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. Standard form of the equation of a parabola.
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4
y = a(x-h)² + k - where the vertex is (h -k)
The greatest common factor is 1 - but the numbers are not necessarily prime.
(y-k)²/a² - (x-h)²/b² = 1

2. Volume of a pyramid
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
V = (1/3)bh
Parentheses - exponents - multiplication - division - addition - subtraction
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

3. If a function is of the nth degree - what is the maximum number of extreme bumps it can have?
(1-r/1-r)
N-1
A = ((s1 + s2)h) / 2
(x-h)²/a² - (y-k)²/b² = 1

4. Formula for arc length
Parentheses - exponents - multiplication - division - addition - subtraction
A = ((s1 + s2)h) / 2
Arc length equals = (degree of the arc / 360)(circumference)
V= (1/3)(pr²h)

5. Standard form for a hyperbola that opens vertically
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.
Their dot product = 0
(y-k)²/a² - (x-h)²/b² = 1
180°

6. What is the triangle inequality rule?
The greatest common factor is 1 - but the numbers are not necessarily 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.
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 = a(x-h)² + k - where the vertex is (h -k)

7. Sum of 2 Angles Formulas
(y-k)²/a² - (x-h)²/b² = 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)]
Final amount = original amount x (1+growth rate)^number of changes

8. What are relatively prime numbers?
An = a1 + (n-1)d
N-1
The greatest common factor is 1 - but the numbers are not necessarily prime.
Arc length equals = (degree of the arc / 360)(circumference)

9. What are the conversion equations for polar coordinates to normal coordinates?
A = (degree of the arc / 360)(area of a circle)
An = a1 + (n-1)d
SA = 4pr²
x=rcos?(theta) y=rsin? (theta)

10. Where is tangent positive/negative?
V= (1/3)(pr²h)
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
A = ((s1 + s2)h) / 2
Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4

11. Formula for the volume of a cone
F(x) = -f(-x)
(x-h)²/a² - (y-k)²/b² = 1
V= (1/3)(pr²h)
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)]

12. Supplementary angles add up to
V = (4/3)pr³
(n/2)(a1 + an)
180°
a1 / 1-r

13. 45-45-90 triangle
SA = pr² +prl
Hypotenuse is xv2 - and the sides are x.
x=rcos?(theta) y=rsin? (theta)
Parentheses - exponents - multiplication - division - addition - subtraction

14. Standard form for a hyperbola that opens to the sides
(x-h)²/a² - (y-k)²/b² = 1
Adding or subtracting 180 to ? and reversing the sign of r.
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
D= sv3

15. 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.
x=rcos?(theta) y=rsin? (theta)
N-1
Parentheses - exponents - multiplication - division - addition - subtraction

16. Double Angle Formulas
Hypotenuse is 2x - short side is x - long side is xv3
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
(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.
Two sides and two angle are equal

17. Formula for calculation exponential growth
x=rcos?(theta) y=rsin? (theta)
An = a1rn?¹
Final amount = original amount x (1+growth rate)^number of changes
The greatest common factor is 1 - but the numbers are not necessarily prime.

18. Isosceles Triangles
y-y1 = m(x-x1)
(x-h)²/a² - (y-k)²/b² = 1
Their dot product = 0
Two sides and two angle are equal

19. Pythagorean Identities
An = a1rn?¹
A = (degree of the arc / 360)(area of a circle)
Their dot product = 0
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x

20. Surface area of a sphere
D = v(l²+w²+h²)
V = (1/3)bh
V= (1/3)(pr²h)
SA = 4pr²

21. Formula for the diagonal length of a cube
Between the vertex and the minor axis on the major axis
180°
N!
D= sv3

22. 30-60-90 triangle
180°
Multiply the inscribed angle by 2
Hypotenuse is 2x - short side is x - long side is xv3
Two sides and two angle are equal

23. Define an odd function.
F(x) = -f(-x)
Hypotenuse is xv2 - and the sides are x.
y = a(x-h)² + k - where the vertex is (h -k)
N-1

24. Formula for the area of a trapezoid
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
SA = pr² +prl
An = a1 + (n-1)d
A = ((s1 + s2)h) / 2

25. Combination formula
C² = a² + b² - 2abcos(C)
Hypotenuse is xv2 - and the sides are x.
x=rcos?(theta) y=rsin? (theta)
NCr = nPr / r! = n! / (n-r)!r!

26. How can you determine the arc degree or central angle of an inscribed angle?
Their dot product = 0
Multiply the inscribed angle by 2
A = ((s1 + s2)h) / 2
All whole numbers except for 0

27. Sum of finite geometric series
Between the vertex and the minor axis on the major axis
F(x) = -f(-x)
Arc length equals = (degree of the arc / 360)(circumference)
(1-r/1-r)

28. Sum of infinite geometric series
All whole numbers except for 0
N-1
(n/2)(a1 + an)
a1 / 1-r

29. Surface area of a cone
(n-2)180
F(x) = f(-x)
x = -b/2a y= c - (b²/4a)
SA = pr² +prl

30. Define an even function.
y-y1 = m(x-x1)
D= sv3
F(x) = f(-x)
NPr = n! / (n-r)!

31. If the general parabola equation is y = ax²+bx+c - what is the vertex of the parabola
(x-h)²/a² - (y-k)²/b² = 1
Hypotenuse is xv2 - and the sides are x.
x = -b/2a y= c - (b²/4a)
The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides.

32. What is the sum of the interior angles for a polygon with n sides?
180°
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.
(n-2)180

33. Standard form equation for an ellipse
NCr = nPr / r! = n! / (n-r)!r!
180°
Hypotenuse is 2x - short side is x - long side is xv3
(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.

34. How many ways can n elements be ordered?
Parentheses - exponents - multiplication - division - addition - subtraction
N!
a1 / 1-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)]

35. Formula for arithmetic sequence
An = a1 + (n-1)d
F(x) = f(-x)
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
NPr = n! / (n-r)!

36. What is the form of a polar coordinate?
(r - ?) - where r is the distance from the origin and ? is the angle from the positive x-axis
Their dot product = 0
a1 / 1-r
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x

37. In an ellipse - where are the foci?
V= (1/3)(pr²h)
(y-k)²/a² - (x-h)²/b² = 1
180°
Between the vertex and the minor axis on the major axis

38. Volume of a sphere
SA = pr² +prl
(y-k)²/a² - (x-h)²/b² = 1
A = (degree of the arc / 360)(area of a circle)
V = (4/3)pr³

39. Scalene triangle
No equal sides and no equal angles
All whole numbers except for 0
x=rcos?(theta) y=rsin? (theta)
F(x) = f(-x)

40. How to determine if a number is prime
Hypotenuse is xv2 - and the sides are x.
A = (degree of the arc / 360)(area of a circle)
V= (1/3)(pr²h)
Approximate a square root - then try to divide the number by all prime numbers below the approximated root

41. Sum of n terms of an arithmetic sequence
Hypotenuse is 2x - short side is x - long side is xv3
Adding or subtracting 180 to ? and reversing the sign of r.
(n/2)(a1 + an)
Arc length equals = (degree of the arc / 360)(circumference)

42. Two vectors are perpendicular if
D= sv3
Sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x
(n/2)(a1 + an)
Their dot product = 0

43. How can multiple polar coordinates be made?
An = a1 + (n-1)d
Adding or subtracting 180 to ? and reversing the sign of r.
V = (4/3)pr³
Arc length equals = (degree of the arc / 360)(circumference)

44. How to find the distance between two points in 3d plane?
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
y = a(x-h)² + k - where the vertex is (h -k)
N!
Square the differences between each coordinate - then square root the sum

45. Formula for the area of a sector
NPr = n! / (n-r)!
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)]
An = a1 + (n-1)d

46. If the point for a line is given as (x1 - y1) - write the equation for the line in point-slope form.
D= sv3
y-y1 = m(x-x1)
NPr = n! / (n-r)!
Multiply the inscribed angle by 2

47. Difference between 2 Angles formulas
Sin2x= 2sinxcosx cos2x = cos²x - sin²x = 2cos²x - 1 = 1 - sin²x
An = a1 + (n-1)d
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)]

48. Permutation formula (ordering)
No equal sides and no equal angles
NPr = n! / (n-r)!
All whole numbers except for 0
V = (1/3)bh

49. What are natural numbers?
All whole numbers except for 0
(n-2)180
Approximate a square root - then try to divide the number by all prime numbers below the approximated root
V= (1/3)(pr²h)

50. Standard form equation for circle
Square the differences between each coordinate - then square root the sum
Multiply the inscribed angle by 2
(x-h)² + (y-k)² = r² - where (h -k) is the center of the circle
No equal sides and no equal angles