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Test your basic knowledge |

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 arc length
Arc length equals = (degree of the arc / 360)(circumference)
90°
Hypotenuse is xv2 - and the sides are x.
V= (1/3)(pr²h)

2. Formula for calculation exponential growth
(1-r/1-r)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Final amount = original amount x (1+growth rate)^number of changes

3. Two vectors are perpendicular if
NPr = n! / (n-r)!
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)

4. What is the form of a polar coordinate?
Hypotenuse is 2x - short side is x - long side is xv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(y-k)²/a² - (x-h)²/b² = 1
Two sides and two angle are equal

5. Scalene triangle
All whole numbers except for 0
SA = pr² +prl
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

6. Sum of n terms of an arithmetic sequence
SA = 4pr²
Between the vertex and the minor axis on the major axis
(n/2)(a1 + an)
SA = pr² +prl

7. Define an odd function.
F(x) = f(-x)
x = -b/2a y= c - (b²/4a)
All whole numbers except for 0
F(x) = -f(-x)

8. Surface area of a sphere
Hypotenuse is 2x - short side is x - long side is xv3
SA = 4pr²
(n/2)(a1 + an)
A = (degree of the arc / 360)(area of a circle)

9. How can multiple polar coordinates be made?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Adding or subtracting 180 to ? and reversing the sign of r.
Their dot product = 0
(n/2)(a1 + an)

10. 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)]
Hypotenuse is 2x - short side is x - long side is xv3
y-y1 = m(x-x1)
All whole numbers except for 0

11. Surface area of a cone
A = ((s1 + s2)h) / 2
SA = pr² +prl
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)

12. Formula for the area of a sector
D = v(l²+w²+h²)
A = (degree of the arc / 360)(area of a circle)
F(x) = f(-x)
x=rcos?(theta) y=rsin? (theta)

13. Isosceles Triangles
Arc length equals = (degree of the arc / 360)(circumference)
x = -b/2a y= c - (b²/4a)
a1 / 1-r
Two sides and two angle are equal

14. Standard form of the equation of a parabola.
(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)
y = a(x-h)² + k - where the vertex is (h -k)
SA = 4pr²

15. Volume of a pyramid
V = (1/3)bh
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Hypotenuse is 2x - short side is x - long side is xv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

16. 45-45-90 triangle
(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)
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is xv2 - and the sides are x.

17. Complimentary angles add up to
90°
Hypotenuse is 2x - short side is x - long side is xv3
Adding or subtracting 180 to ? and reversing the sign of r.
V = (4/3)pr³

18. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
180°
y-y1 = m(x-x1)
NPr = n! / (n-r)!
Multiply the inscribed angle by 2

19. Permutation formula (ordering)
(x-h)²/a² - (y-k)²/b² = 1
y-y1 = m(x-x1)
F(x) = -f(-x)
NPr = n! / (n-r)!

20. What are the conversion equations for polar coordinates to normal coordinates?
x=rcos?(theta) y=rsin? (theta)
N!
V = (4/3)pr³
D = v(l²+w²+h²)

21. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
C² = a² + b² - 2abcos(C)
V= (1/3)(pr²h)
An = a1rn?¹

22. Standard form for a hyperbola that opens to the sides
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(x-h)²/a² - (y-k)²/b² = 1
V = (1/3)bh
Hypotenuse is xv2 - and the sides are x.

23. Law of Cosines
D= sv3
N-1
C² = a² + b² - 2abcos(C)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

24. Where is tangent positive/negative?
NPr = n! / (n-r)!
A = ((s1 + s2)h) / 2
F(x) = f(-x)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

25. Standard form equation for an ellipse
Two sides and two angle are equal
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
NPr = n! / (n-r)!
(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.

26. Sum of 2 Angles Formulas
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(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)]
(n-2)180

27. What are relatively prime numbers?
The greatest common factor is 1 - but the numbers are not necessarily prime.
(x-h)²/a² - (y-k)²/b² = 1
90°
V= (1/3)(pr²h)

28. Formula for arithmetic sequence
An = a1 + (n-1)d
A = (degree of the arc / 360)(area of a circle)
y = a(x-h)² + k - where the vertex is (h -k)
All whole numbers except for 0

29. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
a1 / 1-r
x=rcos?(theta) y=rsin? (theta)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

30. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
No equal sides and no equal angles
NPr = n! / (n-r)!
N-1
An = a1rn?¹

31. Define an even function.
F(x) = f(-x)
A = ((s1 + s2)h) / 2
NCr = nPr / r! = n! / (n-r)!r!
(x-h)²/a² - (y-k)²/b² = 1

32. 30-60-90 triangle
N-1
x = -b/2a y= c - (b²/4a)
(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.
Hypotenuse is 2x - short side is x - long side is xv3

33. Sum of finite geometric series
(1-r/1-r)
Parentheses - exponents - multiplication - division - addition - subtraction
y = a(x-h)² + k - where the vertex is (h -k)
F(x) = -f(-x)

34. Formula for geometric sequence
y-y1 = m(x-x1)
NPr = n! / (n-r)!
An = a1rn?¹
Adding or subtracting 180 to ? and reversing the sign of r.

35. Formula for the area of a trapezoid
180°
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(1-r/1-r)
A = ((s1 + s2)h) / 2

36. Standard form for a hyperbola that opens vertically
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
(y-k)²/a² - (x-h)²/b² = 1
N!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

37. Formula for the diagonal length of a cube
Multiply the inscribed angle by 2
A = ((s1 + s2)h) / 2
D= sv3
No equal sides and no equal angles

38. Double Angle Formulas
N-1
All whole numbers except for 0
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)]
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

39. What is the sum of the interior angles for a polygon with n sides?
Their dot product = 0
All whole numbers except for 0
N-1
(n-2)180

40. 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
Parentheses - exponents - multiplication - division - addition - subtraction
D = v(l²+w²+h²)
An = a1 + (n-1)d

41. What are natural numbers?
All whole numbers except for 0
(1-r/1-r)
The greatest common factor is 1 - but the numbers are not necessarily prime.
x=rcos?(theta) y=rsin? (theta)

42. Volume of a sphere
A = ((s1 + s2)h) / 2
(y-k)²/a² - (x-h)²/b² = 1
V = (4/3)pr³
a1 / 1-r

43. What is the triangle inequality rule?
A = ((s1 + s2)h) / 2
Hypotenuse is 2x - short side is x - long side is xv3
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Arc length equals = (degree of the arc / 360)(circumference)

44. Formula for the volume of a cone
An = a1rn?¹
SA = 4pr²
V= (1/3)(pr²h)
D= sv3

45. Formula for the diagonal length of a rectangular prism
N!
D = v(l²+w²+h²)
Between the vertex and the minor axis on the major axis
(1-r/1-r)

46. Sum of infinite geometric series
C² = a² + b² - 2abcos(C)
Final amount = original amount x (1+growth rate)^number of changes
a1 / 1-r
Adding or subtracting 180 to ? and reversing the sign of r.

47. Supplementary angles add up to
180°
Parentheses - exponents - multiplication - division - addition - subtraction
SA = pr² +prl
Two sides and two angle are equal

48. Combination formula
Arc length equals = (degree of the arc / 360)(circumference)
The greatest common factor is 1 - but the numbers are not necessarily prime.
NCr = nPr / r! = n! / (n-r)!r!
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

49. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
An = a1rn?¹
The greatest common factor is 1 - but the numbers are not necessarily prime.
NPr = n! / (n-r)!

50. How many ways can n elements be ordered?
(x-h)²/a² - (y-k)²/b² = 1
An = a1rn?¹
N!
(n/2)(a1 + an)