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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. For what values of a function is the function undefined?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Avg = sum of n numbers/n
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

2. What is true about the measures of the four angles formed by two intersecting lines?
360°
The two pairs of opposite angles formed are equal to each other.
A = lw
C = p2r

3. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]
A = 2(lw + lh + hw)

4. What are the properties of a square?
A = lw
(n - 2)(180°)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.

5. What are the important properties of 30-60-90 triangle?
Then the product xy is a constant.
Is a right triangle with a ratio of sides x:xv3:2x.
All positive and negative whole numbers - and zero.
Their sum is 90°.

6. Properties of one 3
1 is a divisor (or factor) of every integer.
(b^m)^n = b^mn
A = (1/2)bh.
Their sum is 180°.

7. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = bh
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

8. What is a proportion?
[(x1 + x2)/2] -[(y1 + y2)/2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

9. What is the formula for the area of a parallelogram?
A = bh
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)
B^m/b^n = b^m-n

10. What is the sum of the measures of the four angles in a quadrilateral?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
360°
Is a right triangle with a ratio of sides x:xv3:2x.
For any integer n: 1^n = 1.

11. What is the formula for the volume of a cylinder?
Shifted up 2 units.
At least one of the factors is 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.
V = pr^2h

12. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 2(lw + lh + hw)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

13. What is a Venn diagram?
Shifted right 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

14. What is the probability of an event that cannot occur? That must occur?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Cannot is 0 - must is 1 - all others are in between.
In the expression x^b - x is the base and b is the 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.

15. How do we write the equation of a line?
360°
The two pairs of opposite angles formed are equal to each other.
A = (1/2)bh.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

16. What is the formula for the volume of a rectangular solid?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = bh
C = p2r
V = lwh

17. What is special formula for the area of an equilateral triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is the only number that is neither positive nor negative.

18. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The ratio of corresponding sides of similar triangles.
Shifted right 2 units.

19. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
The product of their slopes is -1 (negative reciprocal).
A = (1/2)bh.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

20. What are similar triangles?
A = 6(l^2)
V = lwh
Set x = 0 - and solve.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

21. Properties of square roots
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°.
Arc = (x°/360)(2pr) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

22. What is the Pythagorean theorem?
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.
For any right triangle - a^2 + b^2 = c^2.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

23. What is the midpoint formula?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
[(x1 + x2)/2] -[(y1 + y2)/2]

24. What is a ratio?

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25. What is the formula for the surface area of a rectangular solid?
0 is a multiple of every integer.
A = 2(lw + lh + hw)
The product of their slopes is -1 (negative reciprocal).
For any integer n: 1^n = 1.

26. Law of exponents 4
Set y = 0 - and solve.
Cannot is 0 - must is 1 - all others are in between.
A^m*b^m = (ab)^m
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.

27. What is a function?
B^m/b^n = b^m-n
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
Cannot is 0 - must is 1 - all others are in between.

28. How do you find the y-intercept of a graph?
Equal slopes.
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.
V = pr^2h
Set x = 0 - and solve.

29. What does it mean if y is inversely proportional to x?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
A = [(s^2*v3)/4]
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

30. Properties of zero 3
A = [(s^2*v3)/4]
0 is a multiple of every integer.
1 is a divisor (or factor) of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

31. Properties of zero 2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
360°
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If a is negative and b is positive - then a < 0 < b.

32. How do you find a percent of a number?
Then the quotient y/x is a constant.
Then the product xy is a constant.
A = bh
Write the percent as a decimal - and multiply.

33. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.
No matter how many angles there are - the sum around the point is 360°.

34. What is the distance formula?
(x + y)(x - y) = x^2 - y^2
[(x1 + x2)/2] -[(y1 + y2)/2]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A^m*b^m = (ab)^m

35. What is the formula for the area of a rectangle?
A = lw
A = (1/2)bh.
For any number n: x^-n means 1/x^n.
C = p2r

36. Important binomial 1
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted up 2 units.
360°
(x + y)(x - y) = x^2 - y^2

37. What is an integer?
The ratio of corresponding sides of similar triangles.
All positive and negative whole numbers - and zero.
(b^m)^n = b^mn
They are both the same. A divisor or factor of an integer leaves no remainder.

38. What is the relationship between a radius of a circle and a line that is tangent to the circle?
360°
Then the product xy is a constant.
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.

39. 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.
The set of all ordered pairs (x -y) such that y = f(x).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

40. What formula is used for an average?
An integer greater than one that is not prime.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Avg = sum of n numbers/n
V = pr^2h

41. What are the quotient and the remainder?

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42. What is a fractional exponent?
Even numbers are divisible by 2 and odd numbers are not.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

43. What are the properties of a rectangle?
No matter how many angles there are - the sum around the point is 360°.
For any number b: b = -b if and only if b = 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any integer n: 1^n = 1.

44. What is the area of a square?
Area = (x°/360)(pr^2) where x is the central angle.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The ratio of corresponding sides of similar triangles.
A = s^2 or A =d^2/2 where d is the diagonal

45. Law of exponents 2
Write the percent as a decimal - and multiply.
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.
Then the quotient y/x is a constant.

46. What is an exterior angle of a triangle?
V = lwh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted down 2 units.

47. What is the triangle inequality?
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.
C = p2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

48. Properties of zero 1
0 is the only number that is neither positive nor negative.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

49. What is a divisor and a factor of an integer?
0 is a multiple of every integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Then the quotient y/x is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.

50. What is an exterior angle of a polygon?
All positive and negative whole numbers - and zero.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.
Corresponding sides of similar triangles are in proportion.