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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 an ellipse
An = a1 + (n-1)d
90°
(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.
Square the differences between each coordinate - then square root the sum

2. Formula for geometric sequence
Hypotenuse is 2x - short side is x - long side is xv3
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1rn?¹
(n-2)180

3. Formula for calculation exponential growth
x=rcos?(theta) y=rsin? (theta)
Final amount = original amount x (1+growth rate)^number of changes
(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)]

4. Formula for the area of a sector
No equal sides and no equal angles
A = (degree of the arc / 360)(area of a circle)
NPr = n! / (n-r)!
Adding or subtracting 180 to ? and reversing the sign of r.

5. What are the conversion equations for polar coordinates to normal coordinates?
A = ((s1 + s2)h) / 2
Arc length equals = (degree of the arc / 360)(circumference)
x=rcos?(theta) y=rsin? (theta)
a1 / 1-r

6. Volume of a sphere
V = (4/3)pr³
y-y1 = m(x-x1)
Multiply the inscribed angle by 2
D= sv3

7. 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)
Arc length equals = (degree of the arc / 360)(circumference)
V= (1/3)(pr²h)
(n/2)(a1 + an)

8. What are relatively prime numbers?
180°
Adding or subtracting 180 to ? and reversing the sign of r.
The greatest common factor is 1 - but the numbers are not necessarily prime.
A = (degree of the arc / 360)(area of a circle)

9. Standard form of the equation of a parabola.
Parentheses - exponents - multiplication - division - addition - subtraction
y = a(x-h)² + k - where the vertex is (h -k)
90°
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

10. In an ellipse - where are the foci?
F(x) = -f(-x)
A = ((s1 + s2)h) / 2
(1-r/1-r)
Between the vertex and the minor axis on the major axis

11. How can you determine the arc degree or central angle of an inscribed angle?
Hypotenuse is xv2 - and the sides are x.
The greatest common factor is 1 - but the numbers are not necessarily prime.
y = a(x-h)² + k - where the vertex is (h -k)
Multiply the inscribed angle by 2

12. What is the triangle inequality rule?
(y-k)²/a² - (x-h)²/b² = 1
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.
(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.

13. Formula for arithmetic sequence
Their dot product = 0
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
An = a1 + (n-1)d

14. Standard form equation for circle
(y-k)²/a² - (x-h)²/b² = 1
(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.
Square the differences between each coordinate - then square root the sum

15. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
(n-2)180
V = (4/3)pr³
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

16. 45-45-90 triangle
F(x) = f(-x)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Hypotenuse is xv2 - and the sides are x.
Final amount = original amount x (1+growth rate)^number of changes

17. Combination formula
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)]
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!
SA = 4pr²

18. 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)
Multiply the inscribed angle by 2
V= (1/3)(pr²h)

19. Sum of infinite geometric series
Final amount = original amount x (1+growth rate)^number of changes
(y-k)²/a² - (x-h)²/b² = 1
a1 / 1-r
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

20. Define an even function.
N-1
a1 / 1-r
SA = 4pr²
F(x) = f(-x)

21. Complimentary angles add up to
C² = a² + b² - 2abcos(C)
90°
D= sv3
Multiply the inscribed angle by 2

22. What is the form of a polar coordinate?
x=rcos?(theta) y=rsin? (theta)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-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.
Final amount = original amount x (1+growth rate)^number of changes

23. Pythagorean Identities
Hypotenuse is xv2 - and the sides are x.
A = ((s1 + s2)h) / 2
x=rcos?(theta) y=rsin? (theta)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

24. Surface area of a sphere
C² = a² + b² - 2abcos(C)
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = 4pr²
Arc length equals = (degree of the arc / 360)(circumference)

25. Permutation formula (ordering)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
F(x) = f(-x)
N!
NPr = n! / (n-r)!

26. Formula for arc length
a1 / 1-r
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)]
(y-k)²/a² - (x-h)²/b² = 1

27. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
F(x) = -f(-x)
D= sv3
SA = pr² +prl

28. Where is tangent positive/negative?
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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-1

29. Sum of finite geometric series
Multiply the inscribed angle by 2
(1-r/1-r)
Two sides and two angle are equal
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

30. Standard form for a hyperbola that opens vertically
D = v(l²+w²+h²)
Arc length equals = (degree of the arc / 360)(circumference)
A = ((s1 + s2)h) / 2
(y-k)²/a² - (x-h)²/b² = 1

31. 30-60-90 triangle
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
An = a1 + (n-1)d
Hypotenuse is 2x - short side is x - long side is xv3

32. Volume of a pyramid
C² = a² + b² - 2abcos(C)
F(x) = f(-x)
Arc length equals = (degree of the arc / 360)(circumference)
V = (1/3)bh

33. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
NPr = n! / (n-r)!
(y-k)²/a² - (x-h)²/b² = 1
N-1
Adding or subtracting 180 to ? and reversing the sign of r.

34. Formula for the diagonal length of a cube
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)]
Square the differences between each coordinate - then square root the sum
SA = pr² +prl
D= sv3

35. How many ways can n elements be ordered?
N!
A = (degree of the arc / 360)(area of a circle)
90°
Hypotenuse is xv2 - and the sides are x.

36. Double Angle Formulas
SA = 4pr²
90°
D= sv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

37. Surface area of a cone
(n-2)180
SA = pr² +prl
A = (degree of the arc / 360)(area of a circle)
Adding or subtracting 180 to ? and reversing the sign of r.

38. Scalene triangle
Final amount = original amount x (1+growth rate)^number of changes
180°
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles

39. What is the order of operations?
Between the vertex and the minor axis on the major axis
SA = pr² +prl
Parentheses - exponents - multiplication - division - addition - subtraction
Hypotenuse is 2x - short side is x - long side is xv3

40. Formula for the area of a trapezoid
Parentheses - exponents - multiplication - division - addition - subtraction
No equal sides and no equal angles
180°
A = ((s1 + s2)h) / 2

41. Standard form for a hyperbola that opens to the sides
Two sides and two angle are equal
Multiply the inscribed angle by 2
x=rcos?(theta) y=rsin? (theta)
(x-h)²/a² - (y-k)²/b² = 1

42. Two vectors are perpendicular if
Their dot product = 0
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
N!

43. Formula for the diagonal length of a rectangular prism
x=rcos?(theta) y=rsin? (theta)
D = v(l²+w²+h²)
D= sv3
Final amount = original amount x (1+growth rate)^number of changes

44. How to determine if a number is prime
V = (4/3)pr³
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
F(x) = f(-x)
F(x) = -f(-x)

45. Sum of n terms of an arithmetic sequence
(n-2)180
(n/2)(a1 + an)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

46. Supplementary angles add up to
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(y-k)²/a² - (x-h)²/b² = 1
180°

47. Law of Cosines
C² = a² + b² - 2abcos(C)
D = v(l²+w²+h²)
Their dot product = 0
(n/2)(a1 + an)

48. Formula for the volume of a cone
V= (1/3)(pr²h)
An = a1 + (n-1)d
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)

49. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
F(x) = -f(-x)
Hypotenuse is 2x - short side is x - long side is xv3
(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.

50. Isosceles Triangles
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
F(x) = f(-x)
Arc length equals = (degree of the arc / 360)(circumference)
Two sides and two angle are equal