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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 a proportion?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
How steep the line is. Horizontal line = 0 - vertical has no slope.
Then the product xy is a constant.

2. What is an exterior angle of a triangle?
Shifted left 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An integer greater than one that is not prime.
A^m/b^m = (a/b)^m

3. Law of exponents 4
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = [(s^2*v3)/4]

4. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Then the quotient y/x is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = bh

5. What is the formula for the volume of a cylinder?
Set x = 0 - and solve.
0 is a multiple of every integer.
V = pr^2h
Even numbers are divisible by 2 and odd numbers are not.

6. If you were given the graph of y = f(x) - what does f(a) represent?
Arc = (x°/360)(2pr) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
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.

7. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
1 is a divisor (or factor) of every integer.
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.

8. In a circle of radius r - what is the formula for the area?
A = pr^2
C = p2r
Cannot is 0 - must is 1 - all others are in between.
Set x = 0 - and solve.

9. How do you find the x-intercept of a graph?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
Set y = 0 - and solve.
Their sum is 90°.

10. What is a prime number?
Then the quotient y/x is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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 any right triangle - a^2 + b^2 = c^2.

11. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
A = bh
A = 6(l^2)
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.

12. Important binomial 3
V = lwh
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 longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

13. What are similar triangles?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

14. What is the midpoint formula?
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
[(x1 + x2)/2] -[(y1 + y2)/2]

15. How do you find the slope of a line?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)

16. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
1 is the smallest positive odd integer.
Their sum is 180°.
A = [(s^2*v3)/4]

17. What are the properties of a parallelogram?
Then the quotient y/x is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

18. What is p?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
They are both the same. A divisor or factor of an integer leaves no remainder.
Set y = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.

19. Law of exponents 3
(b^m)^n = b^mn
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.

20. What is true about the areas of similar triangles?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

21. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x + y)(x - y) = x^2 - y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

22. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted right 2 units.
No matter how many angles there are - the sum around the point is 360°.

23. What is the triangle inequality?
Shifted left 2 units.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Their sum is 180°.

24. What do we mean by the slope of the line?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = lw
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

25. What is special formula for the area of an equilateral triangle?
For any right triangle - a^2 + b^2 = c^2.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted right 2 units.
A = [(s^2*v3)/4]

26. How do you find the y-intercept of a graph?
M = (y2 - y1)/(x2 - x1)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set x = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.

27. What is an integer?
180°. If two or more angles form a straight angle - 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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
All positive and negative whole numbers - and zero.

28. Law of exponents 2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Then the product xy is a constant.
B^m/b^n = b^m-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.

29. In a circle of radius r - what is the formula for the diameter?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. Properties of zero 2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

31. What is a divisor and a factor of an integer?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
They are both the same. A divisor or factor of an integer leaves no remainder.

32. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is the only number that is neither positive nor negative.
(b^m)^n = b^mn

33. What is the graph of a function?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180°)
Cannot is 0 - must is 1 - all others are in between.
The set of all ordered pairs (x -y) such that y = f(x).

34. What is the formula for the area of a rectangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = lw
In the expression x^b - x is the base and b is the exponent.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

35. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted right 2 units.
Shifted up 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.

36. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
A = s^2 or A =d^2/2 where d is the diagonal
A^m/b^m = (a/b)^m

37. Properties of one 3
Cannot is 0 - must is 1 - all others are in between.
1 is a divisor (or factor) of every integer.
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.
Is a right triangle with a ratio of sides x:xv3:2x.

38. What is the formula for the area of a triangle?
360°
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A^m*b^m = (ab)^m
A = (1/2)bh.

39. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is a multiple of every integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Cannot is 0 - must is 1 - all others are in between.

40. What is a multiple of an integer?
Arc = (x°/360)(2pr) where x is the central angle.
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.
0 is a multiple of every integer.

41. What is the volume of a cube?
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°.
V = l^3
At least one of the factors is 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

42. For what values of a function is the function undefined?
A = lw
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

43. What is true about the measures of the four angles formed by two intersecting lines?
V = lwh
The two pairs of opposite angles formed are equal to each other.
Set y = 0 - and solve.
180°. If two or more angles form a straight angle - their sum is 180°.

44. What is a percent?
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.
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100

45. How do you find the length of an arc of a circle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Arc = (x°/360)(2pr) where x is the central angle.
Avg = sum of n numbers/n
[(x1 + x2)/2] -[(y1 + y2)/2]

46. What is the sum of the measures of the four angles in a quadrilateral?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
Set x = 0 - and solve.
A = s^2 or A =d^2/2 where d is the diagonal

47. What is an exponent?
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.
At least one of the factors is 0.
The two pairs of opposite angles formed are equal to each other.
In the expression x^b - x is the base and b is the exponent.

48. What are the important properties of a 45-45 - 90 triangle?
Shifted left 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
No matter how many angles there are - the sum around the point is 360°.

49. What is the ratio of similitude?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The ratio of corresponding sides of similar triangles.
[(x1 + x2)/2] -[(y1 + y2)/2]
M = (y2 - y1)/(x2 - x1)

50. Properties of one 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Equal slopes.
For any number a: a * 1 = a and a / 1 = a.
A = [(s^2*v3)/4]