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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. What are natural numbers?
Their dot product = 0
All whole numbers except for 0
y-y1 = m(x-x1)
Hypotenuse is xv2 - and the sides are x.

2. How many ways can n elements be ordered?
A = ((s1 + s2)h) / 2
N!
An = a1 + (n-1)d
F(x) = -f(-x)

3. Surface area of a cone
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = pr² +prl
x = -b/2a y= c - (b²/4a)
V= (1/3)(pr²h)

4. Sum of infinite geometric series
A = (degree of the arc / 360)(area of a circle)
a1 / 1-r
N!
F(x) = f(-x)

5. Sum of 2 Angles Formulas
y = a(x-h)² + k - where the vertex is (h -k)
(n/2)(a1 + an)
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)

6. What are relatively prime numbers?
F(x) = f(-x)
D= sv3
The greatest common factor is 1 - but the numbers are not necessarily prime.
Square the differences between each coordinate - then square root the sum

7. Formula for arc length
(n-2)180
Arc length equals = (degree of the arc / 360)(circumference)
N!
Two sides and two angle are equal

8. Standard form of the equation of a parabola.
No equal sides and no equal angles
SA = pr² +prl
y = a(x-h)² + k - where the vertex is (h -k)
Multiply the inscribed angle by 2

9. Law of Cosines
An = a1rn?¹
NCr = nPr / r! = n! / (n-r)!r!
Between the vertex and the minor axis on the major axis
C² = a² + b² - 2abcos(C)

10. Formula for calculation exponential growth
x = -b/2a y= c - (b²/4a)
Final amount = original amount x (1+growth rate)^number of changes
An = a1rn?¹
Their dot product = 0

11. Formula for the diagonal length of a rectangular prism
The greatest common factor is 1 - but the numbers are not necessarily prime.
a1 / 1-r
180°
D = v(l²+w²+h²)

12. Scalene triangle
A = (degree of the arc / 360)(area of a circle)
SA = 4pr²
No equal sides and no equal angles
(y-k)²/a² - (x-h)²/b² = 1

13. Define an even function.
(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.
F(x) = f(-x)
A = ((s1 + s2)h) / 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.

14. 30-60-90 triangle
D= sv3
Two sides and two angle are equal
Adding or subtracting 180 to ? and reversing the sign of r.
Hypotenuse is 2x - short side is x - long side is xv3

15. Formula for the area of a trapezoid
Adding or subtracting 180 to ? and reversing the sign of r.
A = ((s1 + s2)h) / 2
No equal sides and no equal angles
90°

16. Formula for the diagonal length of a cube
x=rcos?(theta) y=rsin? (theta)
D= sv3
Hypotenuse is xv2 - and the sides are x.
N!

17. Surface area of a sphere
SA = 4pr²
Between the vertex and the minor axis on the major axis
90°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

18. Permutation formula (ordering)
NPr = n! / (n-r)!
Square the differences between each coordinate - then square root the sum
x=rcos?(theta) y=rsin? (theta)
D = v(l²+w²+h²)

19. 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
SA = pr² +prl
Their dot product = 0
Multiply the inscribed angle by 2

20. What is the triangle inequality rule?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Two sides and two angle are equal
90°
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

21. What are the conversion equations for polar coordinates to normal coordinates?
Arc length equals = (degree of the arc / 360)(circumference)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x=rcos?(theta) y=rsin? (theta)
(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.

22. How can multiple polar coordinates be made?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Adding or subtracting 180 to ? and reversing the sign of r.
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)]

23. Standard form equation for an ellipse
SA = pr² +prl
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(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

24. What is the sum of the interior angles for a polygon with n sides?
V = (4/3)pr³
(n-2)180
(y-k)²/a² - (x-h)²/b² = 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.

25. Double Angle Formulas
(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.
Two sides and two angle are equal
Arc length equals = (degree of the arc / 360)(circumference)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

26. How can you determine the arc degree or central angle of an inscribed angle?
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)
Multiply the inscribed angle by 2
(y-k)²/a² - (x-h)²/b² = 1

27. Pythagorean Identities
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
y-y1 = m(x-x1)
D= sv3

28. In an ellipse - where are the foci?
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)]
A = ((s1 + s2)h) / 2
F(x) = f(-x)

29. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
A = (degree of the arc / 360)(area of a circle)
N!
F(x) = f(-x)
y-y1 = m(x-x1)

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

31. Formula for arithmetic sequence
An = a1 + (n-1)d
(n-2)180
The greatest common factor is 1 - but the numbers are not necessarily prime.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

32. Volume of a sphere
Hypotenuse is xv2 - and the sides are x.
SA = 4pr²
V = (4/3)pr³
(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.

33. Supplementary angles add up to
N!
All whole numbers except for 0
180°
(n-2)180

34. Sum of finite geometric series
(1-r/1-r)
x = -b/2a y= c - (b²/4a)
y-y1 = m(x-x1)
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)]

35. Difference between 2 Angles formulas
y = a(x-h)² + k - where the vertex is (h -k)
(n-2)180
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 = a1rn?¹

36. Complimentary angles add up to
90°
y = a(x-h)² + k - where the vertex is (h -k)
(x-h)²/a² - (y-k)²/b² = 1
N-1

37. What is the form of a polar coordinate?
An = a1 + (n-1)d
C² = a² + b² - 2abcos(C)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
N-1

38. Two vectors are perpendicular if
Their dot product = 0
x=rcos?(theta) y=rsin? (theta)
C² = a² + b² - 2abcos(C)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

39. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
y-y1 = m(x-x1)
Between the vertex and the minor axis on the major axis
Multiply the inscribed angle by 2

40. Combination formula
No equal sides and no equal angles
N!
All whole numbers except for 0
NCr = nPr / r! = n! / (n-r)!r!

41. Formula for the volume of a cone
A = (degree of the arc / 360)(area of a circle)
V= (1/3)(pr²h)
(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)]

42. Isosceles Triangles
SA = 4pr²
Two sides and two angle are equal
(n-2)180
180°

43. Where is tangent positive/negative?
D = v(l²+w²+h²)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Square the differences between each coordinate - then square root the sum
N!

44. Standard form equation for circle
Hypotenuse is 2x - short side is x - long side is xv3
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

45. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
An = a1 + (n-1)d
x = -b/2a y= c - (b²/4a)
Arc length equals = (degree of the arc / 360)(circumference)
Two sides and two angle are equal

46. 45-45-90 triangle
Hypotenuse is xv2 - and the sides are x.
Adding or subtracting 180 to ? and reversing the sign of r.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Between the vertex and the minor axis on the major axis

47. Standard form for a hyperbola that opens vertically
90°
(y-k)²/a² - (x-h)²/b² = 1
F(x) = f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

48. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
(1-r/1-r)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
SA = 4pr²

49. What is the order of operations?
(y-k)²/a² - (x-h)²/b² = 1
Square the differences between each coordinate - then square root the sum
180°
Parentheses - exponents - multiplication - division - addition - subtraction

50. Formula for geometric sequence
An = a1rn?¹
y = a(x-h)² + k - where the vertex is (h -k)
V = (4/3)pr³
F(x) = f(-x)