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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 measure of a straight angle?
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.
A = 6(l^2)

2. In a circle of radius r - what is the formula for the diameter?
D = 2r
An angle formed by extending the side of the polygon.
A = pr^2
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.

3. What is an integer?
All positive and negative whole numbers - and zero.
Shifted down 2 units.
Shifted up 2 units.
A = 6(l^2)

4. In a circle of radius r - what is the formula for the area?
(b^m)^n = b^mn
Cannot is 0 - must is 1 - all others are in between.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = pr^2

5. What is true about the measures of the two acute angles in a right triangle?
For any integer n: 1^n = 1.
Their sum is 90°.
1 is a divisor (or factor) of every integer.
In the expression x^b - x is the base and b is the exponent.

6. Properties of zero 2
The set of all ordered pairs (x -y) such that y = f(x).
If a is negative and b is positive - then a < 0 < b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = pr^2h

7. What is the distributive law?
Write the percent as a decimal - and multiply.
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number a: a * 1 = a and a / 1 = a.

8. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
A = pr^2
Shifted left 2 units.

9. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = 2(lw + lh + hw)
Shifted up 2 units.
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°.
The product of their slopes is -1 (negative reciprocal).

10. What is a negative exponent?
A fraction whose denominator is 100 i.e. 17% = 17/100
For any number a: a * 1 = a and a / 1 = a.
A = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.

11. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = bh

12. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Arc = (x°/360)(2pr) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.

13. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Even numbers are divisible by 2 and odd numbers are not.
Arc = (x°/360)(2pr) where x is the central angle.

14. Properties of one 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number a: a * 1 = a and a / 1 = a.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = 6(l^2)

15. What is the graph of a function?
Set y = 0 - and solve.
The set of all ordered pairs (x -y) such that y = f(x).
360°
At least one of the factors is 0.

16. What is the area of a square?
V = pr^2h
1 is a divisor (or factor) of every integer.
A = bh
A = s^2 or A =d^2/2 where d is the diagonal

17. What does it mean if y is inversely proportional to x?
Set y = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the product xy is a constant.

18. What are the properties of a parallelogram?
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

19. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted up 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

20. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
Their sum is 90°.
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

21. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Avg = sum of n numbers/n

22. How do you find the slope of a line?
[(x1 + x2)/2] -[(y1 + y2)/2]
1 is the smallest positive odd integer.
M = (y2 - y1)/(x2 - x1)
At least one of the factors is 0.

23. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
[(x1 + x2)/2] -[(y1 + y2)/2]
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

24. What is a composite number?
V = lwh
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
Set x = 0 - and solve.

25. What formula is used for an average?
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°.
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.

26. What is the probability of an event that cannot occur? That must occur?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Cannot is 0 - must is 1 - all others are in between.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is a divisor (or factor) of every integer.

27. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
The ratio of corresponding sides of similar triangles.
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)

28. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
Then the quotient y/x is a constant.

29. What are the properties of a square?
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.
An angle formed by extending the side of the polygon.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = pr^2h

30. What is a multiple of an integer?
A = bh
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
A = (1/2)bh.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

31. What is a function?
(b^m)^n = b^mn
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.

32. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
C = p2r
A = [(s^2*v3)/4]
(x + y)(x - y) = x^2 - y^2

33. What is a fractional exponent?
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.
Shifted up 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(Circumference/diameter) of a circle - or approximately 3.14.

34. How do you find the length of an arc of a circle?
(n - 2)(180°)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.

35. Law of exponents 5
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A^m/b^m = (a/b)^m
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

36. 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.
At least one of the factors is 0.
No matter how many angles there are - the sum around the point is 360°.
(n - 2)(180°)

37. Law of exponents 2
All positive and negative whole numbers - and zero.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
B^m/b^n = b^m-n
Avg = sum of n numbers/n

38. What is a ratio?

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39. What are similar triangles?
Shifted down 2 units.
Their sum is 180°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

40. Law of exponents 3
For any number n: x^-n means 1/x^n.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(b^m)^n = b^mn
A = bh

41. Important binomial 2
Then the quotient y/x is a constant.
A = lw
Their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

42. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent over 100 and reduce.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.

43. What is the formula for the surface area of a cube?
A = 6(l^2)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.
They are both the same. A divisor or factor of an integer leaves no remainder.

44. What is p?
M = (y2 - y1)/(x2 - x1)
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is the smallest positive odd integer.
(Circumference/diameter) of a circle - or approximately 3.14.

45. Properties of one 3
For any right triangle - a^2 + b^2 = c^2.
1 is a divisor (or factor) of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.

46. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.
For any number b: b = -b if and only if b = 0.

47. How do you find the probability that an event will occur?
They are both the same. A divisor or factor of an integer leaves no remainder.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Divide - then multiply by 100.
Shifted up 2 units.

48. What is the formula for the volume of a rectangular solid?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = lwh

49. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
B^m/b^n = b^m-n
C = p2r

50. What is true about the measures of the four angles formed by two intersecting lines?
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.
No matter how many angles there are - the sum around the point is 360°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.