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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. Volume of a sphere
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Hypotenuse is xv2 - and the sides are x.
N-1
V = (4/3)pr³

2. 30-60-90 triangle
NCr = nPr / r! = n! / (n-r)!r!
x=rcos?(theta) y=rsin? (theta)
C² = a² + b² - 2abcos(C)
Hypotenuse is 2x - short side is x - long side is xv3

3. Combination formula
(x-h)²/a² - (y-k)²/b² = 1
N!
NCr = nPr / r! = n! / (n-r)!r!
All whole numbers except for 0

4. 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
D = v(l²+w²+h²)
a1 / 1-r
D= sv3

5. Supplementary angles add up to
N-1
No equal sides and no equal angles
D= sv3
180°

6. Standard form of the equation of a parabola.
Parentheses - exponents - multiplication - division - addition - subtraction
y = a(x-h)² + k - where the vertex is (h -k)
SA = pr² +prl
Hypotenuse is xv2 - and the sides are x.

7. Surface area of a sphere
y-y1 = m(x-x1)
SA = 4pr²
(n/2)(a1 + an)
A = (degree of the arc / 360)(area of a circle)

8. Permutation formula (ordering)
SA = pr² +prl
NPr = n! / (n-r)!
x = -b/2a y= c - (b²/4a)
x=rcos?(theta) y=rsin? (theta)

9. In an ellipse - where are the foci?
C² = a² + b² - 2abcos(C)
Hypotenuse is xv2 - and the sides are x.
Between the vertex and the minor axis on the major axis
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

10. Formula for the diagonal length of a rectangular prism
Parentheses - exponents - multiplication - division - addition - subtraction
D = v(l²+w²+h²)
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.

11. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = 4pr²
No equal sides and no equal angles
The greatest common factor is 1 - but the numbers are not necessarily prime.

12. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
NCr = nPr / r! = n! / (n-r)!r!
a1 / 1-r
90°
N-1

13. Isosceles Triangles
Hypotenuse is xv2 - and the sides are x.
Two sides and two angle are equal
(1-r/1-r)
NPr = n! / (n-r)!

14. What is the order of operations?
C² = a² + b² - 2abcos(C)
Multiply the inscribed angle by 2
Parentheses - exponents - multiplication - division - addition - subtraction
F(x) = -f(-x)

15. Standard form equation for an ellipse
NPr = n! / (n-r)!
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.
(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. Pythagorean Identities
Arc length equals = (degree of the arc / 360)(circumference)
F(x) = -f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

17. Surface area of a cone
SA = pr² +prl
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(n/2)(a1 + an)
Hypotenuse is 2x - short side is x - long side is xv3

18. Sum of finite geometric series
(1-r/1-r)
SA = pr² +prl
N-1
N!

19. Sum of n terms of an arithmetic sequence
C² = a² + b² - 2abcos(C)
(n/2)(a1 + an)
D = v(l²+w²+h²)
(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.

20. Define an even function.
SA = pr² +prl
F(x) = f(-x)
An = a1 + (n-1)d
V = (4/3)pr³

21. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
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
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

22. Formula for the diagonal length of a cube
D = v(l²+w²+h²)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
D= sv3
V = (1/3)bh

23. Define an odd function.
(x-h)²/a² - (y-k)²/b² = 1
F(x) = -f(-x)
Parentheses - exponents - multiplication - division - addition - subtraction
x = -b/2a y= c - (b²/4a)

24. 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)]
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Between the vertex and the minor axis on the major axis

25. How can multiple polar coordinates be made?
SA = pr² +prl
A = (degree of the arc / 360)(area of a circle)
Adding or subtracting 180 to ? and reversing the sign of r.
A = ((s1 + s2)h) / 2

26. Formula for the area of a trapezoid
Square the differences between each coordinate - then square root the sum
a1 / 1-r
A = ((s1 + s2)h) / 2
N-1

27. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
SA = 4pr²
Their dot product = 0
y-y1 = m(x-x1)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

28. Law of Cosines
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
SA = pr² +prl
NPr = n! / (n-r)!
C² = a² + b² - 2abcos(C)

29. Formula for the volume of a cone
V= (1/3)(pr²h)
F(x) = f(-x)
D = v(l²+w²+h²)
Multiply the inscribed angle by 2

30. 45-45-90 triangle
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
All whole numbers except for 0
Hypotenuse is xv2 - and the sides are x.
y = a(x-h)² + k - where the vertex is (h -k)

31. How to find the distance between two points in 3d plane?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
D= sv3
Square the differences between each coordinate - then square root the sum
An = a1rn?¹

32. Formula for arc length
Parentheses - exponents - multiplication - division - addition - subtraction
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
A = (degree of the arc / 360)(area of a circle)
Arc length equals = (degree of the arc / 360)(circumference)

33. What is the sum of the interior angles for a polygon with n sides?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
V = (1/3)bh
(n-2)180
An = a1rn?¹

34. What are the conversion equations for polar coordinates to normal coordinates?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
x=rcos?(theta) y=rsin? (theta)
All whole numbers except for 0
An = a1rn?¹

35. Two vectors are perpendicular if
D = v(l²+w²+h²)
Their dot product = 0
N-1
Multiply the inscribed angle by 2

36. Formula for geometric sequence
F(x) = -f(-x)
An = a1rn?¹
Hypotenuse is xv2 - and the sides are x.
Hypotenuse is 2x - short side is x - long side is xv3

37. What are natural numbers?
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum
F(x) = f(-x)
SA = 4pr²

38. Formula for arithmetic sequence
A = ((s1 + s2)h) / 2
V= (1/3)(pr²h)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
An = a1 + (n-1)d

39. Formula for the area of a sector
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
SA = 4pr²
N!

40. Sum of infinite geometric series
x=rcos?(theta) y=rsin? (theta)
a1 / 1-r
V = (4/3)pr³
F(x) = f(-x)

41. Formula for calculation exponential growth
(x-h)²/a² - (y-k)²/b² = 1
Two sides and two angle are equal
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes

42. Complimentary angles add up to
NCr = nPr / r! = n! / (n-r)!r!
90°
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)]
A = (degree of the arc / 360)(area of a circle)

43. What is the form of a polar coordinate?
SA = pr² +prl
(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!
The greatest common factor is 1 - but the numbers are not necessarily prime.

44. Where is tangent positive/negative?
Adding or subtracting 180 to ? and reversing the sign of r.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
An = a1rn?¹
C² = a² + b² - 2abcos(C)

45. Sum of 2 Angles Formulas
(n/2)(a1 + an)
Between the vertex and the minor axis on the major axis
Arc length equals = (degree of the arc / 360)(circumference)
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)]

46. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
y = a(x-h)² + k - where the vertex is (h -k)
Hypotenuse is xv2 - and the sides are x.
x = -b/2a y= c - (b²/4a)
N-1

47. How many ways can n elements be ordered?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
An = a1 + (n-1)d
N!
Hypotenuse is xv2 - and the sides are x.

48. What is the triangle inequality rule?
x = -b/2a y= c - (b²/4a)
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.
A = ((s1 + s2)h) / 2

49. Standard form for a hyperbola that opens vertically
F(x) = f(-x)
V = (4/3)pr³
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(y-k)²/a² - (x-h)²/b² = 1

50. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
The greatest common factor is 1 - but the numbers are not necessarily prime.
Parentheses - exponents - multiplication - division - addition - subtraction
SA = 4pr²