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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. Surface area of a sphere
180°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Square the differences between each coordinate - then square root the sum
SA = 4pr²

2. Standard form equation for an ellipse
N-1
No equal sides and no equal angles
Multiply the inscribed angle by 2
(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.

3. Define an even function.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
x=rcos?(theta) y=rsin? (theta)
F(x) = f(-x)
(x-h)²/a² - (y-k)²/b² = 1

4. Formula for the diagonal length of a rectangular prism
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)]
D = v(l²+w²+h²)
D= sv3
y-y1 = m(x-x1)

5. What is the order of operations?
x = -b/2a y= c - (b²/4a)
SA = pr² +prl
Parentheses - exponents - multiplication - division - addition - subtraction
N!

6. Formula for geometric sequence
N-1
An = a1rn?¹
Their dot product = 0
F(x) = -f(-x)

7. Permutation formula (ordering)
NPr = n! / (n-r)!
Parentheses - exponents - multiplication - division - addition - subtraction
V= (1/3)(pr²h)
SA = 4pr²

8. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
(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 = (4/3)pr³
NPr = n! / (n-r)!

9. Sum of finite geometric series
Square the differences between each coordinate - then square root the sum
(1-r/1-r)
Arc length equals = (degree of the arc / 360)(circumference)
x=rcos?(theta) y=rsin? (theta)

10. What is the form of a polar coordinate?
(n-2)180
NCr = nPr / r! = n! / (n-r)!r!
N-1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

11. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
Hypotenuse is xv2 - and the sides are x.
An = a1rn?¹
F(x) = -f(-x)

12. What is the sum of the interior angles for a polygon with n sides?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Between the vertex and the minor axis on the major axis
(n-2)180
C² = a² + b² - 2abcos(C)

13. Scalene triangle
No equal sides and no equal angles
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)]
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = -f(-x)

14. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
x = -b/2a y= c - (b²/4a)
NCr = nPr / r! = n! / (n-r)!r!

15. 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.
C² = a² + b² - 2abcos(C)
D= sv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

16. Where is tangent positive/negative?
Hypotenuse is 2x - short side is x - long side is xv3
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
V= (1/3)(pr²h)

17. Volume of a pyramid
Between the vertex and the minor axis on the major axis
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
V = (1/3)bh

18. What are natural numbers?
D= sv3
SA = pr² +prl
All whole numbers except for 0
An = a1rn?¹

19. How to determine if a number is prime
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is xv2 - and the sides are x.
Arc length equals = (degree of the arc / 360)(circumference)

20. How can you determine the arc degree or central angle of an inscribed angle?
y-y1 = m(x-x1)
Multiply the inscribed angle by 2
V = (4/3)pr³
SA = 4pr²

21. Formula for the diagonal length of a cube
(y-k)²/a² - (x-h)²/b² = 1
D= sv3
All whole numbers except for 0
y = a(x-h)² + k - where the vertex is (h -k)

22. Formula for the area of a trapezoid
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Final amount = original amount x (1+growth rate)^number of changes
A = ((s1 + s2)h) / 2
F(x) = -f(-x)

23. Isosceles Triangles
NCr = nPr / r! = n! / (n-r)!r!
F(x) = -f(-x)
Two sides and two angle are equal
All whole numbers except for 0

24. 30-60-90 triangle
y = a(x-h)² + k - where the vertex is (h -k)
(n/2)(a1 + an)
All whole numbers except for 0
Hypotenuse is 2x - short side is x - long side is xv3

25. Supplementary angles add up to
Hypotenuse is 2x - short side is x - long side is xv3
180°
SA = pr² +prl
An = a1 + (n-1)d

26. Standard form of the equation of a parabola.
Adding or subtracting 180 to ? and reversing the sign of r.
C² = a² + b² - 2abcos(C)
D= sv3
y = a(x-h)² + k - where the vertex is (h -k)

27. How can multiple polar coordinates be made?
Square the differences between each coordinate - then square root the sum
Adding or subtracting 180 to ? and reversing the sign of r.
The greatest common factor is 1 - but the numbers are not necessarily prime.
Their dot product = 0

28. Sum of n terms of an arithmetic sequence
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(n/2)(a1 + an)
F(x) = -f(-x)
Arc length equals = (degree of the arc / 360)(circumference)

29. Formula for arithmetic sequence
C² = a² + b² - 2abcos(C)
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)]
N-1

30. Formula for calculation exponential growth
D = v(l²+w²+h²)
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)]
Final amount = original amount x (1+growth rate)^number of changes
Arc length equals = (degree of the arc / 360)(circumference)

31. Standard form for a hyperbola that opens vertically
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
a1 / 1-r
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is xv2 - and the sides are x.

32. Formula for the volume of a cone
F(x) = f(-x)
Their dot product = 0
D= sv3
V= (1/3)(pr²h)

33. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is xv2 - and the sides are 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.
An = a1rn?¹

34. Two vectors are perpendicular if
NPr = n! / (n-r)!
Their dot product = 0
(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.
No equal sides and no equal angles

35. Formula for arc length
An = a1rn?¹
Arc length equals = (degree of the arc / 360)(circumference)
N-1
Two sides and two angle are equal

36. Surface area of a cone
SA = pr² +prl
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)
An = a1 + (n-1)d

37. Standard form equation for circle
V= (1/3)(pr²h)
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = (degree of the arc / 360)(area of a circle)

38. Law of Cosines
N-1
C² = a² + b² - 2abcos(C)
y = a(x-h)² + k - where the vertex is (h -k)
Multiply the inscribed angle by 2

39. How many ways can n elements be ordered?
NPr = n! / (n-r)!
N!
180°
D = v(l²+w²+h²)

40. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
D = v(l²+w²+h²)
Multiply the inscribed angle by 2
N!
y-y1 = m(x-x1)

41. What are relatively prime numbers?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
D = v(l²+w²+h²)
A = ((s1 + s2)h) / 2

42. Complimentary angles add up to
A = ((s1 + s2)h) / 2
90°
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.

43. Standard form for a hyperbola that opens to the sides
Two sides and two angle are equal
(x-h)²/a² - (y-k)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!
An = a1rn?¹

44. What are the conversion equations for polar coordinates to normal coordinates?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(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=rcos?(theta) y=rsin? (theta)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

45. Define an odd function.
N!
Square the differences between each coordinate - then square root the sum
An = a1 + (n-1)d
F(x) = -f(-x)

46. Formula for the area of a sector
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
A = (degree of the arc / 360)(area of a circle)
Arc length equals = (degree of the arc / 360)(circumference)

47. Volume of a sphere
SA = 4pr²
C² = a² + b² - 2abcos(C)
Square the differences between each coordinate - then square root the sum
V = (4/3)pr³

48. Combination formula
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
An = a1rn?¹

49. In an ellipse - where are the foci?
Final amount = original amount x (1+growth rate)^number of changes
Their dot product = 0
Between the vertex and the minor axis on the major axis
SA = pr² +prl

50. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
y = a(x-h)² + k - where the vertex is (h -k)
(y-k)²/a² - (x-h)²/b² = 1
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)]