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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. What are natural numbers?
Parentheses - exponents - multiplication - division - addition - subtraction
y-y1 = m(x-x1)
Between the vertex and the minor axis on the major axis
All whole numbers except for 0

2. Surface area of a cone
Adding or subtracting 180 to ? and reversing the sign of r.
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.
N-1

3. 30-60-90 triangle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles
(n/2)(a1 + an)
Hypotenuse is 2x - short side is x - long side is xv3

4. Standard form for a hyperbola that opens vertically
An = a1rn?¹
(y-k)²/a² - (x-h)²/b² = 1
A = (degree of the arc / 360)(area of a circle)
Their dot product = 0

5. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Two sides and two angle are equal
D = v(l²+w²+h²)

6. Two vectors are perpendicular if
An = a1 + (n-1)d
Hypotenuse is 2x - short side is x - long side is xv3
Their dot product = 0
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

7. What is the triangle inequality rule?
180°
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
V = (4/3)pr³

8. 45-45-90 triangle
a1 / 1-r
180°
No equal sides and no equal angles
Hypotenuse is xv2 - and the sides are x.

9. How many ways can n elements be ordered?
N!
An = a1 + (n-1)d
90°
N-1

10. What are the conversion equations for polar coordinates to normal coordinates?
Arc length equals = (degree of the arc / 360)(circumference)
An = a1 + (n-1)d
x=rcos?(theta) y=rsin? (theta)
90°

11. Formula for calculation exponential growth
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)]
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes
(n-2)180

12. Formula for the area of a trapezoid
SA = 4pr²
90°
A = ((s1 + s2)h) / 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)]

13. Difference between 2 Angles formulas
(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
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 = -b/2a y= c - (b²/4a)

14. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
SA = pr² +prl
N-1
90°
(1-r/1-r)

15. Complimentary angles add up to
NPr = n! / (n-r)!
Hypotenuse is 2x - short side is x - long side is xv3
SA = pr² +prl
90°

16. Permutation formula (ordering)
a1 / 1-r
NPr = n! / (n-r)!
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)]

17. Formula for the volume of a cone
90°
N-1
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.

18. Sum of n terms of an arithmetic sequence
x=rcos?(theta) y=rsin? (theta)
Between the vertex and the minor axis on the major axis
(n/2)(a1 + an)
All whole numbers except for 0

19. In an ellipse - where are the foci?
180°
y-y1 = m(x-x1)
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)]

20. Volume of a pyramid
V = (1/3)bh
Between the vertex and the minor axis on the major axis
Arc length equals = (degree of the arc / 360)(circumference)
Final amount = original amount x (1+growth rate)^number of changes

21. How can multiple polar coordinates be made?
A = ((s1 + s2)h) / 2
F(x) = f(-x)
D= sv3
Adding or subtracting 180 to ? and reversing the sign of r.

22. Supplementary angles add up to
180°
V= (1/3)(pr²h)
An = a1 + (n-1)d
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

23. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
180°
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)

24. Formula for the area of a sector
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
A = (degree of the arc / 360)(area of a circle)
V= (1/3)(pr²h)
90°

25. Surface area of a sphere
C² = a² + b² - 2abcos(C)
SA = 4pr²
All whole numbers except for 0
Arc length equals = (degree of the arc / 360)(circumference)

26. Standard form of the equation of a parabola.
y-y1 = m(x-x1)
y = a(x-h)² + k - where the vertex is (h -k)
All whole numbers except for 0
Square the differences between each coordinate - then square root the sum

27. Isosceles Triangles
Two sides and two angle are equal
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)]
V= (1/3)(pr²h)

28. How to determine if a number is prime
No equal sides and no equal angles
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(n-2)180
D= sv3

29. Formula for geometric sequence
y = a(x-h)² + k - where the vertex is (h -k)
Adding or subtracting 180 to ? and reversing the sign of r.
An = a1rn?¹
F(x) = -f(-x)

30. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Arc length equals = (degree of the arc / 360)(circumference)
(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)
N!

31. Define an even function.
(x-h)²/a² - (y-k)²/b² = 1
D = v(l²+w²+h²)
An = a1rn?¹
F(x) = f(-x)

32. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(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)]
a1 / 1-r

33. Volume of a sphere
V = (4/3)pr³
F(x) = f(-x)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
An = a1 + (n-1)d

34. How can you determine the arc degree or central angle of an inscribed angle?
(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.
Multiply the inscribed angle by 2
Adding or subtracting 180 to ? and reversing the sign of r.
x = -b/2a y= c - (b²/4a)

35. 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
Arc length equals = (degree of the arc / 360)(circumference)
All whole numbers except for 0
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

36. Define an odd function.
F(x) = -f(-x)
V= (1/3)(pr²h)
90°
F(x) = f(-x)

37. Sum of finite geometric series
V = (4/3)pr³
C² = a² + b² - 2abcos(C)
(1-r/1-r)
Hypotenuse is xv2 - and the sides are x.

38. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
(n/2)(a1 + an)
y-y1 = m(x-x1)
(n-2)180
Two sides and two angle are equal

39. Sum of 2 Angles Formulas
C² = a² + b² - 2abcos(C)
NCr = nPr / r! = n! / (n-r)!r!
x=rcos?(theta) y=rsin? (theta)
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)]

40. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
(x-h)²/a² - (y-k)²/b² = 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)]
A = ((s1 + s2)h) / 2

41. Pythagorean Identities
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
90°
Two sides and two angle are equal
Hypotenuse is 2x - short side is x - long side is xv3

42. Law of Cosines
C² = a² + b² - 2abcos(C)
V= (1/3)(pr²h)
x=rcos?(theta) y=rsin? (theta)
Parentheses - exponents - multiplication - division - addition - subtraction

43. Formula for the diagonal length of a rectangular prism
All whole numbers except for 0
D = v(l²+w²+h²)
V= (1/3)(pr²h)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

44. Formula for arc length
An = a1rn?¹
Parentheses - exponents - multiplication - division - addition - subtraction
Arc length equals = (degree of the arc / 360)(circumference)
Adding or subtracting 180 to ? and reversing the sign of r.

45. Standard form equation for an ellipse
SA = 4pr²
(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!
N-1

46. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
C² = a² + b² - 2abcos(C)
V = (1/3)bh
(x-h)²/a² - (y-k)²/b² = 1

47. Formula for the diagonal length of a cube
x=rcos?(theta) y=rsin? (theta)
Arc length equals = (degree of the arc / 360)(circumference)
D= sv3
V= (1/3)(pr²h)

48. Formula for arithmetic sequence
An = a1 + (n-1)d
(x-h)²/a² - (y-k)²/b² = 1
F(x) = -f(-x)
An = a1rn?¹

49. What are relatively prime numbers?
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily 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.
V = (4/3)pr³

50. Standard form equation for circle
x=rcos?(theta) y=rsin? (theta)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
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.