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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 convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
All positive and negative whole numbers - and zero.
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 product xy is a constant.

2. Properties of one 4
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°.
1 is the smallest positive odd integer.
All positive and negative whole numbers - and zero.
(Circumference/diameter) of a circle - or approximately 3.14.

3. What is the area of a square?
Then the quotient y/x is a constant.
0 is a multiple of every integer.
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

4. What are the sum - difference - products - and quotient of two numbers?
C = p2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

5. What is a negative exponent?
For any number a: a * 1 = a and a / 1 = a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any number n: x^-n means 1/x^n.
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.

6. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
A fraction whose denominator is 100 i.e. 17% = 17/100
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

7. What is the distributive law?
1 is the smallest positive odd integer.
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

8. In a circle of radius r - what is the formula for the area?
A = pr^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted down 2 units.
Set y = 0 - and solve.

9. What is the triangle inequality?
Then the quotient y/x is a constant.
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.
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.

10. What does it mean if y is inversely proportional to x?
0 is the only number that is neither positive nor negative.
Then the product xy is a constant.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is a multiple of every integer.

11. What is the sum of the measures of the four angles in a quadrilateral?
Then the product xy is a constant.
360°
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

12. What important property do similar triangles have?
The ratio of corresponding sides of similar triangles.
Shifted right 2 units.
Set y = 0 - and solve.
Corresponding sides of similar triangles are in proportion.

13. What does it mean if y is directly proportional to x?
A = lw
Then the quotient y/x is a constant.
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

14. Properties of square roots
M = (y2 - y1)/(x2 - x1)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.
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.

15. Properties of one 3
A = 2(lw + lh + hw)
180°. If two or more angles form a straight angle - their sum is 180°.
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

16. How do you find the area of a sector of a circle?
(b^m)^n = b^mn
Write the percent as a decimal - and multiply.
Area = (x°/360)(pr^2) where x is the central angle.
A^m/b^m = (a/b)^m

17. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At least one of the factors is 0.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Corresponding sides of similar triangles are in proportion.

18. For what values of a function is the function undefined?
V = lwh
A = lw
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

19. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = 6(l^2)

20. What is the relationship between a radius of a circle and a line that is tangent to the circle?
360°
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.

21. What is a proportion?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = 2(lw + lh + hw)
B^m*b^n = b^m+n
An equation that states that two ratios are equivalent. 4/6 = 10/15

22. What are the properties of a parallelogram?
A = 6(l^2)
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.
If a is negative and b is positive - then a < 0 < b.

23. How you convert a fraction or a decimal to a percent?
A = 6(l^2)
1 is a divisor (or factor) of every integer.
Divide - then multiply by 100.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

24. Important binomial 1
(n - 2)(180°)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x + y)(x - y) = x^2 - y^2
360°

25. How do you find the slope of a line?
Write the percent as a decimal - and multiply.
M = (y2 - y1)/(x2 - x1)
Corresponding sides of similar triangles are in proportion.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

26. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).
The product of their slopes is -1 (negative reciprocal).

27. Law of exponents 3
At least one of the factors is 0.
A^m*b^m = (ab)^m
V = l^3
(b^m)^n = b^mn

28. What are similar triangles?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
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.

29. How do you find the probability that an event will occur?
A = pr^2
A = 2(lw + lh + hw)
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. Properties of one 2
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = bh
360°

31. What is a function?
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.
Area = (x°/360)(pr^2) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

32. If the product of two or more numbers is 0 - what do you know about the numbers?
Their sum is 180°.
360°
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

33. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
A = [(s^2*v3)/4]
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)

34. What is true about the measures of the two acute angles in a right triangle?
Then the product xy is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Their sum is 90°.
1 is the smallest positive odd integer.

35. What is a composite number?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An integer greater than one that is not prime.
(x + y)(x - y) = x^2 - y^2
At least one of the factors is 0.

36. What is the formula for the surface area of a cube?
A = s^2 or A =d^2/2 where d is the diagonal
A = 6(l^2)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(Circumference/diameter) of a circle - or approximately 3.14.

37. Properties of zero 4
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.
C = p2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
In the expression x^b - x is the base and b is the exponent.

38. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
D = 2r
V = l^3
The two pairs of opposite angles formed are equal to each other.

39. If you were given the graph of y = f(x) - what does f(a) represent?
Write the percent over 100 and reduce.
A = pr^2
A = [(s^2*v3)/4]
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

40. What is an integer?
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.
All positive and negative whole numbers - and zero.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

41. What is the formula for the surface area of a rectangular solid?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
M = (y2 - y1)/(x2 - x1)
1 is the smallest positive odd integer.
A = 2(lw + lh + hw)

42. What is the sum of the measures of all angles around a point?
Set x = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
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°.

43. Properties of zero 1
Write the percent over 100 and reduce.
B^m/b^n = b^m-n
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is the only number that is neither positive nor negative.

44. What is the formula for the volume of a rectangular solid?
V = l^3
Equal slopes.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = lwh

45. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
A = bh
(x + y)(x - y) = x^2 - y^2
A = pr^2

46. In a circle of radius r - what is the formula for the diameter?
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.
D = 2r
A = (1/2)bh.

47. Law of exponents 4
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^m*b^m = (ab)^m
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

48. What is the graph of a function?
The two pairs of opposite angles formed are equal to each other.
(x + y)(x - y) = x^2 - y^2
No matter how many angles there are - the sum around the point is 360°.
The set of all ordered pairs (x -y) such that y = f(x).

49. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(n - 2)(180°)
Shifted up 2 units.
Equal slopes.
The product of their slopes is -1 (negative reciprocal).

50. What is the square root of a number?
M = (y2 - y1)/(x2 - x1)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
D = 2r