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. How can multiple polar coordinates be made?
The greatest common factor is 1 - but the numbers are not necessarily prime.
Adding or subtracting 180 to ? and reversing the sign of r.
Arc length equals = (degree of the arc / 360)(circumference)
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)]

2. Law of Cosines
C² = a² + b² - 2abcos(C)
F(x) = f(-x)
(1-r/1-r)
(n-2)180

3. What are relatively prime numbers?
F(x) = -f(-x)
N!
Final amount = original amount x (1+growth rate)^number of changes
The greatest common factor is 1 - but the numbers are not necessarily prime.

4. How many ways can n elements be ordered?
Between the vertex and the minor axis on the major axis
Square the differences between each coordinate - then square root the sum
N!
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

5. Sum of infinite geometric series
Arc length equals = (degree of the arc / 360)(circumference)
F(x) = -f(-x)
SA = 4pr²
a1 / 1-r

6. Complimentary angles add up to
(y-k)²/a² - (x-h)²/b² = 1
(x-h)²/a² - (y-k)²/b² = 1
90°
Two sides and two angle are equal

7. Standard form for a hyperbola that opens to the sides
An = a1rn?¹
y = a(x-h)² + k - where the vertex is (h -k)
Parentheses - exponents - multiplication - division - addition - subtraction
(x-h)²/a² - (y-k)²/b² = 1

8. How to find the distance between two points in 3d plane?
Square the differences between each coordinate - then square root the sum
180°
x = -b/2a y= c - (b²/4a)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

9. Formula for arithmetic sequence
An = a1 + (n-1)d
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 + (y-k)² = r² - where (h -k) is the center of the circle
x = -b/2a y= c - (b²/4a)

10. Volume of a pyramid
x = -b/2a y= c - (b²/4a)
y-y1 = m(x-x1)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
V = (1/3)bh

11. Formula for geometric sequence
An = a1rn?¹
C² = a² + b² - 2abcos(C)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
The greatest common factor is 1 - but the numbers are not necessarily prime.

12. Surface area of a cone
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
x=rcos?(theta) y=rsin? (theta)
All whole numbers except for 0
SA = pr² +prl

13. Combination formula
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)]
SA = 4pr²
Two sides and two angle are equal

14. Formula for the diagonal length of a cube
D= sv3
V = (4/3)pr³
(n/2)(a1 + an)
x = -b/2a y= c - (b²/4a)

15. Sum of n terms of an arithmetic sequence
Hypotenuse is 2x - short side is x - long side is xv3
(n/2)(a1 + an)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Between the vertex and the minor axis on the major axis

16. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Multiply the inscribed angle by 2
x = -b/2a y= c - (b²/4a)
D= sv3
Parentheses - exponents - multiplication - division - addition - subtraction

17. Volume of a sphere
SA = 4pr²
V = (4/3)pr³
x=rcos?(theta) y=rsin? (theta)
N-1

18. Permutation formula (ordering)
NPr = n! / (n-r)!
Final amount = original amount x (1+growth rate)^number of changes
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Between the vertex and the minor axis on the major axis

19. What is the sum of the interior angles for a polygon with n sides?
Hypotenuse is xv2 - and the sides are x.
(n-2)180
x=rcos?(theta) y=rsin? (theta)
A = ((s1 + s2)h) / 2

20. Scalene triangle
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
No equal sides and no equal angles
NCr = nPr / r! = n! / (n-r)!r!
Final amount = original amount x (1+growth rate)^number of changes

21. Sum of finite geometric series
The greatest common factor is 1 - but the numbers are not necessarily prime.
(1-r/1-r)
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)]

22. Formula for calculation exponential growth
Final amount = original amount x (1+growth rate)^number of changes
A = ((s1 + s2)h) / 2
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)]

23. Formula for the area of a trapezoid
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.
A = ((s1 + s2)h) / 2
A = (degree of the arc / 360)(area of a circle)

24. 45-45-90 triangle
N-1
Parentheses - exponents - multiplication - division - addition - subtraction
Hypotenuse is xv2 - and the sides are x.
N!

25. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
Their dot product = 0
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
V = (4/3)pr³

26. In an ellipse - where are the foci?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x = -b/2a y= c - (b²/4a)
Between the vertex and the minor axis on the major axis
C² = a² + b² - 2abcos(C)

27. Standard form equation for circle
NCr = nPr / r! = n! / (n-r)!r!
SA = 4pr²
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(y-k)²/a² - (x-h)²/b² = 1

28. Formula for arc length
SA = 4pr²
A = (degree of the arc / 360)(area of a circle)
Arc length equals = (degree of the arc / 360)(circumference)
(n/2)(a1 + an)

29. Pythagorean Identities
Square the differences between each coordinate - then square root the sum
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
All whole numbers except for 0
(x-h)²/a² - (y-k)²/b² = 1

30. What is the triangle inequality rule?
(1-r/1-r)
SA = 4pr²
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.

31. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
y-y1 = m(x-x1)
Final amount = original amount x (1+growth rate)^number of changes
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.

32. What is the order of operations?
Arc length equals = (degree of the arc / 360)(circumference)
Parentheses - exponents - multiplication - division - addition - subtraction
a1 / 1-r
V = (1/3)bh

33. What are the conversion equations for polar coordinates to normal coordinates?
(1-r/1-r)
a1 / 1-r
x=rcos?(theta) y=rsin? (theta)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

34. Sum of 2 Angles Formulas
A = (degree of the arc / 360)(area of a circle)
C² = a² + b² - 2abcos(C)
V = (4/3)pr³
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. Formula for the volume of a cone
Parentheses - exponents - multiplication - division - addition - subtraction
(x-h)²/a² - (y-k)²/b² = 1
(n/2)(a1 + an)
V= (1/3)(pr²h)

36. Two vectors are perpendicular if
y-y1 = m(x-x1)
SA = pr² +prl
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)]
Their dot product = 0

37. Standard form for a hyperbola that opens vertically
Final amount = original amount x (1+growth rate)^number of changes
(y-k)²/a² - (x-h)²/b² = 1
Hypotenuse is xv2 - and the sides are x.
N!

38. Double Angle Formulas
An = a1 + (n-1)d
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

39. Supplementary angles add up to
All whole numbers except for 0
NPr = n! / (n-r)!
(n-2)180
180°

40. Where is tangent positive/negative?
D = v(l²+w²+h²)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
N-1
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

41. Formula for the area of a sector
(1-r/1-r)
x=rcos?(theta) y=rsin? (theta)
Square the differences between each coordinate - then square root the sum
A = (degree of the arc / 360)(area of a circle)

42. Standard form equation for an ellipse
(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 = (1/3)bh
An = a1rn?¹
(1-r/1-r)

43. Define an odd function.
x=rcos?(theta) y=rsin? (theta)
NPr = n! / (n-r)!
F(x) = -f(-x)
a1 / 1-r

44. Define an even function.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Arc length equals = (degree of the arc / 360)(circumference)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
F(x) = f(-x)

45. Formula for the diagonal length of a rectangular prism
F(x) = f(-x)
D= sv3
180°
D = v(l²+w²+h²)

46. 30-60-90 triangle
D= sv3
x=rcos?(theta) y=rsin? (theta)
No equal sides and no equal angles
Hypotenuse is 2x - short side is x - long side is xv3

47. Surface area of a sphere
An = a1rn?¹
A = (degree of the arc / 360)(area of a circle)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
SA = 4pr²

48. What is the form of a polar coordinate?
NCr = nPr / r! = n! / (n-r)!r!
D= sv3
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

49. What are natural numbers?
All whole numbers except for 0
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1
A = ((s1 + s2)h) / 2

50. How can you determine the arc degree or central angle of an inscribed angle?
Multiply the inscribed angle by 2
A = (degree of the arc / 360)(area of a circle)
Final amount = original amount x (1+growth rate)^number of changes
Their dot product = 0