amount = original amount x (1+growth rate)^number of changes
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

14. Volume of a sphere
V = (4/3)pr³
y = a(x-h)² + k - where the vertex is (h -k)
90°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

15. Sum of 2 Angles Formulas
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
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 + (y-k)² = r² - where (h -k) is the center of the circle
NPr = n! / (n-r)!

16. Sum of infinite geometric series
(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.
x = -b/2a y= c - (b²/4a)
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.

17. Formula for calculation exponential growth
NCr = nPr / r! = n! / (n-r)!r!
Final amount = original amount x (1+growth rate)^number of changes
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
NPr = n! / (n-r)!

18. 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)]
Arc length equals = (degree of the arc / 360)(circumference)
Multiply the inscribed angle by 2
y-y1 = m(x-x1)

19. How to determine if a number is prime
All whole numbers except for 0
Hypotenuse is 2x - short side is x - long side is xv3
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

20. How to find the distance between two points in 3d plane?
Final amount = original amount x (1+growth rate)^number of changes
All whole numbers except for 0
Hypotenuse is xv2 - and the sides are x.
Square the differences between each coordinate - then square root the sum

21. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = -f(-x)
A = (degree of the arc / 360)(area of a circle)
D = v(l²+w²+h²)

22. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n/2)(a1 + an)
V = (4/3)pr³
Hypotenuse is 2x - short side is x - long side is xv3

23. What is the form of a polar coordinate?
N-1
(n/2)(a1 + an)
NPr = n! / (n-r)!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

24. 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.
(1-r/1-r)
Multiply the inscribed angle by 2
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

25. Surface area of a cone
SA = pr² +prl
180°
Hypotenuse is xv2 - and the sides are x.
V= (1/3)(pr²h)

26. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is 2x - short side is x - long side is xv3
SA = pr² +prl

27. How many ways can n elements be ordered?
N!
SA = 4pr²
(n/2)(a1 + an)
V = (4/3)pr³

28. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
An = a1 + (n-1)d
N!
No equal sides and no equal angles

29. What is the sum of the interior angles for a polygon with n sides?
All whole numbers except for 0
(n-2)180
N!
Between the vertex and the minor axis on the major axis

30. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
y = a(x-h)² + k - where the vertex is (h -k)
Final amount = original amount x (1+growth rate)^number of changes
No equal sides and no equal angles
N-1

31. In an ellipse - where are the foci?
C² = a² + b² - 2abcos(C)
F(x) = -f(-x)
Between the vertex and the minor axis on the major axis
No equal sides and no equal angles

32. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is xv2 - and the sides are x.
N!

33. Volume of a pyramid
Hypotenuse is 2x - short side is x - long side is xv3
N-1
V = (1/3)bh
Hypotenuse is xv2 - and the sides are x.

34. Define an even function.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(x-h)²/a² - (y-k)²/b² = 1
(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.
F(x) = f(-x)

35. Supplementary angles add up to
NCr = nPr / r! = n! / (n-r)!r!
180°
NPr = n! / (n-r)!
90°

36. Formula for the area of a sector
F(x) = -f(-x)
Between the vertex and the minor axis on the major axis
A = (degree of the arc / 360)(area of a circle)
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)]

37. Formula for the volume of a cone
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Hypotenuse is 2x - short side is x - long side is xv3
V= (1/3)(pr²h)
An = a1rn?¹

38. 45-45-90 triangle
Multiply the inscribed angle by 2
V = (1/3)bh
N!
Hypotenuse is xv2 - and the sides are x.

39. How can you determine the arc degree or central angle of an inscribed angle?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
x = -b/2a y= c - (b²/4a)
(y-k)²/a² - (x-h)²/b² = 1
Multiply the inscribed angle by 2

40. What is the order of operations?
F(x) = f(-x)
Parentheses - exponents - multiplication - division - addition - subtraction
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
V = (1/3)bh

41. What are natural 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.
An = a1rn?¹
C² = a² + b² - 2abcos(C)
All whole numbers except for 0

42. What are relatively prime numbers?
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)]
An = a1 + (n-1)d
(n/2)(a1 + an)

43. Standard form for a hyperbola that opens to the sides
SA = 4pr²
A = (degree of the arc / 360)(area of a circle)
V = (4/3)pr³
(x-h)²/a² - (y-k)²/b² = 1

44. Law of Cosines
D= sv3
N!
(1-r/1-r)
C² = a² + b² - 2abcos(C)

45. Isosceles Triangles
(1-r/1-r)
Two sides and two angle are equal
C² = a² + b² - 2abcos(C)
V = (1/3)bh

46. Combination formula
Two sides and two angle are equal
NCr = nPr / r! = n! / (n-r)!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.
F(x) = -f(-x)

47. Formula for geometric sequence
SA = pr² +prl
N!
All whole numbers except for 0
An = a1rn?¹

48. Surface area of a sphere
SA = 4pr²
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)
The greatest common factor is 1 - but the numbers are not necessarily prime.

49. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
NCr = nPr / r! = n! / (n-r)!r!
x = -b/2a y= c - (b²/4a)
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)]
F(x) = -f(-x)

50. Formula for the diagonal length of a cube
C² = a² + b² - 2abcos(C)
y-y1 = m(x-x1)
D= sv3
An = a1rn?¹