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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. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Two sides and two angle are equal
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)]
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 - (b²/4a)

2. Formula for the volume of a cone
Arc length equals = (degree of the arc / 360)(circumference)
V= (1/3)(pr²h)
y = a(x-h)² + k - where the vertex is (h -k)
Between the vertex and the minor axis on the major axis

3. Volume of a sphere
(n/2)(a1 + an)
y-y1 = m(x-x1)
V = (4/3)pr³
N!

4. Formula for the diagonal length of a cube
Square the differences between each coordinate - then square root the sum
(1-r/1-r)
D= sv3
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

5. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
Between the vertex and the minor axis on the major axis
Final amount = original amount x (1+growth rate)^number of changes
180°

6. Complimentary angles add up to
(1-r/1-r)
Square the differences between each coordinate - then square root the sum
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)]

7. Formula for the diagonal length of a rectangular prism
All whole numbers except for 0
No equal sides and no equal angles
F(x) = -f(-x)
D = v(l²+w²+h²)

8. Sum of finite geometric series
x=rcos?(theta) y=rsin? (theta)
An = a1rn?¹
Between the vertex and the minor axis on the major axis
(1-r/1-r)

9. Two vectors are perpendicular if
(n-2)180
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)]
SA = pr² +prl

10. 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.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
F(x) = f(-x)
A = ((s1 + s2)h) / 2

11. What are natural numbers?
Their dot product = 0
All whole numbers except for 0
Final amount = original amount x (1+growth rate)^number of changes
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

12. In an ellipse - where are the foci?
SA = 4pr²
(1-r/1-r)
Between the vertex and the minor axis on the major axis
Hypotenuse is xv2 - and the sides are x.

13. Sum of 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)]
A = (degree of the arc / 360)(area of a circle)
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.

14. Permutation formula (ordering)
(x-h)²/a² - (y-k)²/b² = 1
NPr = n! / (n-r)!
Square the differences between each coordinate - then square root the sum
V = (1/3)bh

15. What is the triangle inequality rule?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
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)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

16. Standard form equation for circle
SA = pr² +prl
No equal sides and no equal angles
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Hypotenuse is xv2 - and the sides are x.

17. Standard form for a hyperbola that opens to the sides
Adding or subtracting 180 to ? and reversing the sign of r.
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1
(x-h)²/a² - (y-k)²/b² = 1

18. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
V= (1/3)(pr²h)
Parentheses - exponents - multiplication - division - addition - subtraction
V = (4/3)pr³

19. What are relatively prime numbers?
No equal sides and no equal angles
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = pr² +prl
NPr = n! / (n-r)!

20. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
(x-h)²/a² - (y-k)²/b² = 1

21. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
Square the differences between each coordinate - then square root the sum
C² = a² + b² - 2abcos(C)
y-y1 = m(x-x1)

22. Law of Cosines
C² = a² + b² - 2abcos(C)
A = (degree of the arc / 360)(area of a circle)
An = a1 + (n-1)d
(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.

23. How to find the distance between two points in 3d plane?
NCr = nPr / r! = n! / (n-r)!r!
Between the vertex and the minor axis on the major axis
Square the differences between each coordinate - then square root the sum
A = ((s1 + s2)h) / 2

24. Difference between 2 Angles formulas
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)]
N!
V= (1/3)(pr²h)

25. How many ways can n elements be ordered?
N-1
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
N!
Square the differences between each coordinate - then square root the sum

26. Formula for the area of a sector
Parentheses - exponents - multiplication - division - addition - subtraction
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)
Two sides and two angle are equal

27. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(n-2)180
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Final amount = original amount x (1+growth rate)^number of changes

28. What is the form of a polar coordinate?
90°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
V= (1/3)(pr²h)
N-1

29. Formula for calculation exponential growth
180°
Final amount = original amount x (1+growth rate)^number of changes
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)

30. Double Angle Formulas
(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.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(x-h)²/a² - (y-k)²/b² = 1
Arc length equals = (degree of the arc / 360)(circumference)

31. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
Arc length equals = (degree of the arc / 360)(circumference)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
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)]

32. Surface area of a sphere
D= sv3
No equal sides and no equal angles
Between the vertex and the minor axis on the major axis
SA = 4pr²

33. Volume of a pyramid
V = (1/3)bh
SA = 4pr²
Arc length equals = (degree of the arc / 360)(circumference)
NCr = nPr / r! = n! / (n-r)!r!

34. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
(y-k)²/a² - (x-h)²/b² = 1
N-1
A = (degree of the arc / 360)(area of a circle)
y-y1 = m(x-x1)

35. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is 2x - short side is x - long side is xv3

36. Define an odd function.
Final amount = original amount x (1+growth rate)^number of changes
x = -b/2a y= c - (b²/4a)
F(x) = -f(-x)
(x-h)²/a² - (y-k)²/b² = 1

37. Formula for geometric sequence
An = a1rn?¹
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NPr = n! / (n-r)!
(x-h)²/a² - (y-k)²/b² = 1

38. Where is tangent positive/negative?
x=rcos?(theta) y=rsin? (theta)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = pr² +prl
Square the differences between each coordinate - then square root the sum

39. Formula for arithmetic sequence
An = a1 + (n-1)d
x = -b/2a y= c - (b²/4a)
(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.
a1 / 1-r

40. 45-45-90 triangle
No equal sides and no equal angles
Hypotenuse is xv2 - and the sides are x.
D = v(l²+w²+h²)
Final amount = original amount x (1+growth rate)^number of changes

41. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
90°
y-y1 = m(x-x1)
Hypotenuse is 2x - short side is x - long side is xv3
F(x) = -f(-x)

42. Supplementary angles add up to
Square the differences between each coordinate - then square root the sum
180°
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
A = ((s1 + s2)h) / 2

43. Standard form for a hyperbola that opens vertically
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1
(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.

44. Formula for the area of a trapezoid
F(x) = f(-x)
(n/2)(a1 + an)
a1 / 1-r
A = ((s1 + s2)h) / 2

45. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
Parentheses - exponents - multiplication - division - addition - subtraction
Arc length equals = (degree of the arc / 360)(circumference)
Adding or subtracting 180 to ? and reversing the sign of r.

46. Define an even function.
F(x) = f(-x)
(y-k)²/a² - (x-h)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.
Hypotenuse is 2x - short side is x - long side is xv3

47. Sum of n terms of an arithmetic sequence
180°
An = a1 + (n-1)d
(n/2)(a1 + an)
Their dot product = 0

48. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NCr = nPr / r! = n! / (n-r)!r!
180°

49. 30-60-90 triangle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y-y1 = m(x-x1)
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is 2x - short side is x - long side is xv3

50. Surface area of a cone
F(x) = f(-x)
SA = pr² +prl
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)]
Their dot product = 0