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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. How do you find the length of an arc of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Arc = (x°/360)(2pr) where x is the central angle.
C = p2r

2. Properties of one 2
[(x1 + x2)/2] -[(y1 + y2)/2]
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
For any integer n: 1^n = 1.

3. If you were given the graph of y = f(x) - what does f(a) represent?
V = pr^2h
360°
At least one of the factors is 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

4. 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.
Then the product xy is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

5. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
For any number n: x^-n means 1/x^n.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

6. What is the ratio of similitude?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°
A = s^2 or A =d^2/2 where d is the diagonal
The ratio of corresponding sides of similar triangles.

7. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = pr^2h
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.
A = bh

8. What is the midpoint formula?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A fraction whose denominator is 100 i.e. 17% = 17/100

9. Properties of zero 1
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is the only number that is neither positive nor negative.
For any right triangle - a^2 + b^2 = c^2.

10. What is the formula for the surface area of a cube?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = 6(l^2)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

11. What do we mean by the slope of the line?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
How steep the line is. Horizontal line = 0 - vertical has no slope.
D = 2r
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

12. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal
Write the percent as a decimal - and multiply.

13. What is a multiple of an integer?
Set x = 0 - and solve.
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.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

14. 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.
V = pr^2h
The set of all ordered pairs (x -y) such that y = f(x).
For any right triangle - a^2 + b^2 = c^2.

15. How do you find the y-intercept of a graph?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set x = 0 - and solve.
For any number n: x^-n means 1/x^n.
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.

16. Properties of zero 3
0 is a multiple of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any right triangle - a^2 + b^2 = c^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15

17. Properties of zero 5
A = lw
180°. If two or more angles form a straight angle - their sum is 180°.
An integer greater than one that is not prime.
For any number b: b = -b if and only if b = 0.

18. Important binomial 2
Set y = 0 - and solve.
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
(b^m)^n = b^mn

19. What is an exterior angle of a polygon?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted right 2 units.
An angle formed by extending the side of the polygon.

20. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
A^m*b^m = (ab)^m

21. How you convert a fraction or a decimal to a percent?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Divide - then multiply by 100.
360°
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
V = pr^2h
A = bh
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

23. What are the properties of a rectangle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
They are both the same. A divisor or factor of an integer leaves no remainder.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

24. What is a percent?
Write the percent over 100 and reduce.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(x + y)(x - y) = x^2 - y^2
A fraction whose denominator is 100 i.e. 17% = 17/100

25. In a circle of radius r - what is the formula for the area?
(n - 2)(180°)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = pr^2

26. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

27. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
For any integer n: 1^n = 1.
An angle formed by extending the side of the polygon.
Shifted up 2 units.

28. If the product of two or more numbers is 0 - what do you know about the numbers?
0 is a multiple of every integer.
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.
If a is negative and b is positive - then a < 0 < b.
At least one of the factors is 0.

29. Law of exponents 2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
B^m/b^n = b^m-n
A = lw
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. What is an integer?
V = lwh
For any integer n: 1^n = 1.
No matter how many angles there are - the sum around the point is 360°.
All positive and negative whole numbers - and zero.

31. What is the measure of a straight angle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

32. For what values of a function is the function undefined?
Equal slopes.
A = pr^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

33. 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.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

34. Properties of one 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = l^3
For any number a: a * 1 = a and a / 1 = a.
Then the quotient y/x is a constant.

35. What is p?
B^m/b^n = b^m-n
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

36. In a circle of radius r - what is the formula for the circumference?
(Circumference/diameter) of a circle - or approximately 3.14.
Then the quotient y/x is a constant.
C = p2r
The set of all ordered pairs (x -y) such that y = f(x).

37. What is the formula for the volume of a rectangular solid?
At least one of the factors is 0.
V = lwh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.

38. 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.
Their sum is 90°.
Arc = (x°/360)(2pr) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

39. What is the Pythagorean theorem?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

40. Properties of one 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

41. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The set of all ordered pairs (x -y) such that y = f(x).
(b^m)^n = b^mn
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

42. Properties of square roots
V = pr^2h
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At least one of the factors is 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

43. What is a negative exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
[(x1 + x2)/2] -[(y1 + y2)/2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number n: x^-n means 1/x^n.

44. In a circle of radius r - what is the formula for the diameter?
A = lw
D = 2r
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

45. What is the probability of an event that cannot occur? That must occur?
(Circumference/diameter) of a circle - or approximately 3.14.
A = lw
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.

46. How do you find the x-intercept of a graph?
Arc = (x°/360)(2pr) where x is the central angle.
360°
Set y = 0 - and solve.
Divide - then multiply by 100.

47. Properties of zero 2
A fraction whose denominator is 100 i.e. 17% = 17/100
If a is negative and b is positive - then a < 0 < b.
Shifted down 2 units.
An integer greater than one that is not prime.

48. Law of exponents 4
Avg = sum of n numbers/n
A^m*b^m = (ab)^m
(Circumference/diameter) of a circle - or approximately 3.14.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

49. What are the important properties of 30-60-90 triangle?
[(x1 + x2)/2] -[(y1 + y2)/2]
They are both the same. A divisor or factor of an integer leaves no remainder.
Is a right triangle with a ratio of sides x:xv3:2x.
Their sum is 90°.

50. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set y = 0 - and solve.
Shifted up 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.