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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. Properties of zero 2
Shifted left 2 units.
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
If a is negative and b is positive - then a < 0 < b.

2. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
Their sum is 180°.

3. What are the sum - difference - products - and quotient of two numbers?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

4. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
360°
(Circumference/diameter) of a circle - or approximately 3.14.
Their sum is 180°.

5. Important binomial 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 180°.
An integer greater than one that is not prime.

6. What is the triangle inequality?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
Is a right triangle with a ratio of sides x:xv3:2x.
For any number a: a * 1 = a and a / 1 = a.

7. What is true about the measures of the three angles in a triangle?
Their sum is 90°.
Their sum is 180°.
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).

8. What is an exponent?
Even numbers are divisible by 2 and odd numbers are not.
C = p2r
In the expression x^b - x is the base and b is the exponent.
Their sum is 90°.

9. What is a negative exponent?
For any number n: x^-n means 1/x^n.
(x + y)(x - y) = x^2 - y^2
C = p2r
The two pairs of opposite angles formed are equal to each other.

10. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
A = s^2 or A =d^2/2 where d is the diagonal
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.

11. What is the graph of a function?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
C = p2r
Write the percent over 100 and reduce.
The set of all ordered pairs (x -y) such that y = f(x).

12. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Write the percent as a decimal - and multiply.
180°. If two or more angles form a straight angle - their sum is 180°.
360°

13. Law of exponents 5
B^m*b^n = b^m+n
The set of all ordered pairs (x -y) such that y = f(x).
A^m/b^m = (a/b)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

14. In a circle of radius r - what is the formula for the circumference?
For any number a: a * 1 = a and a / 1 = a.
360°
C = p2r
A^m/b^m = (a/b)^m

15. Properties of one 2
Set x = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(n - 2)(180°)
For any integer n: 1^n = 1.

16. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
The ratio of corresponding sides of similar triangles.
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.

17. What is p?
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.
1 is the smallest positive odd integer.
(Circumference/diameter) of a circle - or approximately 3.14.

18. What is the probability of an event that cannot occur? That must occur?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Cannot is 0 - must is 1 - all others are in between.
The ratio of corresponding sides of similar triangles.
A = bh

19. Properties of zero 3
A = s^2 or A =d^2/2 where d is the diagonal
0 is a multiple of every integer.
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°.
Equal slopes.

20. Properties of zero 5
Shifted down 2 units.
For any number b: b = -b if and only if b = 0.
The ratio of corresponding sides of similar triangles.
360°

21. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.

22. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = 6(l^2)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Is a right triangle with a ratio of sides x:xv3:2x.

23. What is an exterior angle of a polygon?
Avg = sum of n numbers/n
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. What is the formula for the area of a parallelogram?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = bh
For any number n: x^-n means 1/x^n.

25. What is special formula for the area of an equilateral triangle?
(x + y)(x - y) = x^2 - y^2
An angle formed by extending the side of the polygon.
A = [(s^2*v3)/4]
A = 6(l^2)

26. What are the properties of a square?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A^m*b^m = (ab)^m
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.

27. What are the quotient and the remainder?

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28. What is the formula for the area of a rectangle?
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh
Divide - then multiply by 100.

29. Properties of one 3
1 is a divisor (or factor) of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set x = 0 - and solve.

30. What are similar triangles?
Divide - then multiply by 100.
A = s^2 or A =d^2/2 where d is the diagonal
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

31. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Then the quotient y/x is a constant.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent as a decimal - and multiply.

32. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
Shifted up 2 units.
Shifted right 2 units.

33. What are the properties of a rectangle?
0 is the only number that is neither positive nor negative.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.

34. What is the relationship between a radius of a circle and a line that is tangent to the circle?
The product of their slopes is -1 (negative reciprocal).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted right 2 units.
For any right triangle - a^2 + b^2 = c^2.

35. What is a function?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
They are both the same. A divisor or factor of an integer leaves no remainder.
In the expression x^b - x is the base and b is the exponent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

36. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

37. What is an integer?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.
Shifted up 2 units.
C = p2r

38. How do you find the area of a sector of a circle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent over 100 and reduce.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Area = (x°/360)(pr^2) where x is the central angle.

39. Properties of zero 1
0 is the only number that is neither positive nor negative.
A = [(s^2*v3)/4]
Equal slopes.
A = bh

40. What is a percent?
V = l^3
Then the quotient y/x is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A fraction whose denominator is 100 i.e. 17% = 17/100

41. How do you find a percent of a number?
A^m*b^m = (ab)^m
V = lwh
Write the percent as a decimal - and multiply.
A = bh

42. What is the distance formula?
V = lwh
No matter how many angles there are - the sum around the point is 360°.
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

43. How do you calculate percent increases and decreases?
Shifted up 2 units.
M = (y2 - y1)/(x2 - x1)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m*b^n = b^m+n

44. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Arc = (x°/360)(2pr) where x is the central angle.
A = bh

45. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
If a is negative and b is positive - then a < 0 < b.
Equal slopes.
Their sum is 180°.

46. How do you calculate a weighted average?
Write the percent over 100 and reduce.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Corresponding sides of similar triangles are in proportion.
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.

47. Law of exponents 2
At least one of the factors is 0.
B^m/b^n = b^m-n
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A^m*b^m = (ab)^m

48. How you convert a fraction or a decimal to a percent?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent over 100 and reduce.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.

49. What is the sum of the measures of all angles around a point?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
No matter how many angles there are - the sum around the point is 360°.
A = s^2 or A =d^2/2 where d is the diagonal

50. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.
A = s^2 or A =d^2/2 where d is the diagonal