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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. Formula for the diagonal length of a cube
An = a1 + (n-1)d
D= sv3
No equal sides and no equal angles
SA = 4pr²

2. Permutation formula (ordering)
NPr = n! / (n-r)!
Their dot product = 0
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

3. What is the form of a polar coordinate?
(y-k)²/a² - (x-h)²/b² = 1
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(x-h)²/a² - (y-k)²/b² = 1
V = (4/3)pr³

4. What is the triangle inequality rule?
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
Adding or subtracting 180 to ? and reversing the sign of r.
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

5. Double Angle Formulas
Square the differences between each coordinate - then square root the sum
An = a1 + (n-1)d
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

6. How to find the distance between two points in 3d plane?
Hypotenuse is 2x - short side is x - long side is xv3
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
NCr = nPr / r! = n! / (n-r)!r!

7. Define an even function.
SA = 4pr²
F(x) = f(-x)
(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)]

8. Sum of finite geometric series
SA = 4pr²
(1-r/1-r)
Arc length equals = (degree of the arc / 360)(circumference)
Between the vertex and the minor axis on the major axis

9. Pythagorean Identities
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
180°
N-1

10. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
SA = pr² +prl
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

11. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Two sides and two angle are equal
x = -b/2a y= c - (b²/4a)
SA = 4pr²
C² = a² + b² - 2abcos(C)

12. Standard form of the equation of a parabola.
D = v(l²+w²+h²)
y = a(x-h)² + k - where the vertex is (h -k)
Parentheses - exponents - multiplication - division - addition - subtraction
Arc length equals = (degree of the arc / 360)(circumference)

13. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
180°
F(x) = -f(-x)
(y-k)²/a² - (x-h)²/b² = 1

14. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
180°
(n/2)(a1 + an)
Their dot product = 0

15. Standard form equation for circle
Square the differences between each coordinate - then square root the sum
SA = 4pr²
Adding or subtracting 180 to ? and reversing the sign of r.
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

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
N-1
y-y1 = m(x-x1)
Between the vertex and the minor axis on the major axis

17. Formula for the volume of a cone
Parentheses - exponents - multiplication - division - addition - subtraction
Two sides and two angle are equal
V= (1/3)(pr²h)
The greatest common factor is 1 - but the numbers are not necessarily prime.

18. What is the order of operations?
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
90°
x = -b/2a y= c - (b²/4a)
Parentheses - exponents - multiplication - division - addition - subtraction

19. How can you determine the arc degree or central angle of an inscribed angle?
F(x) = f(-x)
Between the vertex and the minor axis on the major axis
All whole numbers except for 0
Multiply the inscribed angle by 2

20. Volume of a pyramid
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)
V = (1/3)bh
(y-k)²/a² - (x-h)²/b² = 1

21. Combination formula
NCr = nPr / r! = n! / (n-r)!r!
(1-r/1-r)
N!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

22. Formula for arc length
An = a1 + (n-1)d
Final amount = original amount x (1+growth rate)^number of changes
F(x) = -f(-x)
Arc length equals = (degree of the arc / 360)(circumference)

23. Surface area of a sphere
An = a1rn?¹
An = a1 + (n-1)d
SA = 4pr²
Final amount = original amount x (1+growth rate)^number of changes

24. Standard form for a hyperbola that opens vertically
(y-k)²/a² - (x-h)²/b² = 1
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.
D= sv3

25. Standard form equation for an ellipse
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(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.
D = v(l²+w²+h²)

26. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
x = -b/2a y= c - (b²/4a)
Multiply the inscribed angle by 2
An = a1rn?¹

27. Two vectors are perpendicular if
90°
Their dot product = 0
NPr = n! / (n-r)!
V = (4/3)pr³

28. What is the sum of the interior angles for a polygon with n sides?
D = v(l²+w²+h²)
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)bh
(n-2)180

29. Complimentary angles add up to
SA = pr² +prl
N-1
90°
An = a1 + (n-1)d

30. Standard form for a hyperbola that opens to the sides
180°
(x-h)²/a² - (y-k)²/b² = 1
An = a1 + (n-1)d
No equal sides and no equal angles

31. How many ways can n elements be ordered?
No equal sides and no equal angles
Final amount = original amount x (1+growth rate)^number of changes
Multiply the inscribed angle by 2
N!

32. Define an odd function.
(n/2)(a1 + an)
Between the vertex and the minor axis on the major axis
C² = a² + b² - 2abcos(C)
F(x) = -f(-x)

33. Where is tangent positive/negative?
All whole numbers except for 0
(1-r/1-r)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
SA = 4pr²

34. Scalene triangle
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(n/2)(a1 + an)
180°
No equal sides and no equal angles

35. Formula for geometric sequence
Two sides and two angle are equal
(y-k)²/a² - (x-h)²/b² = 1
An = a1rn?¹
D = v(l²+w²+h²)

36. What are natural numbers?
All whole numbers except for 0
V= (1/3)(pr²h)
y-y1 = m(x-x1)
Parentheses - exponents - multiplication - division - addition - subtraction

37. Surface area of a cone
Square the differences between each coordinate - then square root the sum
SA = pr² +prl
Arc length equals = (degree of the arc / 360)(circumference)
Two sides and two angle are equal

38. 45-45-90 triangle
Hypotenuse is xv2 - and the sides are x.
180°
Final amount = original amount x (1+growth rate)^number of changes
a1 / 1-r

39. Sum of infinite geometric series
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
V = (4/3)pr³
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
a1 / 1-r

40. Sum of 2 Angles Formulas
x = -b/2a y= c - (b²/4a)
All whole numbers except for 0
F(x) = f(-x)
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 relatively prime numbers?
An = a1 + (n-1)d
The greatest common factor is 1 - but the numbers are not necessarily prime.
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Adding or subtracting 180 to ? and reversing the sign of r.

42. Formula for the area of a sector
A = ((s1 + s2)h) / 2
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)]
(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.

43. Sum of n terms of an arithmetic sequence
NPr = n! / (n-r)!
(n/2)(a1 + an)
The greatest common factor is 1 - but the numbers are not necessarily prime.
90°

44. Isosceles Triangles
Adding or subtracting 180 to ? and reversing the sign of r.
SA = pr² +prl
Two sides and two angle are equal
x=rcos?(theta) y=rsin? (theta)

45. In an ellipse - where are the foci?
Two sides and two angle are equal
Multiply the inscribed angle by 2
90°
Between the vertex and the minor axis on the major axis

46. How can multiple polar coordinates be made?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Adding or subtracting 180 to ? and reversing the sign of r.
(n/2)(a1 + an)
N-1

47. Supplementary angles add up to
180°
(n/2)(a1 + an)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

48. Difference between 2 Angles formulas
NCr = nPr / r! = n! / (n-r)!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)]
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
The greatest common factor is 1 - but the numbers are not necessarily prime.

49. Formula for the diagonal length of a rectangular prism
x=rcos?(theta) y=rsin? (theta)
D = v(l²+w²+h²)
F(x) = -f(-x)
(n-2)180

50. Law of Cosines
An = a1 + (n-1)d
C² = a² + b² - 2abcos(C)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
NPr = n! / (n-r)!