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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.
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. Formula for calculation exponential growth
(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.
(n-2)180
Final amount = original amount x (1+growth rate)^number of changes
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

2. What are the conversion equations for polar coordinates to normal coordinates?
N-1
x=rcos?(theta) y=rsin? (theta)
V= (1/3)(pr²h)
NPr = n! / (n-r)!

3. Permutation formula (ordering)
Hypotenuse is 2x - short side is x - long side is xv3
NPr = n! / (n-r)!
y-y1 = m(x-x1)
(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.

4. Double Angle Formulas
NCr = nPr / r! = n! / (n-r)!r!
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
D= sv3

5. What are relatively prime numbers?
(n/2)(a1 + an)
The greatest common factor is 1 - but the numbers are not necessarily prime.
Arc length equals = (degree of the arc / 360)(circumference)
V= (1/3)(pr²h)

6. Formula for arc length
NPr = n! / (n-r)!
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.
Arc length equals = (degree of the arc / 360)(circumference)

7. Formula for the diagonal length of a cube
D= sv3
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.
NCr = nPr / r! = n! / (n-r)!r!

8. Surface area of a cone
SA = pr² +prl
a1 / 1-r
V = (1/3)bh
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

9. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
y-y1 = m(x-x1)
An = a1 + (n-1)d
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

10. Sum of 2 Angles Formulas
A = ((s1 + s2)h) / 2
N!
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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

11. Two vectors are perpendicular if
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Their dot product = 0
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is 2x - short side is x - long side is xv3

12. How many ways can n elements be ordered?
Between the vertex and the minor axis on the major axis
N!
Square the differences between each coordinate - then square root the sum
Multiply the inscribed angle by 2

13. What is the order of operations?
An = a1rn?¹
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
V = (1/3)bh
Parentheses - exponents - multiplication - division - addition - subtraction

14. Volume of a sphere
An = a1rn?¹
F(x) = f(-x)
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.

15. Isosceles Triangles
(y-k)²/a² - (x-h)²/b² = 1
F(x) = -f(-x)
Two sides and two angle are equal
F(x) = f(-x)

16. What are natural numbers?
Two sides and two angle are equal
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
D = v(l²+w²+h²)

17. Formula for the volume of a cone
F(x) = -f(-x)
V= (1/3)(pr²h)
N!
F(x) = f(-x)

18. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(n/2)(a1 + an)
C² = a² + b² - 2abcos(C)
No equal sides and no equal angles

19. In an ellipse - where are the foci?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Parentheses - exponents - multiplication - division - addition - subtraction
Between the vertex and the minor axis on the major axis
V = (1/3)bh

20. Formula for the area of a sector
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NCr = nPr / r! = n! / (n-r)!r!
A = (degree of the arc / 360)(area of a circle)

21. Standard form for a hyperbola that opens vertically
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(y-k)²/a² - (x-h)²/b² = 1
x=rcos?(theta) y=rsin? (theta)
V = (1/3)bh

22. Standard form equation for an ellipse
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = -f(-x)
(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.
V= (1/3)(pr²h)

23. How can you determine the arc degree or central angle of an inscribed angle?
Their dot product = 0
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)]
Multiply the inscribed angle by 2

24. Pythagorean Identities
A = ((s1 + s2)h) / 2
N-1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(1-r/1-r)

25. Formula for the diagonal length of a rectangular prism
V = (1/3)bh
(1-r/1-r)
180°
D = v(l²+w²+h²)

26. 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)]
(y-k)²/a² - (x-h)²/b² = 1
y = a(x-h)² + k - where the vertex is (h -k)
N!

27. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = f(-x)
SA = pr² +prl
Adding or subtracting 180 to ? and reversing the sign of r.

28. 30-60-90 triangle
Between the vertex and the minor axis on the major axis
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NCr = nPr / r! = n! / (n-r)!r!

29. Sum of finite geometric series
(1-r/1-r)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)

30. What is the triangle inequality rule?
y = a(x-h)² + k - where the vertex is (h -k)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
NCr = nPr / r! = n! / (n-r)!r!
A = ((s1 + s2)h) / 2

31. Sum of infinite geometric series
Two sides and two angle are equal
N-1
D = v(l²+w²+h²)
a1 / 1-r

32. Scalene triangle
Between the vertex and the minor axis on the major axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
No equal sides and no equal angles
(x-h)²/a² - (y-k)²/b² = 1

33. Formula for geometric sequence
An = a1rn?¹
(n-2)180
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
V = (1/3)bh

34. Define an odd function.
(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)
No equal sides and no equal angles
x = -b/2a y= c - (b²/4a)

35. How to find the distance between two points in 3d plane?
Final amount = original amount x (1+growth rate)^number of changes
Square the differences between each coordinate - then square root the sum
y-y1 = m(x-x1)
N!

36. 45-45-90 triangle
Hypotenuse is xv2 - and the sides are x.
F(x) = f(-x)
x=rcos?(theta) y=rsin? (theta)
Square the differences between each coordinate - then square root the sum

37. How can multiple polar coordinates be made?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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.
D = v(l²+w²+h²)

38. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
(n-2)180
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
180°

39. Complimentary angles add up to
(1-r/1-r)
(n/2)(a1 + an)
An = a1rn?¹
90°

40. What is the form of a polar coordinate?
x = -b/2a y= c - (b²/4a)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
An = a1 + (n-1)d

41. Volume of a pyramid
V = (1/3)bh
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
F(x) = -f(-x)

42. Surface area of a sphere
SA = 4pr²
(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.
C² = a² + b² - 2abcos(C)
(1-r/1-r)

43. Standard form equation for circle
y = a(x-h)² + k - where the vertex is (h -k)
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)]
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

44. How to determine if a number is prime
180°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
D= sv3

45. What is the sum of the interior angles for a polygon with n sides?
NCr = nPr / r! = n! / (n-r)!r!
V = (1/3)bh
(n-2)180
D= sv3

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

47. Combination formula
(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)
NCr = nPr / r! = n! / (n-r)!r!
An = a1 + (n-1)d

48. Law of Cosines
An = a1 + (n-1)d
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum
C² = a² + b² - 2abcos(C)

49. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
An = a1 + (n-1)d
180°
x = -b/2a y= c - (b²/4a)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

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.
(n/2)(a1 + an)
V = (4/3)pr³
D= sv3