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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. Formula for the area of a trapezoid
Their dot product = 0
D= sv3
(1-r/1-r)
A = ((s1 + s2)h) / 2

2. Formula for the volume of a cone
90°
V= (1/3)(pr²h)
C² = a² + b² - 2abcos(C)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

3. Difference between 2 Angles formulas
(x-h)² + (y-k)² = r² - where (h -k) is the center of the 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)]
V= (1/3)(pr²h)
(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.

4. What are the conversion equations for polar coordinates to normal coordinates?
F(x) = -f(-x)
F(x) = f(-x)
x=rcos?(theta) y=rsin? (theta)
NCr = nPr / r! = n! / (n-r)!r!

5. Formula for geometric sequence
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
No equal sides and no equal angles
An = a1rn?¹
y = a(x-h)² + k - where the vertex is (h -k)

6. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(n-2)180
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
NPr = n! / (n-r)!

7. Formula for the area of a sector
An = a1 + (n-1)d
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)

8. Formula for the diagonal length of a rectangular prism
D = v(l²+w²+h²)
V = (1/3)bh
D= sv3
y-y1 = m(x-x1)

9. Complimentary angles add up to
V = (1/3)bh
90°
Square the differences between each coordinate - then square root the sum
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

10. Law of Cosines
A = (degree of the arc / 360)(area of a circle)
No equal sides and no equal angles
C² = a² + b² - 2abcos(C)
SA = pr² +prl

11. Scalene triangle
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
x = -b/2a y= c - (b²/4a)
SA = 4pr²
No equal sides and no equal angles

12. What are relatively prime numbers?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
NCr = nPr / r! = n! / (n-r)!r!
N-1
The greatest common factor is 1 - but the numbers are not necessarily prime.

13. Double Angle Formulas
D = v(l²+w²+h²)
Adding or subtracting 180 to ? and reversing the sign of r.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(n/2)(a1 + an)

14. Define an odd function.
Adding or subtracting 180 to ? and reversing the sign of r.
N!
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = -f(-x)

15. Sum of infinite geometric series
Parentheses - exponents - multiplication - division - addition - subtraction
(1-r/1-r)
a1 / 1-r
(x-h)²/a² - (y-k)²/b² = 1

16. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Their dot product = 0
A = (degree of the arc / 360)(area of a circle)
y-y1 = m(x-x1)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

17. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
a1 / 1-r
F(x) = -f(-x)
V = (1/3)bh

18. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
Multiply the inscribed angle by 2
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x = -b/2a y= c - (b²/4a)

19. Define an even function.
x = -b/2a y= c - (b²/4a)
V = (1/3)bh
F(x) = f(-x)
An = a1 + (n-1)d

20. How many ways can n elements be ordered?
N!
Final amount = original amount x (1+growth rate)^number of changes
(x-h)²/a² - (y-k)²/b² = 1
(y-k)²/a² - (x-h)²/b² = 1

21. 30-60-90 triangle
(n/2)(a1 + an)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

22. Standard form for a hyperbola that opens vertically
(y-k)²/a² - (x-h)²/b² = 1
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes
Hypotenuse is 2x - short side is x - long side is xv3

23. Isosceles Triangles
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
Two sides and two angle are equal
V = (1/3)bh

24. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
180°
x = -b/2a y= c - (b²/4a)
An = a1rn?¹
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

25. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
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.

26. Formula for calculation exponential growth
D= sv3
Final amount = original amount x (1+growth rate)^number of changes
Parentheses - exponents - multiplication - division - addition - subtraction
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

27. In an ellipse - where are the foci?
Between the vertex and the minor axis on 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-h)² + (y-k)² = r² - where (h -k) is the center of the circle

28. Where is tangent positive/negative?
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.
D = v(l²+w²+h²)
Their dot product = 0

29. Supplementary angles add up to
V= (1/3)(pr²h)
Arc length equals = (degree of the arc / 360)(circumference)
C² = a² + b² - 2abcos(C)
180°

30. Sum of n terms of an arithmetic sequence
(n/2)(a1 + an)
Final amount = original amount x (1+growth rate)^number of changes
V = (4/3)pr³
(1-r/1-r)

31. Combination formula
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!
a1 / 1-r

32. Formula for the diagonal length of a cube
D= sv3
(1-r/1-r)
F(x) = -f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

33. Standard form equation for circle
Arc length equals = (degree of the arc / 360)(circumference)
x = -b/2a y= c - (b²/4a)
(n/2)(a1 + an)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

34. 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.
(n-2)180
All whole numbers except for 0
90°

35. 45-45-90 triangle
The greatest common factor is 1 - but the numbers are not necessarily prime.
Two sides and two angle are equal
All whole numbers except for 0
Hypotenuse is xv2 - and the sides are x.

36. Volume of a sphere
All whole numbers except for 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.
V = (4/3)pr³
The greatest common factor is 1 - but the numbers are not necessarily prime.

37. How can multiple polar coordinates be made?
y = a(x-h)² + k - where the vertex is (h -k)
(n-2)180
90°
Adding or subtracting 180 to ? and reversing the sign of r.

38. How to find the distance between two points in 3d plane?
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)]
C² = a² + b² - 2abcos(C)
(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.
Square the differences between each coordinate - then square root the sum

39. Standard form equation for an ellipse
SA = 4pr²
NPr = n! / (n-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.
x = -b/2a y= c - (b²/4a)

40. Sum of 2 Angles Formulas
Arc length equals = (degree of the arc / 360)(circumference)
N-1
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)]

41. What are natural numbers?
All whole numbers except for 0
N-1
SA = pr² +prl
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

42. Sum of finite geometric series
Adding or subtracting 180 to ? and reversing the sign of r.
(1-r/1-r)
x = -b/2a y= c - (b²/4a)
Parentheses - exponents - multiplication - division - addition - subtraction

43. 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
An = a1rn?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)]
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

44. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
The greatest common factor is 1 - but the numbers are not necessarily prime.
N-1
(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.
(n-2)180

45. Surface area of a cone
SA = pr² +prl
(y-k)²/a² - (x-h)²/b² = 1
N-1
(n-2)180

46. Volume of a pyramid
NPr = n! / (n-r)!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
F(x) = f(-x)
V = (1/3)bh

47. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
Multiply the inscribed angle by 2
V = (4/3)pr³
F(x) = -f(-x)

48. Surface area of a sphere
Multiply the inscribed angle by 2
90°
C² = a² + b² - 2abcos(C)
SA = 4pr²

49. Formula for arc length
Adding or subtracting 180 to ? and reversing the sign of r.
x=rcos?(theta) y=rsin? (theta)
C² = a² + b² - 2abcos(C)
Arc length equals = (degree of the arc / 360)(circumference)

50. How to determine if a number is prime
Between the vertex and the minor axis on the major axis
(x-h)²/a² - (y-k)²/b² = 1
Hypotenuse is 2x - short side is x - long side is xv3
Approximate a square root - then try to divide the number by all prime numbers below the approximated root