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)
Square the differences between each coordinate - then square root the sum
Multiply the inscribed angle by 2
SA = pr² +prl

2. Standard form for a hyperbola that opens to the sides
Square the differences between each coordinate - then square root the sum
(x-h)²/a² - (y-k)²/b² = 1
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!

3. Pythagorean Identities
No equal sides and no equal angles
(y-k)²/a² - (x-h)²/b² = 1
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Adding or subtracting 180 to ? and reversing the sign of r.

4. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(n-2)180
x = -b/2a y= c - (b²/4a)
(1-r/1-r)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

5. Formula for the diagonal length of a cube
y-y1 = m(x-x1)
Adding or subtracting 180 to ? and reversing the sign of 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.
D= sv3

6. What are natural numbers?
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
All whole numbers except for 0
Their dot product = 0
(n-2)180

7. Define an odd function.
Between the vertex and the minor axis on the major axis
F(x) = -f(-x)
A = ((s1 + s2)h) / 2
Hypotenuse is 2x - short side is x - long side is xv3

8. 30-60-90 triangle
SA = pr² +prl
V = (4/3)pr³
Hypotenuse is 2x - short side is x - long side is xv3
The greatest common factor is 1 - but the numbers are not necessarily prime.

9. Sum of finite geometric series
180°
(1-r/1-r)
No equal sides and no equal angles
SA = pr² +prl

10. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
N-1
All whole numbers except for 0
(y-k)²/a² - (x-h)²/b² = 1
D = v(l²+w²+h²)

11. Formula for the area of a trapezoid
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)]
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

12. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
C² = a² + b² - 2abcos(C)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y-y1 = m(x-x1)
Multiply the inscribed angle by 2

13. Volume of a pyramid
V= (1/3)(pr²h)
V = (1/3)bh
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Multiply the inscribed angle by 2

14. Sum of n terms of an arithmetic sequence
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)
x = -b/2a y= c - (b²/4a)
(n/2)(a1 + an)

15. Formula for geometric sequence
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
V = (4/3)pr³
An = a1rn?¹
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

16. Combination formula
Hypotenuse is 2x - short side is x - long side is xv3
NCr = nPr / r! = n! / (n-r)!r!
90°
Two sides and two angle are equal

17. Where is tangent positive/negative?
(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.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!
An = a1 + (n-1)d

18. Double Angle Formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x=rcos?(theta) y=rsin? (theta)
x = -b/2a y= c - (b²/4a)

19. What are relatively prime numbers?
N!
SA = 4pr²
A = ((s1 + s2)h) / 2
The greatest common factor is 1 - but the numbers are not necessarily prime.

20. Permutation formula (ordering)
NPr = n! / (n-r)!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
V= (1/3)(pr²h)
Arc length equals = (degree of the arc / 360)(circumference)

21. How can multiple polar coordinates be made?
Multiply the inscribed angle by 2
Their dot product = 0
Two sides and two angle are equal
Adding or subtracting 180 to ? and reversing the sign of r.

22. Formula for the volume of a cone
D= sv3
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)(pr²h)
Multiply the inscribed angle by 2

23. Volume of a sphere
V = (4/3)pr³
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
A = ((s1 + s2)h) / 2

24. Scalene triangle
An = a1rn?¹
A = ((s1 + s2)h) / 2
Adding or subtracting 180 to ? and reversing the sign of r.
No equal sides and no equal angles

25. Surface area of a sphere
x = -b/2a y= c - (b²/4a)
Hypotenuse is xv2 - and the sides are x.
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
SA = 4pr²

26. What are the conversion equations for polar coordinates to normal coordinates?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
x=rcos?(theta) y=rsin? (theta)
An = a1 + (n-1)d
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

27. How can you determine the arc degree or central angle of an inscribed angle?
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-y1 = m(x-x1)
Arc length equals = (degree of the arc / 360)(circumference)
Multiply the inscribed angle by 2

28. What is the form of a polar coordinate?
An = a1 + (n-1)d
A = (degree of the arc / 360)(area of a circle)
x = -b/2a y= c - (b²/4a)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

29. Define an even function.
F(x) = f(-x)
a1 / 1-r
Between the vertex and the minor axis on the major axis
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

30. Standard form of the equation of a parabola.
y = a(x-h)² + k - where the vertex is (h -k)
(n-2)180
All whole numbers except for 0
V = (4/3)pr³

31. What is the order of operations?
Parentheses - exponents - multiplication - division - addition - subtraction
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-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)]
Two sides and two angle are equal

32. Sum of infinite geometric series
a1 / 1-r
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
C² = a² + b² - 2abcos(C)
(x-h)²/a² - (y-k)²/b² = 1

33. Difference between 2 Angles formulas
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)]
An = a1 + (n-1)d
NCr = nPr / r! = n! / (n-r)!r!

34. In an ellipse - where are the foci?
C² = a² + b² - 2abcos(C)
A = (degree of the arc / 360)(area of a circle)
Between the vertex and the minor axis on the major 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.

35. Formula for the area of a sector
(x-h)²/a² - (y-k)²/b² = 1
A = (degree of the arc / 360)(area of a circle)
(1-r/1-r)
The greatest common factor is 1 - but the numbers are not necessarily prime.

36. Supplementary angles add up to
An = a1rn?¹
V = (4/3)pr³
180°
Multiply the inscribed angle by 2

37. 45-45-90 triangle
All whole numbers except for 0
Hypotenuse is xv2 - and the sides are x.
D= sv3
The greatest common factor is 1 - but the numbers are not necessarily prime.

38. Isosceles Triangles
SA = pr² +prl
Two sides and two angle are equal
y-y1 = m(x-x1)
Arc length equals = (degree of the arc / 360)(circumference)

39. How to determine if a number is prime
C² = a² + b² - 2abcos(C)
NCr = nPr / r! = n! / (n-r)!r!
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Square the differences between each coordinate - then square root the sum

40. Two vectors are perpendicular if
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
y = a(x-h)² + k - where the vertex is (h -k)
Their dot product = 0
An = a1rn?¹

41. How to find the distance between two points in 3d plane?
90°
Square the differences between each coordinate - then square root the sum
F(x) = f(-x)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

42. 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)]
No equal sides and no equal angles
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)]
y-y1 = m(x-x1)

43. Formula for calculation exponential growth
180°
Final amount = original amount x (1+growth rate)^number of changes
90°
Hypotenuse is xv2 - and the sides are x.

44. Standard form equation for circle
(n/2)(a1 + an)
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
(y-k)²/a² - (x-h)²/b² = 1
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle

45. Standard form equation for an ellipse
Final amount = original amount x (1+growth rate)^number of changes
SA = pr² +prl
Hypotenuse is xv2 - and the sides are x.
(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.

46. Law of Cosines
(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.
C² = a² + b² - 2abcos(C)
NPr = n! / (n-r)!
Parentheses - exponents - multiplication - division - addition - subtraction

47. What is the sum of the interior angles for a polygon with n sides?
No equal sides and no equal angles
C² = a² + b² - 2abcos(C)
Multiply the inscribed angle by 2
(n-2)180

48. What is the triangle inequality rule?
D= sv3
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.
Parentheses - exponents - multiplication - division - addition - subtraction

49. Surface area of a cone
SA = 4pr²
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)]
SA = pr² +prl

50. How many ways can n elements be ordered?
N!
Final amount = original amount x (1+growth rate)^number of changes
An = a1rn?¹
N-1