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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. What are the conversion equations for polar coordinates to normal coordinates?
V = (4/3)pr³
Parentheses - exponents - multiplication - division - addition - subtraction
x=rcos?(theta) y=rsin? (theta)
SA = pr² +prl

2. Formula for the diagonal length of a cube
Adding or subtracting 180 to ? and reversing the sign of r.
D = v(l²+w²+h²)
D= sv3
Between the vertex and the minor axis on the major axis

3. Scalene triangle
D = v(l²+w²+h²)
No equal sides and no equal angles
An = a1rn?¹
x = -b/2a y= c - (b²/4a)

4. Isosceles Triangles
SA = pr² +prl
Multiply the inscribed angle by 2
(n/2)(a1 + an)
Two sides and two angle are equal

5. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
D= sv3
The greatest common factor is 1 - but the numbers are not necessarily prime.
a1 / 1-r

6. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
Two sides and two angle are equal
Their dot product = 0
y = a(x-h)² + k - where the vertex is (h -k)

7. Difference between 2 Angles formulas
V= (1/3)(pr²h)
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)]
a1 / 1-r
x=rcos?(theta) y=rsin? (theta)

8. Standard form equation for circle
x=rcos?(theta) y=rsin? (theta)
Square the differences between each coordinate - then square root the sum
No equal sides and no equal angles
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

9. What is the order of operations?
Square the differences between each coordinate - then square root the sum
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
A = ((s1 + s2)h) / 2
Parentheses - exponents - multiplication - division - addition - subtraction

10. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
Adding or subtracting 180 to ? and reversing the sign of r.
Between the vertex and the minor axis on the major axis
Their dot product = 0

11. Define an even function.
F(x) = -f(-x)
Multiply the inscribed angle by 2
F(x) = f(-x)
y = a(x-h)² + k - where the vertex is (h -k)

12. Double Angle 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)]
All whole numbers except for 0
V = (1/3)bh
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

13. Pythagorean Identities
a1 / 1-r
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
N!

14. Formula for geometric sequence
Hypotenuse is xv2 - and the sides are x.
180°
Final amount = original amount x (1+growth rate)^number of changes
An = a1rn?¹

15. Two vectors are perpendicular if
Between the vertex and the minor axis on the major axis
Their dot product = 0
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.

16. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y-y1 = m(x-x1)
V= (1/3)(pr²h)

17. 30-60-90 triangle
Final amount = original amount x (1+growth rate)^number of changes
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
SA = pr² +prl

18. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
a1 / 1-r
Hypotenuse is 2x - short side is x - long side is xv3
Adding or subtracting 180 to ? and reversing the sign of r.

19. Standard form for a hyperbola that opens vertically
Arc length equals = (degree of the arc / 360)(circumference)
All whole numbers except for 0
(y-k)²/a² - (x-h)²/b² = 1
Their dot product = 0

20. Law of Cosines
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Multiply the inscribed angle by 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
C² = a² + b² - 2abcos(C)

21. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
V= (1/3)(pr²h)
N!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

22. Surface area of a sphere
(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.
SA = 4pr²
N-1
F(x) = -f(-x)

23. Where is tangent positive/negative?
(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
SA = 4pr²
y = a(x-h)² + k - where the vertex is (h -k)

24. Complimentary angles add up to
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
An = a1rn?¹
90°

25. What is the triangle inequality rule?
Hypotenuse is xv2 - and the sides are x.
Their dot product = 0
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
y = a(x-h)² + k - where the vertex is (h -k)

26. Surface area of a cone
C² = a² + b² - 2abcos(C)
An = a1rn?¹
SA = pr² +prl
An = a1 + (n-1)d

27. How can multiple polar coordinates be made?
D= sv3
Adding or subtracting 180 to ? and reversing the sign of r.
C² = a² + b² - 2abcos(C)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

28. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
N!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
D= sv3

29. Sum of n terms of an arithmetic sequence
(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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
N!

30. 45-45-90 triangle
A = ((s1 + s2)h) / 2
Hypotenuse is xv2 - and the sides are x.
D = v(l²+w²+h²)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

31. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
y-y1 = m(x-x1)
The greatest common factor is 1 - but the numbers are not necessarily prime.
No equal sides and no equal angles
180°

32. How many ways can n elements be ordered?
Adding or subtracting 180 to ? and reversing the sign of r.
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)]
N!

33. Formula for the volume of a cone
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is 2x - short side is x - long side is xv3
90°
V= (1/3)(pr²h)

34. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Adding or subtracting 180 to ? and reversing the sign of r.
Between the vertex and the minor axis on the major axis

35. Volume of a sphere
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)]
V = (1/3)bh
V = (4/3)pr³

36. How to find the distance between two points in 3d plane?
An = a1rn?¹
Square the differences between each coordinate - then square root the sum
Between the vertex and the minor axis on the major axis
F(x) = -f(-x)

37. Supplementary angles add up to
180°
A = (degree of the arc / 360)(area of a circle)
(n-2)180
V= (1/3)(pr²h)

38. Sum of 2 Angles Formulas
An = a1 + (n-1)d
180°
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 = a(x-h)² + k - where the vertex is (h -k)

39. Formula for the diagonal length of a rectangular prism
Between the vertex and the minor axis on the major axis
D = v(l²+w²+h²)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

40. Permutation formula (ordering)
(n/2)(a1 + an)
V = (4/3)pr³
NPr = n! / (n-r)!
(y-k)²/a² - (x-h)²/b² = 1

41. Define an odd function.
F(x) = f(-x)
x=rcos?(theta) y=rsin? (theta)
All whole numbers except for 0
F(x) = -f(-x)

42. Standard form equation for an ellipse
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.
a1 / 1-r
NCr = nPr / r! = n! / (n-r)!r!

43. Formula for the area of a sector
F(x) = -f(-x)
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)
N-1

44. What are relatively prime numbers?
SA = 4pr²
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)]
The greatest common factor is 1 - but the numbers are not necessarily prime.
a1 / 1-r

45. Combination formula
Hypotenuse is xv2 - and the sides are x.
NCr = nPr / r! = n! / (n-r)!r!
(y-k)²/a² - (x-h)²/b² = 1
Final amount = original amount x (1+growth rate)^number of changes

46. Volume of a pyramid
N-1
NPr = n! / (n-r)!
V = (1/3)bh
Between the vertex and the minor axis on the major axis

47. What is the form of a polar coordinate?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Two sides and two angle are equal
180°

48. Sum of finite geometric series
y-y1 = m(x-x1)
SA = 4pr²
Square the differences between each coordinate - then square root the sum
(1-r/1-r)

49. Sum of infinite geometric series
180°
Arc length equals = (degree of the arc / 360)(circumference)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
a1 / 1-r

50. In an ellipse - where are the foci?
y = a(x-h)² + k - where the vertex is (h -k)
SA = 4pr²
Between the vertex and the minor axis on the major axis
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.