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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. How can multiple polar coordinates be made?
90°
V= (1/3)(pr²h)
Final amount = original amount x (1+growth rate)^number of changes
Adding or subtracting 180 to ? and reversing the sign of r.

2. Supplementary angles add up to
180°
(n-2)180
N-1
F(x) = f(-x)

3. Isosceles Triangles
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Two sides and two angle are equal
(n-2)180
NCr = nPr / r! = n! / (n-r)!r!

4. What is the order of operations?
A = (degree of the arc / 360)(area of a circle)
Parentheses - exponents - multiplication - division - addition - subtraction
Their dot product = 0
An = a1 + (n-1)d

5. How to find the distance between two points in 3d plane?
V= (1/3)(pr²h)
Square the differences between each coordinate - then square root the sum
The greatest common factor is 1 - but the numbers are not necessarily prime.
F(x) = f(-x)

6. How to determine if a number is prime
Arc length equals = (degree of the arc / 360)(circumference)
A = (degree of the arc / 360)(area of a circle)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
D = v(l²+w²+h²)

7. Formula for the volume of a cone
(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)
V= (1/3)(pr²h)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

8. Formula for the diagonal length of a rectangular prism
(x-h)²/a² - (y-k)²/b² = 1
D = v(l²+w²+h²)
A = (degree of the arc / 360)(area of a circle)
An = a1 + (n-1)d

9. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
V = (1/3)bh
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D= sv3

10. Complimentary angles add up to
Hypotenuse is xv2 - and the sides are x.
Multiply the inscribed angle by 2
Their dot product = 0
90°

11. What is the form of a polar coordinate?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
A = ((s1 + s2)h) / 2
Their dot product = 0
V = (4/3)pr³

12. Formula for geometric 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.
Parentheses - exponents - multiplication - division - addition - subtraction
(n/2)(a1 + an)
An = a1rn?¹

13. 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
Hypotenuse is xv2 - and the sides are x.
Arc length equals = (degree of the arc / 360)(circumference)

14. In an ellipse - where are the foci?
Their dot product = 0
Between the vertex and the minor axis on the major axis
N!
a1 / 1-r

15. What are natural numbers?
NPr = n! / (n-r)!
Adding or subtracting 180 to ? and reversing the sign of r.
All whole numbers except for 0
Arc length equals = (degree of the arc / 360)(circumference)

16. How can you determine the arc degree or central angle of an inscribed angle?
NCr = nPr / r! = n! / (n-r)!r!
Multiply the inscribed angle by 2
SA = pr² +prl
(n-2)180

17. What are the conversion equations for polar coordinates to normal coordinates?
(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.
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)]
x=rcos?(theta) y=rsin? (theta)

18. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
y = a(x-h)² + k - where the vertex is (h -k)
D = v(l²+w²+h²)
No equal sides and no equal angles

19. Two vectors are perpendicular if
x=rcos?(theta) y=rsin? (theta)
The greatest common factor is 1 - but the numbers are not necessarily prime.
Their dot product = 0
Multiply the inscribed angle by 2

20. Define an odd function.
Multiply the inscribed angle by 2
(n/2)(a1 + an)
F(x) = -f(-x)
Square the differences between each coordinate - then square root the sum

21. 45-45-90 triangle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
x = -b/2a y= c - (b²/4a)
Hypotenuse is xv2 - and the sides are x.
Hypotenuse is 2x - short side is x - long side is xv3

22. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
A = ((s1 + s2)h) / 2
No equal sides and no equal angles
(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. Define an even function.
F(x) = f(-x)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
x = -b/2a y= c - (b²/4a)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

24. Formula for arithmetic sequence
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)180
x = -b/2a y= c - (b²/4a)
An = a1 + (n-1)d

25. Scalene triangle
N-1
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NPr = n! / (n-r)!
No equal sides and no equal angles

26. Where is tangent positive/negative?
Their dot product = 0
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

27. Standard form for a hyperbola that opens to the sides
D= sv3
a1 / 1-r
(x-h)²/a² - (y-k)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!

28. Standard form of the equation of a parabola.
y = a(x-h)² + 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
Multiply the inscribed angle by 2
Two sides and two angle are equal

29. Formula for the area of a sector
SA = 4pr²
A = (degree of the arc / 360)(area of a circle)
SA = pr² +prl
NCr = nPr / r! = n! / (n-r)!r!

30. Pythagorean Identities
a1 / 1-r
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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)]

31. Standard form for a hyperbola that opens vertically
Hypotenuse is 2x - short side is x - long side is xv3
180°
(y-k)²/a² - (x-h)²/b² = 1
V = (4/3)pr³

32. How many ways can n elements be ordered?
F(x) = f(-x)
(1-r/1-r)
N!
No equal sides and no equal angles

33. Law of Cosines
C² = a² + b² - 2abcos(C)
Hypotenuse is xv2 - and the sides are 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.
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)]

34. Sum of infinite geometric series
a1 / 1-r
(y-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Hypotenuse is 2x - short side is x - long side is xv3

35. What are relatively prime numbers?
Two sides and two angle are equal
An = a1 + (n-1)d
Square the differences between each coordinate - then square root the sum
The greatest common factor is 1 - but the numbers are not necessarily prime.

36. Standard form equation for an ellipse
NCr = nPr / r! = n! / (n-r)!r!
(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)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

37. Volume of a sphere
y-y1 = m(x-x1)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
V = (4/3)pr³
NPr = n! / (n-r)!

38. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(x-h)²/a² - (y-k)²/b² = 1
x = -b/2a y= c - (b²/4a)
(1-r/1-r)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

39. 30-60-90 triangle
Parentheses - exponents - multiplication - division - addition - subtraction
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

40. Sum of finite geometric series
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(1-r/1-r)
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)]

41. Surface area of a sphere
F(x) = -f(-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)]
Their dot product = 0
SA = 4pr²

42. What is the triangle inequality rule?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Two sides and two angle are equal

43. Surface area of a cone
SA = pr² +prl
SA = 4pr²
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-1

44. Volume of a pyramid
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
(1-r/1-r)
A = ((s1 + s2)h) / 2

45. Permutation formula (ordering)
V = (4/3)pr³
NPr = n! / (n-r)!
F(x) = f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

46. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
V = (4/3)pr³
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/a² - (y-k)²/b² = 1

47. What is the sum of the interior angles for a polygon with n sides?
Hypotenuse is 2x - short side is x - long side is xv3
SA = pr² +prl
(n-2)180
The greatest common factor is 1 - but the numbers are not necessarily prime.

48. Formula for arc length
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
N-1
Arc length equals = (degree of the arc / 360)(circumference)

49. Formula for the diagonal length of a cube
D= sv3
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(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)]

50. Difference between 2 Angles formulas
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)]
V = (4/3)pr³
x = -b/2a y= c - (b²/4a)