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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. Standard form equation for an ellipse
V= (1/3)(pr²h)
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.
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)]

2. Formula for the area of a sector
V = (1/3)bh
Arc length equals = (degree of the arc / 360)(circumference)
A = (degree of the arc / 360)(area of a circle)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

3. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
F(x) = f(-x)
NPr = n! / (n-r)!

4. Standard form for a hyperbola that opens to the sides
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
SA = pr² +prl
(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-h)²/a² - (y-k)²/b² = 1

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

6. Sum of infinite geometric series
V = (1/3)bh
F(x) = f(-x)
a1 / 1-r
Parentheses - exponents - multiplication - division - addition - subtraction

7. What is the sum of the interior angles for a polygon with n sides?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
x=rcos?(theta) y=rsin? (theta)
(n-2)180
(x-h)²/a² - (y-k)²/b² = 1

8. Two vectors are perpendicular if
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(1-r/1-r)
Their dot product = 0
(x-h)²/a² - (y-k)²/b² = 1

9. How can multiple polar coordinates be made?
Adding or subtracting 180 to ? and reversing the sign of r.
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.
Two sides and two angle are equal

10. Standard form equation for circle
F(x) = -f(-x)
All whole numbers except for 0
V = (1/3)bh
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

11. Permutation formula (ordering)
a1 / 1-r
A = ((s1 + s2)h) / 2
NPr = n! / (n-r)!
V = (4/3)pr³

12. How can you determine the arc degree or central angle of an inscribed angle?
V = (4/3)pr³
y = a(x-h)² + k - where the vertex is (h -k)
90°
Multiply the inscribed angle by 2

13. Formula for the diagonal length of a cube
D= sv3
F(x) = -f(-x)
All whole numbers except for 0
y = a(x-h)² + k - where the vertex is (h -k)

14. Formula for the area of a trapezoid
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)]
Arc length equals = (degree of the arc / 360)(circumference)
A = ((s1 + s2)h) / 2

15. Surface area of a cone
SA = pr² +prl
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
x = -b/2a y= c - (b²/4a)
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)]

16. Supplementary angles add up to
All whole numbers except for 0
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
180°
Hypotenuse is xv2 - and the sides are x.

17. Formula for arc length
Final amount = original amount x (1+growth rate)^number of changes
D= sv3
(n/2)(a1 + an)
Arc length equals = (degree of the arc / 360)(circumference)

18. Volume of a pyramid
V = (1/3)bh
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
N!
A = ((s1 + s2)h) / 2

19. Formula for calculation exponential growth
Multiply the inscribed angle by 2
N-1
All whole numbers except for 0
Final amount = original amount x (1+growth rate)^number of changes

20. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
SA = pr² +prl
A = (degree of the arc / 360)(area of a circle)
x = -b/2a y= c - (b²/4a)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

21. Scalene triangle
A = ((s1 + s2)h) / 2
An = a1 + (n-1)d
No equal sides and no equal angles
SA = 4pr²

22. Formula for the volume of a cone
Final amount = original amount x (1+growth rate)^number of changes
90°
V= (1/3)(pr²h)
Two sides and two angle are equal

23. What are the conversion equations for polar coordinates to normal coordinates?
(1-r/1-r)
NCr = nPr / r! = n! / (n-r)!r!
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is xv2 - and the sides are x.

24. Combination formula
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
x = -b/2a y= c - (b²/4a)
A = (degree of the arc / 360)(area of a circle)
NCr = nPr / r! = n! / (n-r)!r!

25. 45-45-90 triangle
SA = 4pr²
No equal sides and no equal angles
Hypotenuse is xv2 - and the sides are x.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

26. Difference between 2 Angles formulas
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)
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)!

27. What is the form of a polar coordinate?
D= sv3
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 = a1 + (n-1)d
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

28. Define an odd function.
N-1
F(x) = -f(-x)
V= (1/3)(pr²h)
No equal sides and no equal angles

29. What are relatively prime numbers?
Parentheses - exponents - multiplication - division - addition - subtraction
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(n/2)(a1 + an)
The greatest common factor is 1 - but the numbers are not necessarily prime.

30. Complimentary angles add up to
D= sv3
90°
x = -b/2a y= c - (b²/4a)
V = (4/3)pr³

31. Surface area of a sphere
D = v(l²+w²+h²)
D= sv3
N-1
SA = 4pr²

32. Sum of n terms of an arithmetic sequence
SA = 4pr²
(n/2)(a1 + an)
x = -b/2a y= c - (b²/4a)
a1 / 1-r

33. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
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)]
Parentheses - exponents - multiplication - division - addition - subtraction
N-1

34. Formula for arithmetic sequence
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
An = a1 + (n-1)d
Multiply the inscribed angle by 2
N!

35. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D= sv3
y-y1 = m(x-x1)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

36. Sum of finite geometric series
D= sv3
(n-2)180
(1-r/1-r)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

37. Standard form for a hyperbola that opens vertically
C² = a² + b² - 2abcos(C)
V = (4/3)pr³
(y-k)²/a² - (x-h)²/b² = 1
The greatest common factor is 1 - but the numbers are not necessarily prime.

38. 30-60-90 triangle
(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
Multiply the inscribed angle by 2
D= sv3

39. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

40. How to determine if a number is prime
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Parentheses - exponents - multiplication - division - addition - subtraction
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.

41. Isosceles Triangles
F(x) = f(-x)
NPr = n! / (n-r)!
Adding or subtracting 180 to ? and reversing the sign of r.
Two sides and two angle are equal

42. What is the triangle inequality rule?
Between the vertex and the minor axis on the major axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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 = a1 + (n-1)d

43. Law of Cosines
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NCr = nPr / r! = n! / (n-r)!r!
x=rcos?(theta) y=rsin? (theta)
C² = a² + b² - 2abcos(C)

44. What is the order of operations?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Their dot product = 0
N!
Parentheses - exponents - multiplication - division - addition - subtraction

45. Pythagorean Identities
(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.
C² = a² + b² - 2abcos(C)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

46. Where is tangent positive/negative?
F(x) = f(-x)
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
N!

47. What are natural numbers?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
An = a1rn?¹
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
All whole numbers except for 0

48. Sum of 2 Angles Formulas
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)]
a1 / 1-r
Between the vertex and the minor axis on the major axis

49. Define an even function.
(x-h)²/a² - (y-k)²/b² = 1
F(x) = f(-x)
D= sv3
An = a1 + (n-1)d

50. In an ellipse - where are the foci?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is 2x - short side is x - long side is xv3
Between the vertex and the minor axis on the major axis