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?
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
Adding or subtracting 180 to ? and reversing the sign of r.
D = v(l²+w²+h²)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

2. What is the form of a polar coordinate?
Two sides and two angle are equal
An = a1 + (n-1)d
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
F(x) = -f(-x)

3. How to determine if a number is prime
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
x=rcos?(theta) y=rsin? (theta)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Between the vertex and the minor axis on the major axis

4. Surface area of a cone
A = ((s1 + s2)h) / 2
Final amount = original amount x (1+growth rate)^number of changes
An = a1 + (n-1)d
SA = pr² +prl

5. How many ways can n elements be ordered?
D= sv3
(x-h)²/a² - (y-k)²/b² = 1
N!
N-1

6. Pythagorean Identities
(n-2)180
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(1-r/1-r)
SA = 4pr²

7. Supplementary angles add up to
90°
A = (degree of the arc / 360)(area of a circle)
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
180°

8. Formula for the area of a sector
V= (1/3)(pr²h)
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
A = (degree of the arc / 360)(area of a circle)
y-y1 = m(x-x1)

9. Difference between 2 Angles formulas
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
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)]
NPr = n! / (n-r)!

10. How can you determine the arc degree or central angle of an inscribed angle?
Two sides and two angle are equal
90°
Multiply the inscribed angle by 2
(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.

11. Complimentary angles add up to
y-y1 = m(x-x1)
No equal sides and no equal angles
90°
Hypotenuse is 2x - short side is x - long side is xv3

12. Sum of infinite geometric series
Two sides and two angle are equal
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)]
a1 / 1-r

13. Formula for the area of a trapezoid
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Hypotenuse is 2x - short side is x - long side is xv3
y-y1 = m(x-x1)

14. Two vectors are perpendicular if
N-1
V = (4/3)pr³
D = v(l²+w²+h²)
Their dot product = 0

15. What are natural numbers?
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
V= (1/3)(pr²h)
All whole numbers except for 0

16. Isosceles Triangles
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)]
Between the vertex and the minor axis on the major axis
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
Two sides and two angle are equal

17. What are relatively prime numbers?
N-1
V = (1/3)bh
The greatest common factor is 1 - but the numbers are not necessarily prime.
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis

18. Combination formula
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
NCr = nPr / r! = n! / (n-r)!r!
SA = pr² +prl
Square the differences between each coordinate - then square root the sum

19. Scalene triangle
A = (degree of the arc / 360)(area of a circle)
y = a(x-h)² + k - where the vertex is (h -k)
No equal sides and no equal angles
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

20. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
Between the vertex and the minor axis on the major axis
y-y1 = m(x-x1)
The greatest common factor is 1 - but the numbers are not necessarily prime.
N-1

21. Standard form of the equation of a parabola.
A = ((s1 + s2)h) / 2
D= sv3
Two sides and two angle are equal
y = a(x-h)² + k - where the vertex is (h -k)

22. How to find the distance between two points in 3d plane?
V= (1/3)(pr²h)
Square the differences between each coordinate - then square root the sum
Final amount = original amount x (1+growth rate)^number of changes
Their dot product = 0

23. In an ellipse - where are the foci?
Between the vertex and the minor axis on the major axis
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
(x-h)²/a² - (y-k)²/b² = 1
Multiply the inscribed angle by 2

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

25. 45-45-90 triangle
(y-k)²/a² - (x-h)²/b² = 1
NCr = nPr / r! = n! / (n-r)!r!
Hypotenuse is xv2 - and the sides are x.
V = (1/3)bh

26. Standard form equation for an ellipse
a1 / 1-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.
Final amount = original amount x (1+growth rate)^number of changes
SA = pr² +prl

27. 30-60-90 triangle
Hypotenuse is 2x - short side is x - long side is xv3
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
Arc length equals = (degree of the arc / 360)(circumference)
a1 / 1-r

28. Surface area of a sphere
x=rcos?(theta) y=rsin? (theta)
Between the vertex and the minor axis on the major axis
The greatest common factor is 1 - but the numbers are not necessarily prime.
SA = 4pr²

29. Formula for geometric sequence
Two sides and two angle are equal
An = a1rn?¹
Adding or subtracting 180 to ? and reversing the sign of r.
V= (1/3)(pr²h)

30. Formula for arithmetic sequence
a1 / 1-r
Two sides and two angle are equal
An = a1 + (n-1)d
(x-h)²/a² - (y-k)²/b² = 1

31. Standard form equation for circle
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
F(x) = f(-x)
C² = a² + b² - 2abcos(C)
x = -b/2a y= c - (b²/4a)

32. Sum of 2 Angles Formulas
No equal sides and no equal angles
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)]
D= sv3

33. Formula for the diagonal length of a cube
D= sv3
C² = a² + b² - 2abcos(C)
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1

34. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
Hypotenuse is xv2 - and the sides are x.
N-1
(y-k)²/a² - (x-h)²/b² = 1
Final amount = original amount x (1+growth rate)^number of changes

35. Standard form for a hyperbola that opens vertically
x = -b/2a y= c - (b²/4a)
a1 / 1-r
(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

36. Permutation formula (ordering)
An = a1 + (n-1)d
NPr = n! / (n-r)!
A = (degree of the arc / 360)(area of a circle)
x = -b/2a y= c - (b²/4a)

37. What is the sum of the interior angles for a polygon with n sides?
(n-2)180
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
D = v(l²+w²+h²)
Multiply the inscribed angle by 2

38. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
Hypotenuse is xv2 - and the sides are x.
F(x) = -f(-x)
Final amount = original amount x (1+growth rate)^number of changes
x = -b/2a y= c - (b²/4a)

39. Define an even function.
a1 / 1-r
N-1
F(x) = f(-x)
Parentheses - exponents - multiplication - division - addition - subtraction

40. Formula for the diagonal length of a rectangular prism
Final amount = original amount x (1+growth rate)^number of changes
y = a(x-h)² + k - where the vertex is (h -k)
x=rcos?(theta) y=rsin? (theta)
D = v(l²+w²+h²)

41. Formula for the volume of a cone
The greatest common factor is 1 - but the numbers are not necessarily prime.
V= (1/3)(pr²h)
NCr = nPr / r! = n! / (n-r)!r!
x=rcos?(theta) y=rsin? (theta)

42. Where is tangent positive/negative?
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
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
N-1

43. What is the triangle inequality rule?
D= sv3
(n/2)(a1 + an)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
a1 / 1-r

44. What is the order of operations?
(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.
All whole numbers except for 0
An = a1 + (n-1)d
Parentheses - exponents - multiplication - division - addition - subtraction

45. Law of Cosines
Their dot product = 0
NCr = nPr / r! = n! / (n-r)!r!
D= sv3
C² = a² + b² - 2abcos(C)

46. Volume of a pyramid
C² = a² + b² - 2abcos(C)
V = (1/3)bh
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

47. Define an odd function.
F(x) = -f(-x)
F(x) = f(-x)
Two sides and two angle are equal
(n-2)180

48. Sum of finite geometric series
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
90°
C² = a² + b² - 2abcos(C)
(1-r/1-r)

49. Formula for arc length
Arc length equals = (degree of the arc / 360)(circumference)
x=rcos?(theta) y=rsin? (theta)
A = (degree of the arc / 360)(area of a circle)
A = ((s1 + s2)h) / 2

50. What are the conversion equations for polar coordinates to normal coordinates?
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
x=rcos?(theta) y=rsin? (theta)
Hypotenuse is xv2 - and the sides are x.
Multiply the inscribed angle by 2