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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 exponent?
In the expression x^b - x is the base and b is the exponent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
V = l^3
V = lwh
[(x1 + x2)/2] -[(y1 + y2)/2]
360°

3. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Then the quotient y/x is a constant.
Their sum is 180°.

4. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number a: a * 1 = a and a / 1 = a.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = l^3

5. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
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.
For any number b: b = -b if and only if b = 0.

6. Properties of square roots
Set y = 0 - and solve.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted right 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. What is true about the slopes of parallel lines?
M = (y2 - y1)/(x2 - x1)
Shifted up 2 units.
Equal slopes.
360°

8. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set y = 0 - and solve.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Is a right triangle with a ratio of sides x:xv3:2x.

9. What does it mean if y is directly proportional to x?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Then the quotient y/x is a constant.
Shifted up 2 units.

10. What is an even and an odd number?
An integer greater than one that is not prime.
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.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.

11. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent as a decimal - and multiply.
Corresponding sides of similar triangles are in proportion.
The two pairs of opposite angles formed are equal to each other.

12. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
0 is a multiple of every integer.
Avg = sum of n numbers/n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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°.

13. What is true about the measures of the four angles formed by two intersecting lines?
Write the percent over 100 and reduce.
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
M = (y2 - y1)/(x2 - x1)

14. Properties of one 4
Equal slopes.
1 is the smallest positive odd integer.
(b^m)^n = b^mn
Divide - then multiply by 100.

15. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

16. Properties of zero 1
For any right triangle - a^2 + b^2 = c^2.
0 is the only number that is neither positive nor negative.
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.

17. What is an exterior angle of a triangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°
Area = (x°/360)(pr^2) where x is the central angle.

18. How do you calculate a weighted average?
B^m*b^n = b^m+n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The set of all ordered pairs (x -y) such that y = f(x).
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

19. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
An integer greater than one that is not prime.
A fraction whose denominator is 100 i.e. 17% = 17/100
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

20. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An angle formed by extending the side of the polygon.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

21. What is true about the measures of the three angles in a triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = (1/2)bh.
For any integer n: 1^n = 1.
Their sum is 180°.

22. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180°.
(b^m)^n = b^mn
All positive and negative whole numbers - and zero.

23. What are the median and the mode of a set of data?
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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^m/b^m = (a/b)^m

24. What are the quotient and the remainder?

25. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A^m/b^m = (a/b)^m
A = pr^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted left 2 units.

26. Properties of zero 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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If a is negative and b is positive - then a < 0 < b.
(x + y)(x - y) = x^2 - y^2

27. What is a negative exponent?
A = bh
For any number n: x^-n means 1/x^n.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)(x - y) = x^2 - y^2

28. What are the properties of a square?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
For any number n: x^-n means 1/x^n.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

29. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
180°. If two or more angles form a straight angle - their sum is 180°.
(b^m)^n = b^mn

30. What is the formula for the volume of a cylinder?
V = pr^2h
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.

31. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
They are both the same. A divisor or factor of an integer leaves no remainder.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
How steep the line is. Horizontal line = 0 - vertical has no slope.

32. What is an exterior angle of a polygon?
0 is the only number that is neither positive nor negative.
A = bh
An angle formed by extending the side of the polygon.
For any number n: x^-n means 1/x^n.

33. What is the formula for the surface area of a rectangular solid?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An angle formed by extending the side of the polygon.
A = 2(lw + lh + hw)

34. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Divide - then multiply by 100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.

35. What is the distance formula?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Then the quotient y/x is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

36. What is the Pythagorean theorem?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
For any right triangle - a^2 + b^2 = c^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.

37. In a circle of radius r - what is the formula for the diameter?
D = 2r
Divide - then multiply by 100.
(x + y)(x - y) = x^2 - y^2
An angle formed by extending the side of the polygon.

38. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
No matter how many angles there are - the sum around the point is 360°.
[(x1 + x2)/2] -[(y1 + y2)/2]
C = p2r

39. In a circle of radius r - what is the formula for the circumference?
Their sum is 90°.
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = pr^2

40. What is the probability of an event that cannot occur? That must occur?
Avg = sum of n numbers/n
Cannot is 0 - must is 1 - all others are in between.
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.
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.

41. Properties of zero 5
Their sum is 90°.
If a is negative and b is positive - then a < 0 < b.
The product of their slopes is -1 (negative reciprocal).
For any number b: b = -b if and only if b = 0.

42. How do you find the length of an arc of a circle?
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.
M = (y2 - y1)/(x2 - x1)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

43. For what values of a function is the function undefined?
A = [(s^2*v3)/4]
(Circumference/diameter) of a circle - or approximately 3.14.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

44. What is the formula for the volume of a rectangular solid?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = lwh
A fraction whose denominator is 100 i.e. 17% = 17/100

45. What is p?
All positive and negative whole numbers - and zero.
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.
Cannot is 0 - must is 1 - all others are in between.
(Circumference/diameter) of a circle - or approximately 3.14.

46. What is the relationship between a radius of a circle and a line that is tangent to the circle?
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.
Set y = 0 - and solve.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

47. What is a multiple of an integer?
Equal slopes.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

48. What are the properties of a rectangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
No matter how many angles there are - the sum around the point is 360°.

49. What is the sum of the measures of the n angles of a polygon with n sides?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Divide - then multiply by 100.
(n - 2)(180°)
The two pairs of opposite angles formed are equal to each other.

50. What is a divisor and a factor of an integer?
The two pairs of opposite angles formed are equal to each other.
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted left 2 units.
An integer greater than one that is not prime.