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SAT Math 2

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Double Angle Formulas
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)]
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(y-k)²/a² - (x-h)²/b² = 1

2. Formula for the diagonal length of a rectangular prism
All whole numbers except for 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)]
D = v(l²+w²+h²)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

3. 45-45-90 triangle
N-1
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Hypotenuse is xv2 - and the sides are x.
Two sides and two angle are equal

4. Scalene triangle
NCr = nPr / r! = n! / (n-r)!r!
No equal sides and no equal angles
An = a1rn?¹
V = (4/3)pr³

5. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
(x-h)²/a² - (y-k)²/b² = 1
y-y1 = m(x-x1)
SA = 4pr²

6. Supplementary angles add up to
180°
N-1
The greatest common factor is 1 - but the numbers are not necessarily prime.
An = a1 + (n-1)d

7. How to find the distance between two points in 3d plane?
All whole numbers except for 0
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Square the differences between each coordinate - then square root the sum
No equal sides and no equal angles

8. Surface area of a cone
NCr = nPr / r! = n! / (n-r)!r!
x = -b/2a y= c - (b²/4a)
SA = pr² +prl
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

9. Sum of infinite geometric series
(x-h)²/a² - (y-k)²/b² = 1
All whole numbers except for 0
a1 / 1-r
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

10. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
NCr = nPr / r! = n! / (n-r)!r!
NPr = n! / (n-r)!
180°

11. Sum of finite geometric series
Parentheses - exponents - multiplication - division - addition - subtraction
(1-r/1-r)
NPr = n! / (n-r)!
V= (1/3)(pr²h)

12. Standard form for a hyperbola that opens to the sides
y-y1 = m(x-x1)
(x-h)²/a² - (y-k)²/b² = 1
The greatest common factor is 1 - but the numbers are not necessarily prime.
(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 geometric sequence
D= sv3
An = a1rn?¹
NCr = nPr / r! = n! / (n-r)!r!
No equal sides and no equal angles

14. Two vectors are perpendicular if
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
Their dot product = 0
Hypotenuse is xv2 - and the sides are x.

15. Surface area of a sphere
C² = a² + b² - 2abcos(C)
SA = 4pr²
(x-h)²/a² - (y-k)²/b² = 1
NPr = n! / (n-r)!

16. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
F(x) = -f(-x)
(y-k)²/a² - (x-h)²/b² = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

17. What is the sum of the interior angles for a polygon with n sides?
V= (1/3)(pr²h)
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!
(n-2)180

18. 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.
V = (4/3)pr³
Arc length equals = (degree of the arc / 360)(circumference)
(y-k)²/a² - (x-h)²/b² = 1

19. Formula for arithmetic sequence
An = a1 + (n-1)d
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.
180°

20. Isosceles Triangles
Two sides and two angle are equal
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)]
NPr = n! / (n-r)!

21. Sum of n terms of an arithmetic 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.
Hypotenuse is 2x - short side is x - long side is xv3
x = -b/2a y= c - (b²/4a)
(n/2)(a1 + an)

22. What is the order of operations?
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)]
Parentheses - exponents - multiplication - division - addition - subtraction
Multiply the inscribed angle by 2

23. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
F(x) = -f(-x)
x = -b/2a y= c - (b²/4a)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
y-y1 = m(x-x1)

24. Permutation formula (ordering)
An = a1rn?¹
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
NPr = n! / (n-r)!
No equal sides and no equal angles

25. Standard form equation for circle
Between the vertex and the minor axis on 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)]
(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

26. Standard form for a hyperbola that opens vertically
(y-k)²/a² - (x-h)²/b² = 1
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.
a1 / 1-r

27. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
An = a1 + (n-1)d
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)]

28. Where is tangent positive/negative?
A = ((s1 + s2)h) / 2
y-y1 = m(x-x1)
Multiply the inscribed angle by 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

29. Pythagorean Identities
Hypotenuse is xv2 - and the sides are x.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)²/a² - (y-k)²/b² = 1

30. Combination formula
The greatest common factor is 1 - but the numbers are not necessarily prime.
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.
NCr = nPr / r! = n! / (n-r)!r!

31. Formula for the area of a sector
A = (degree of the arc / 360)(area of a circle)
NCr = nPr / r! = n! / (n-r)!r!
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

32. Complimentary angles add up to
Parentheses - exponents - multiplication - division - addition - subtraction
90°
y-y1 = m(x-x1)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

33. Sum of 2 Angles Formulas
(y-k)²/a² - (x-h)²/b² = 1
D= sv3
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)]

34. Define an even function.
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.
180°
F(x) = f(-x)

35. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
D = v(l²+w²+h²)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

36. Formula for the diagonal length of a cube
90°
(n/2)(a1 + an)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
D= sv3

37. 30-60-90 triangle
180°
Their dot product = 0
Hypotenuse is 2x - short side is x - long side is xv3
NPr = n! / (n-r)!

38. Volume of a pyramid
V = (1/3)bh
Square the differences between each coordinate - then square root the sum
(n/2)(a1 + an)
Two sides and two angle are equal

39. 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)]
x=rcos?(theta) y=rsin? (theta)
(1-r/1-r)
V= (1/3)(pr²h)

40. Law of Cosines
All whole numbers except for 0
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D = v(l²+w²+h²)
C² = a² + b² - 2abcos(C)

41. What are the conversion equations for polar coordinates to normal coordinates?
Square the differences between each coordinate - then square root the sum
180°
x=rcos?(theta) y=rsin? (theta)
V = (4/3)pr³

42. Formula for calculation exponential growth
All whole numbers except for 0
(1-r/1-r)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Final amount = original amount x (1+growth rate)^number of changes

43. What is the form of a polar coordinate?
V= (1/3)(pr²h)
Their dot product = 0
Adding or subtracting 180 to ? and reversing the sign of r.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

44. What are natural numbers?
(n-2)180
(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-y1 = m(x-x1)
All whole numbers except for 0

45. How many ways can n elements be ordered?
N-1
Two sides and two angle are equal
N!
Adding or subtracting 180 to ? and reversing the sign of r.

46. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1 + (n-1)d

47. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
A = (degree of the arc / 360)(area of a circle)
N-1
(x-h)²/a² - (y-k)²/b² = 1

48. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
V = (1/3)bh
(n-2)180
All whole numbers except for 0

49. Volume of a sphere
Parentheses - exponents - multiplication - division - addition - subtraction
V = (4/3)pr³
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(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. Define an odd function.
Multiply the inscribed angle by 2
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)]
An = a1rn?¹