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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 for a hyperbola that opens to the sides
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(n-2)180
(x-h)²/a² - (y-k)²/b² = 1

2. Complimentary angles add up to
Parentheses - exponents - multiplication - division - addition - subtraction
D= sv3
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
90°

3. Formula for calculation exponential growth
An = a1rn?¹
Final amount = original amount x (1+growth rate)^number of changes
A = ((s1 + s2)h) / 2
(x-h)²/a² - (y-k)²/b² = 1

4. Volume of a sphere
F(x) = f(-x)
All whole numbers except for 0
V = (4/3)pr³
C² = a² + b² - 2abcos(C)

5. Volume of a pyramid
(1-r/1-r)
V = (1/3)bh
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Adding or subtracting 180 to ? and reversing the sign of r.

6. Sum of 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)]
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d
(n-2)180

7. Standard form equation for an ellipse
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/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.
No equal sides and no equal angles
A = ((s1 + s2)h) / 2

8. Surface area of a sphere
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
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
SA = 4pr²

9. Formula for the diagonal length of a cube
A = (degree of the arc / 360)(area of a circle)
D= sv3
All whole numbers except for 0
Between the vertex and the minor axis on the major axis

10. Two vectors are perpendicular if
Their dot product = 0
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
F(x) = -f(-x)
The greatest common factor is 1 - but the numbers are not necessarily prime.

11. Formula for the area of a trapezoid
N-1
C² = a² + b² - 2abcos(C)
An = a1rn?¹
A = ((s1 + s2)h) / 2

12. Formula for geometric sequence
V = (4/3)pr³
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Final amount = original amount x (1+growth rate)^number of changes
An = a1rn?¹

13. Supplementary angles add up to
Two sides and two angle are equal
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
180°
An = a1rn?¹

14. Double Angle Formulas
NPr = n! / (n-r)!
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
y = a(x-h)² + k - where the vertex is (h -k)
(n/2)(a1 + an)

15. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
F(x) = -f(-x)
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

16. Define an even function.
Final amount = original amount x (1+growth rate)^number of changes
All whole numbers except for 0
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
F(x) = f(-x)

17. Combination formula
Parentheses - exponents - multiplication - division - addition - subtraction
NCr = nPr / r! = n! / (n-r)!r!
N-1
(y-k)²/a² - (x-h)²/b² = 1

18. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
x = -b/2a y= c - (b²/4a)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
SA = 4pr²
An = a1 + (n-1)d

19. Formula for the volume of a cone
(n-2)180
V= (1/3)(pr²h)
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)]

20. 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.
V= (1/3)(pr²h)
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)]

21. Formula for arithmetic sequence
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(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)]
An = a1 + (n-1)d

22. Surface area of a cone
SA = pr² +prl
C² = a² + b² - 2abcos(C)
A = (degree of the arc / 360)(area of a 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.

23. Formula for the diagonal length of a rectangular prism
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Final amount = original amount x (1+growth rate)^number of changes
D = v(l²+w²+h²)
Square the differences between each coordinate - then square root the sum

24. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
An = a1rn?¹
y-y1 = m(x-x1)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
C² = a² + b² - 2abcos(C)

25. Sum of finite geometric series
(1-r/1-r)
F(x) = f(-x)
The greatest common factor is 1 - but the numbers are not necessarily prime.
Arc length equals = (degree of the arc / 360)(circumference)

26. 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 - 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.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(1-r/1-r)

27. Sum of infinite geometric series
a1 / 1-r
Square the differences between each coordinate - then square root the sum
SA = pr² +prl
Arc length equals = (degree of the arc / 360)(circumference)

28. What are natural numbers?
F(x) = -f(-x)
All whole numbers except for 0
A = ((s1 + s2)h) / 2
(n-2)180

29. Where is tangent positive/negative?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Adding or subtracting 180 to ? and reversing the sign of r.
No equal sides and no equal angles

30. What is the order of operations?
90°
(x-h)²/a² - (y-k)²/b² = 1
The greatest common factor is 1 - but the numbers are not necessarily prime.
Parentheses - exponents - multiplication - division - addition - subtraction

31. Law of Cosines
C² = a² + b² - 2abcos(C)
V= (1/3)(pr²h)
All whole numbers except for 0
180°

32. Standard form for a hyperbola that opens vertically
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is xv2 - and the sides are x.
(y-k)²/a² - (x-h)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!

33. What is the form of a polar coordinate?
V = (1/3)bh
No equal sides and no equal angles
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
C² = a² + b² - 2abcos(C)

34. Formula for arc length
NPr = n! / (n-r)!
Arc length equals = (degree of the arc / 360)(circumference)
Hypotenuse is xv2 - and the sides are x.
F(x) = -f(-x)

35. Formula for the area of a sector
A = ((s1 + s2)h) / 2
Multiply the inscribed angle by 2
A = (degree of the arc / 360)(area of a circle)
SA = pr² +prl

36. Define an odd function.
SA = 4pr²
180°
A = (degree of the arc / 360)(area of a circle)
F(x) = -f(-x)

37. Permutation formula (ordering)
NPr = n! / (n-r)!
y = a(x-h)² + k - where the vertex is (h -k)
The greatest common factor is 1 - but the numbers are not necessarily prime.
(x-h)²/a² - (y-k)²/b² = 1

38. How many ways can n elements be ordered?
90°
Parentheses - exponents - multiplication - division - addition - subtraction
Arc length equals = (degree of the arc / 360)(circumference)
N!

39. Isosceles Triangles
Two sides and two angle are equal
(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 + (y-k)² = r² - where (h -k) is the center of the circle
V = (4/3)pr³

40. Standard form equation for circle
V = (1/3)bh
N-1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
N!

41. Difference between 2 Angles formulas
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
A = ((s1 + s2)h) / 2
a1 / 1-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)]

42. How can multiple polar coordinates be made?
N!
A = (degree of the arc / 360)(area of a circle)
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is xv2 - and the sides are x.

43. 45-45-90 triangle
Their dot product = 0
An = a1 + (n-1)d
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Hypotenuse is xv2 - and the sides are x.

44. 30-60-90 triangle
A = ((s1 + s2)h) / 2
(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
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

45. How to find the distance between two points in 3d plane?
90°
Square the differences between each coordinate - then square root the sum
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

46. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
The greatest common factor is 1 - but the numbers are not necessarily prime.
F(x) = -f(-x)

47. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is 2x - short side is x - long side is xv3
(x-h)²/a² - (y-k)²/b² = 1

48. How to determine if a number is prime
Final amount = original amount x (1+growth rate)^number of changes
F(x) = f(-x)
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)

49. Standard form of the equation of a parabola.
D = v(l²+w²+h²)
SA = 4pr²
(n-2)180
y = a(x-h)² + k - where the vertex is (h -k)

50. What are relatively prime numbers?
C² = a² + b² - 2abcos(C)
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = 4pr²
(x-h)²/a² - (y-k)²/b² = 1