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GRE Math: Facts

Subjects : gre, 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. What is the formula for the volume of a cylinder?
1 is a divisor (or factor) of every integer.
An integer greater than one that is not prime.
V = pr^2h
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

2. What is the triangle inequality?
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
V = pr^2h
Even numbers are divisible by 2 and odd numbers are not.

3. What is the square root of a number?
Their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = (1/2)bh.

4. What are the properties of a rectangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

5. Properties of zero 1
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Area = (x°/360)(pr^2) where x is the central angle.
0 is the only number that is neither positive nor negative.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

6. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
A = pr^2
Set y = 0 - and solve.
Their sum is 90°.

7. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.
A fraction whose denominator is 100 i.e. 17% = 17/100

8. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
Area = (x°/360)(pr^2) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

9. In a circle of radius r - what is the formula for the diameter?
D = 2r
A = pr^2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°

10. What is a negative exponent?
A = pr^2
Arc = (x°/360)(2pr) where x is the central angle.
A = (1/2)bh.
For any number n: x^-n means 1/x^n.

11. What is true about the slopes of parallel lines?
Shifted up 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = 2(lw + lh + hw)
Equal slopes.

12. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
The set of all ordered pairs (x -y) such that y = f(x).
An angle formed by extending the side of the polygon.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

14. How do you calculate a weighted average?
A = (1/2)bh.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
In the expression x^b - x is the base and b is the exponent.
How steep the line is. Horizontal line = 0 - vertical has no slope.

15. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
360°
Shifted left 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

16. What is a composite number?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An integer greater than one that is not prime.
V = l^3

17. How do you find the area of a sector of a circle?
At least one of the factors is 0.
Area = (x°/360)(pr^2) where x is the central angle.
The ratio of corresponding sides of similar triangles.
Set y = 0 - and solve.

18. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The set of all ordered pairs (x -y) such that y = f(x).
The ratio of corresponding sides of similar triangles.
Shifted right 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

19. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw
1 is a divisor (or factor) of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. What is an even and an odd number?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)

21. What is true about the measures of the four angles formed by two intersecting lines?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The two pairs of opposite angles formed are equal to each other.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

22. What is the formula for the surface area of a rectangular solid?
360°
A = 2(lw + lh + hw)
A = 6(l^2)
C = p2r

23. What are similar triangles?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.

24. What are the median and the mode of a set of data?
A^m*b^m = (ab)^m
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An integer greater than one that is not prime.

25. What is the sum of the measures of the four angles in a quadrilateral?
Their sum is 90°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = pr^2h
360°

26. What is p?
An integer greater than one that is not prime.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number b: b = -b if and only if b = 0.
Then the product xy is a constant.

27. What are the properties of a parallelogram?
For any number a: a * 1 = a and a / 1 = a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

28. Law of exponents 2
B^m/b^n = b^m-n
A = pr^2
1 is the smallest positive odd integer.
(n - 2)(180°)

29. What is an exponent?
A^m/b^m = (a/b)^m
In the expression x^b - x is the base and b is the exponent.
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]

30. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.
The two pairs of opposite angles formed are equal to each other.
V = lwh

31. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number n: x^-n means 1/x^n.

32. Law of exponents 5
Equal slopes.
An angle formed by extending the side of the polygon.
A^m/b^m = (a/b)^m
V = pr^2h

33. Properties of one 2
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
360°

34. Properties of zero 3
For any number b: b = -b if and only if b = 0.
0 is a multiple of every integer.
(n - 2)(180°)
1 is the smallest positive odd integer.

35. What is the probability of an event that cannot occur? That must occur?
360°
Cannot is 0 - must is 1 - all others are in between.
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).

36. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted left 2 units.
Cannot is 0 - must is 1 - all others are in between.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

37. What does it mean if y is inversely proportional to x?
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the product xy is a constant.
Even numbers are divisible by 2 and odd numbers are not.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

38. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(b^m)^n = b^mn
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = 6(l^2)

39. What is the formula for the area of a rectangle?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = lw
A = (1/2)bh.
How steep the line is. Horizontal line = 0 - vertical has no slope.

40. How do we write the equation of a line?
A = 6(l^2)
A fraction whose denominator is 100 i.e. 17% = 17/100
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number b: b = -b if and only if b = 0.

41. What is the sum of the measures of all angles around a point?
For any number b: b = -b if and only if b = 0.
No matter how many angles there are - the sum around the point is 360°.
Shifted down 2 units.
All positive and negative whole numbers - and zero.

42. What is the distributive law?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Area = (x°/360)(pr^2) where x is the central angle.

43. Properties of one 4
1 is the smallest positive odd integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.

44. What are the properties of a square?
For any number b: b = -b if and only if b = 0.
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
V = lwh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

45. What is an integer?
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
All positive and negative whole numbers - and zero.

46. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
V = pr^2h
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

47. What formula is used for an average?
For any number n: x^-n means 1/x^n.
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
Divide - then multiply by 100.
Avg = sum of n numbers/n

48. What is the relationship between a radius of a circle and a line that is tangent to the circle?
For any right triangle - a^2 + b^2 = c^2.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = lwh

49. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

50. What is a fractional exponent?
Set x = 0 - and solve.
A = s^2 or A =d^2/2 where d is the diagonal
For any integer n: 1^n = 1.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.