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SAT Math Subject Test 1 And 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. Cylinder inscribed in a sphere

2. Long diagonal of a cylinder
Two sets of 45-45-90 right triangles (with side measures of x - x - and xroot2
Cylinder
Circumscribed
D^2 = 4r^2 + h^2 (pythagorean theorem)

3. Surface area of a cube
V = lwh
SA = 6s^2
A = h/2 (b1 + b2)
x^2 - y^2

4. Volume of a sphere
1. each of the four interior angles measures 90 degrees 2. diagonals of a rectangle are of equal length
Cone
(4/3)pir^3
And

5. 2 additional properties of a rectangle
Inscribed
Remainder (note all remainders are always integers)
(degree/360) x 2pir
1. each of the four interior angles measures 90 degrees 2. diagonals of a rectangle are of equal length

6. Time =
Original x (1 + rate)^number of changes
Distance / rate
1. each of the four interior angles measures 90 degrees 2. diagonals of a rectangle are of equal length
(n-2)180 (divide this by n to find individual angle measures)

7. Relation between central angle and minor arc
D = sroot3
Both will be same fraction of circle (60 degrees = 1/6 of circle)
F = sroot2
The angle is a right angle

8. Area of a parallelogram (geometry)
V = s^3
Both will be same fraction of circle (60 degrees = 1/6 of circle)
Cone
A = bh (h is hight from base to vertex and creating a right angle)

9. Long diagonal of a cube
Distance / rate
Sum of the area of each face (no definite equation)
F = sroot2
D = sroot3

10. Volume of a rectangular solid
V = lwh
The angle is a right angle
Original x (1 - rate)^number of changes
V= pir^2h

11. In an inequality - what conjunction is used with less than
SA = pirl + pir^2 (where l is slant of cone)
Proportion (ratio is same)
Distance / rate
And

12. Area of a sector
Sphere's diameter is equal to diagonal of rectangle formed by cylinder's height and diameter (other words - diagonal of cylinder equals sphere's diameter)
x^2 - y^2
Inscribed angle will be half of arc (and therefore half of central angle)
(degree/360) x pir^2

13. Sphere inscribed in a cylinder
V = lwh
A = bh (both sides of the rectangle)
Both solids have same diameter
1. opposite angles in a parallelogram are equal 2. adjacent angles in a parallelogram are supplementary; they add up to 180 degrees (think transversal) 3. opposite sides in a parallelogram are of equal length 4. diagonals of a parallelogram bisect ea

14. Surface area of a cone
Proportion (ratio is same)
SA = pirl + pir^2 (where l is slant of cone)
SA = 2pir^2 + 2pirh
1. opposite angles in a parallelogram are equal 2. adjacent angles in a parallelogram are supplementary; they add up to 180 degrees (think transversal) 3. opposite sides in a parallelogram are of equal length 4. diagonals of a parallelogram bisect ea

15. Area of a rectangle
1. all sides are same length 2. all angles are same size
V= pir^2h
SA = 2lw + 2hw + 2lh
A = bh (both sides of the rectangle)

16. Right triangle rotated around one leg
Cone
Original x (1 + rate)^number of changes
Diameter of sphere is equal to length of cube's side
Or

17. What 2 properties does an isosceles triangle have?
A = absinx (where x is the angle between sides a and b)
1. distances from points of tangency will be equal on both sides 2. Angle created will be equal at circle's center 3. Will create right angles on both sides at point of tangency
1. two equal sides 2. two equal angles of those sides
Inscribed angle will be half of arc (and therefore half of central angle)

18. What two triangles compose a square?
Two sets of 45-45-90 right triangles (with side measures of x - x - and xroot2
A = 1/2bh
And
Original x (1 + rate)^number of changes

19. Circumference of a circle
C = 2pir (or C = pi x d)
(degree/360) x 2pir
A = h/2 (b1 + b2)
A = bh (h is hight from base to vertex and creating a right angle)

20. Surface area of a sphere
A= pir^2
Original x (1 - rate)^number of changes
SA 4pir^2
(degree/360) x 2pir

21. a shape that is in another shape - placed inside that shape with tightest fit possible
Inscribed
SA = 6s^2
Cone
And

22. Area of a triangle (trig)
A = absinx (where x is the angle between sides a and b)
A = 1/2absinx (where x is included angle of sides a and b)
1. all sides are same length 2. all angles are same size
1. two equal sides 2. two equal angles of those sides

23. Relation between inscribed angle and minor arc
D^2 = 4r^2 + h^2 (pythagorean theorem)
SA = 6s^2
Right angle formed from height radius and slant
Inscribed angle will be half of arc (and therefore half of central angle)

24. 4 Properties of a parallelogram
1. opposite angles in a parallelogram are equal 2. adjacent angles in a parallelogram are supplementary; they add up to 180 degrees (think transversal) 3. opposite sides in a parallelogram are of equal length 4. diagonals of a parallelogram bisect ea
A = 1/2bh
Cone
(degree/360) x 2pir

25. Average pie
(n-2)180 (divide this by n to find individual angle measures)
A = absinx (where x is the angle between sides a and b)
Total = number of things x average
1. all sides are same length 2. all angles are same size

26. Sphere inscribed in a cube

27. An integer that has exactly two distinct factors: itself and 1
A = 1/2absinx (where x is included angle of sides a and b)
Prime number (2 is only even prime number - 1 and 0 are not prime)
A= pir^2
Inscribed angle will be half of arc (and therefore half of central angle)

28. Area of a circle
Two sets of 45-45-90 right triangles (with side measures of x - x - and xroot2
A= pir^2
Cone
A = s^2 A = d^2/2 (where d is long diagonal 45 45 90 triangle)

29. Surface area of a cylinder
SA 4pir^2
Sum of the area of each face (no definite equation)
Both solids have same diameter
SA = 2pir^2 + 2pirh

30. Main property of a cone
A = h/2 (b1 + b2)
SA = 2pir^2 + 2pirh
Both solids have same diameter
Right angle formed from height radius and slant

31. Cube or rectangular solid inscribed in a sphere
SA 4pir^2
A = bh (both sides of the rectangle)
Long diagonal of solid is equal to diameter of sphere
Inscribed

32. Area of a trapezoid
1. all sides are same length 2. all angles are same size
A = h/2 (b1 + b2)
Diameter of sphere is equal to length of cube's side
V = (1/3)bh (where b is the area of the base figure)

33. Surface area of a pyramid
Sum of the area of each face (no definite equation)
(4/3)pir^3
V = lwh
Long diagonal of solid is equal to diameter of sphere

34. (x+y)^2
Or
Cone
Prime number (2 is only even prime number - 1 and 0 are not prime)
x^2 + 2xy + y^2

35. Rectangle rotated around a central line or one side
Inscribed
SA = 6s^2
D^2 = a^2 + b^2 + c^2 (Super Pythagorean Theorem)
Cylinder

36. What do you use to solve for indirect variation?
(degree/360) x 2pir
Multiplication (product is same)
V = s^3
Right angle formed from height radius and slant

37. Area of a triangle (geometry)
Total = number of things x average
Diameter of sphere is equal to length of cube's side
A = 1/2bh
SA = 6s^2

38. Three properties of tangent lines extending from a point to a circle

39. What do you use to solve for direct variation?
Proportion (ratio is same)
Sphere's diameter is equal to diagonal of rectangle formed by cylinder's height and diameter (other words - diagonal of cylinder equals sphere's diameter)
Both will be same fraction of circle (60 degrees = 1/6 of circle)
(degree/360) x 2pir

40. Percent decrease
(degree/360) x 2pir
Original x (1 - rate)^number of changes
F = sroot2
The angle is a right angle

41. Surface area of a rectangular solid
A = 1/2bh
D^2 = a^2 + b^2 + c^2 (Super Pythagorean Theorem)
Circumscribed
SA = 2lw + 2hw + 2lh

42. Face diagonal of a cube
(degree/360) x pir^2
(n-2)180 (divide this by n to find individual angle measures)
Sum of the area of each face (no definite equation)
F = sroot2

43. Area of a parallelogram (trig)
A = 1/2bh
A = absinx (where x is the angle between sides a and b)
Multiplication (product is same)
V = s^3

44. The integer left over after dividing two numbers
V = s^3
Prime number (2 is only even prime number - 1 and 0 are not prime)
Remainder (note all remainders are always integers)
A = h/2 (b1 + b2)

45. (x-y)^2
A = bh (h is hight from base to vertex and creating a right angle)
Long diagonal of solid is equal to diameter of sphere
x^2 - 2xy + y^2
A = 1/2bh

46. (x+y)(x-y)
Distance / rate
Or
D^2 = a^2 + b^2 + c^2 (Super Pythagorean Theorem)
x^2 - y^2

47. Volume of a cube
V = s^3
The angle is a right angle
SA = 2lw + 2hw + 2lh
V = (1/3)pir^2h

48. Volume of a pyramid
Both solids have same diameter
Sum of the area of each face (no definite equation)
V = (1/3)bh (where b is the area of the base figure)
V = s^3

49. Long diagonal of a rectangular solid
Original x (1 + rate)^number of changes
x^2 + 2xy + y^2
Diameter of sphere is equal to length of cube's side
D^2 = a^2 + b^2 + c^2 (Super Pythagorean Theorem)

50. length of an arc
x^2 + 2xy + y^2
Or
V= pir^2h
(degree/360) x 2pir