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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 y-intercept of a graph?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Set x = 0 - and solve.

2. In a circle of radius r - what is the formula for the circumference?
C = p2r
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
1 is a divisor (or factor) of every integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted down 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
360°
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.

4. What is true about the slopes of perpendicular lines?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The product of their slopes is -1 (negative reciprocal).
An integer greater than one that is not prime.
For any right triangle - a^2 + b^2 = c^2.

5. How do you calculate a weighted average?
For any number b: b = -b if and only if b = 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
180°. If two or more angles form a straight angle - their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

6. What is a composite number?
An integer greater than one that is not prime.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.

7. How do you find the slope of a line?
(b^m)^n = b^mn
For any right triangle - a^2 + b^2 = c^2.
M = (y2 - y1)/(x2 - x1)
D = 2r

8. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If a is negative and b is positive - then a < 0 < b.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = s^2 or A =d^2/2 where d is the diagonal

9. What are the important properties of a 45-45 - 90 triangle?
The product of their slopes is -1 (negative reciprocal).
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Divide - then multiply by 100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

10. How do you find the x-intercept of a graph?
The two pairs of opposite angles formed are equal to each other.
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Set y = 0 - and solve.

11. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A = 2(lw + lh + hw)
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
Shifted up 2 units.

12. How do you find a percent of a number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent as a decimal - and multiply.
A = 6(l^2)
V = lwh

13. What is a prime number?
At least one of the factors is 0.
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 a multiple of every integer.
A^m*b^m = (ab)^m

14. How do you convert a percent to a fraction or a decimal?
(x + y)(x - y) = x^2 - y^2
M = (y2 - y1)/(x2 - x1)
A = 2(lw + lh + hw)
Write the percent over 100 and reduce.

15. Properties of one 4
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is the only number that is neither positive nor negative.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.

16. What is the triangle inequality?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = s^2 or A =d^2/2 where d is the diagonal
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.

17. What is true about the measures of the four angles formed by two intersecting lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
Arc = (x°/360)(2pr) where x is the central angle.

18. What is a divisor and a factor of an integer?
Shifted down 2 units.
Set x = 0 - and solve.
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.

19. What is the measure of a straight angle?
If a is negative and b is positive - then a < 0 < b.
180°. If two or more angles form a straight angle - their sum is 180°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

20. What are similar triangles?
D = 2r
No matter how many angles there are - the sum around the point is 360°.
A = [(s^2*v3)/4]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

21. What is an exterior angle of a polygon?
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.
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°.
An angle formed by extending the side of the polygon.
180°. If two or more angles form a straight angle - their sum is 180°.

22. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
V = l^3
Cannot is 0 - must is 1 - all others are in between.

23. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
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.
Set y = 0 - and solve.
Equal slopes.

24. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
A = bh
V = lwh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

25. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
An angle formed by extending the side of the polygon.
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]

26. What is a Venn diagram?
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

27. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
[(x1 + x2)/2] -[(y1 + y2)/2]
An integer greater than one that is not prime.
For any number n: x^-n means 1/x^n.

28. Properties of one 2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Then the product xy is a constant.
For any integer n: 1^n = 1.
At least one of the factors is 0.

29. What is the sum of the measures of the four angles in a quadrilateral?
A = (1/2)bh.
M = (y2 - y1)/(x2 - x1)
360°
A = s^2 or A =d^2/2 where d is the diagonal

30. What important property do similar triangles have?
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.
Corresponding sides of similar triangles are in proportion.
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.

31. Important binomial 2
A = s^2 or A =d^2/2 where d is the diagonal
Is a right triangle with a ratio of sides x:xv3:2x.
All positive and negative whole numbers - and zero.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

32. Law of exponents 1
All positive and negative whole numbers - and zero.
For any number b: b = -b if and only if b = 0.
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.
B^m*b^n = b^m+n

33. What is the formula for the surface area of a cube?
A = 6(l^2)
1 is a divisor (or factor) of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number n: x^-n means 1/x^n.

34. For what values of a function is the function undefined?
M = (y2 - y1)/(x2 - x1)
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = pr^2

35. In a circle of radius r - what is the formula for the diameter?
Write the percent over 100 and reduce.
D = 2r
A^m/b^m = (a/b)^m
The product of their slopes is -1 (negative reciprocal).

36. Properties of zero 4
1 is a divisor (or factor) of every integer.
All positive and negative whole numbers - and zero.
A = pr^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

37. What are the median and the mode of a set of data?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The ratio of corresponding sides of similar triangles.
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.
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.

38. What is the formula for the area of a rectangle?
A = [(s^2*v3)/4]
A = lw
A = bh
180°. If two or more angles form a straight angle - their sum is 180°.

39. 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The set of all ordered pairs (x -y) such that y = f(x).
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

40. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = [(s^2*v3)/4]
Their sum is 90°.

41. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is the smallest positive odd integer.
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

42. What is the formula for the volume of a cylinder?
Avg = sum of n numbers/n
An integer greater than one that is not prime.
The ratio of corresponding sides of similar triangles.
V = pr^2h

43. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
V = lwh
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.
Shifted right 2 units.
In the expression x^b - x is the base and b is the exponent.

44. Properties of square roots
How steep the line is. Horizontal line = 0 - vertical has no slope.
C = p2r
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

45. Law of exponents 5
Cannot is 0 - must is 1 - all others are in between.
1 is a divisor (or factor) of every integer.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A^m/b^m = (a/b)^m

46. What is the formula for the area of a parallelogram?
(Circumference/diameter) of a circle - or approximately 3.14.
A = bh
Area = (x°/360)(pr^2) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

47. What do we mean by the slope of the line?
A = pr^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = bh
The product of their slopes is -1 (negative reciprocal).

48. What are the sum - difference - products - and quotient of two numbers?
(n - 2)(180°)
If a is negative and b is positive - then a < 0 < b.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

49. What is the formula for the surface area of a rectangular solid?
Then the product xy is a constant.
A = 2(lw + lh + hw)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
All positive and negative whole numbers - and zero.

50. What is an integer?
A^m*b^m = (ab)^m
All positive and negative whole numbers - and zero.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.