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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 an integer?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Corresponding sides of similar triangles are in proportion.
All positive and negative whole numbers - and zero.
B^m*b^n = b^m+n

2. What is a Venn diagram?
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 equation that states that two ratios are equivalent. 4/6 = 10/15
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
0 is the only number that is neither positive nor negative.

3. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
0 is a multiple of every integer.
Set x = 0 - and solve.
(x + y)(x - y) = x^2 - y^2

4. Law of exponents 5
A^m/b^m = (a/b)^m
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If a is negative and b is positive - then a < 0 < b.

5. What is a prime number?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 90°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.

6. Properties of one 1
Avg = sum of n numbers/n
For any number a: a * 1 = a and a / 1 = a.
B^m/b^n = b^m-n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

7. What is p?
For any integer n: 1^n = 1.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number n: x^-n means 1/x^n.

8. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
M = (y2 - y1)/(x2 - x1)
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.
Then the quotient y/x is a constant.

9. In a circle of radius r - what is the formula for the circumference?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
C = p2r
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

10. 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.
A fraction whose denominator is 100 i.e. 17% = 17/100
V = pr^2h
Divide - then multiply by 100.

11. What is a percent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An integer greater than one that is not prime.
Set x = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100

12. Properties of zero 5
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent over 100 and reduce.
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.

13. Properties of one 2
For any integer n: 1^n = 1.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Their sum is 90°.
Shifted down 2 units.

14. What is the formula for the volume of a rectangular solid?
V = lwh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.
1 is a divisor (or factor) of every integer.

15. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
Divide - then multiply by 100.
For any integer n: 1^n = 1.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

16. What is special formula for the area of an equilateral triangle?
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.
0 is the only number that is neither positive nor negative.
Their sum is 90°.
A = [(s^2*v3)/4]

17. What does it mean if y is directly proportional to x?
V = lwh
A fraction whose denominator is 100 i.e. 17% = 17/100
Cannot is 0 - must is 1 - all others are in between.
Then the quotient y/x is a constant.

18. What is the formula for the surface area of a rectangular solid?
Write the percent over 100 and reduce.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = lwh
A = 2(lw + lh + hw)

19. What is a negative exponent?
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
All positive and negative whole numbers - and zero.
For any number n: x^-n means 1/x^n.

20. How do you calculate percent increases and decreases?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
A = (1/2)bh.

21. What is an exponent?
A = 2(lw + lh + hw)
Their sum is 180°.
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.

22. If the product of two or more numbers is 0 - what do you know about the numbers?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
At least one of the factors is 0.

23. What are the properties of a parallelogram?
1 is the smallest positive odd integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The set of all ordered pairs (x -y) such that y = f(x).

24. What is true about the measures of the four angles formed by two intersecting lines?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
360°
The product of their slopes is -1 (negative reciprocal).

25. What is a function?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted left 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

26. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
At least one of the factors is 0.

27. How do you find the length of an arc of a circle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Write the percent as a decimal - and multiply.
A^m*b^m = (ab)^m
Arc = (x°/360)(2pr) where x is the central angle.

28. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Area = (x°/360)(pr^2) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(Circumference/diameter) of a circle - or approximately 3.14.

29. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
C = p2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted up 2 units.
An integer greater than one that is not prime.

30. What is the sum of the measures of all angles around a point?
Their sum is 180°.
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 = 2(lw + lh + hw)
No matter how many angles there are - the sum around the point is 360°.

31. What is the sum of the measures of the n angles of a polygon with n sides?
Shifted left 2 units.
Corresponding sides of similar triangles are in proportion.
(n - 2)(180°)
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.

32. How do you convert a percent to a fraction or a decimal?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent over 100 and reduce.

33. What is true about the measures of the three angles in a triangle?
Corresponding sides of similar triangles are in proportion.
Their sum is 180°.
D = 2r
For any integer n: 1^n = 1.

34. Important binomial 1
No matter how many angles there are - the sum around the point is 360°.
C = p2r
(x + y)(x - y) = x^2 - y^2
Shifted right 2 units.

35. How do you find the y-intercept of a graph?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Set x = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.
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.

36. What is the sum of the measures of the four angles in a quadrilateral?
Area = (x°/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°

37. What is the relationship between a radius of a circle and a line that is tangent to the circle?
The ratio of corresponding sides of similar triangles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Then the product xy is a constant.
C = p2r

38. What is true about the measures of the two acute angles in a right triangle?
Shifted right 2 units.
Their sum is 90°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.

39. What is true about the slopes of parallel lines?
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3
Equal slopes.
A = [(s^2*v3)/4]

40. Properties of one 3
A = 6(l^2)
A = [(s^2*v3)/4]
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.

41. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
They are both the same. A divisor or factor of an integer leaves no remainder.
Their sum is 180°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

42. What is the formula for the area of a triangle?
For any right triangle - a^2 + b^2 = c^2.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

43. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
Divide - then multiply by 100.
Area = (x°/360)(pr^2) where x is the central angle.
For any integer n: 1^n = 1.

44. Law of exponents 4
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]
A^m*b^m = (ab)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

45. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Area = (x°/360)(pr^2) where x is the central angle.
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 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.

46. Properties of one 4
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
Shifted down 2 units.
1 is the smallest positive odd integer.

47. How do you find the slope of a line?
A^m*b^m = (ab)^m
An angle formed by extending the side of the polygon.
M = (y2 - y1)/(x2 - x1)
In the expression x^b - x is the base and b is the exponent.

48. Properties of square roots
0 is the only number that is neither positive nor negative.
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
M = (y2 - y1)/(x2 - x1)

49. What are the important properties of 30-60-90 triangle?
Corresponding sides of similar triangles are in proportion.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Is a right triangle with a ratio of sides x:xv3:2x.
V = l^3

50. Law of exponents 2
A^m/b^m = (a/b)^m
B^m/b^n = b^m-n
(Circumference/diameter) of a circle - or approximately 3.14.
180°. If two or more angles form a straight angle - their sum is 180°.