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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. What is an exponent?
360°
Shifted up 2 units.
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.
In the expression x^b - x is the base and b is the exponent.

2. How do you find the x-intercept of a graph?
Arc = (x°/360)(2pr) where x is the central angle.
Set y = 0 - and solve.
Divide - then multiply by 100.
The product of their slopes is -1 (negative reciprocal).

3. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted down 2 units.
Equal slopes.
D = 2r

4. What is true about the areas of similar triangles?
(Circumference/diameter) of a circle - or approximately 3.14.
Set x = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

5. What is a Venn diagram?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x + y)(x - y) = x^2 - y^2
Shifted down 2 units.

6. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is a multiple of every integer.
Set x = 0 - and solve.
Avg = sum of n numbers/n

7. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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 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°.
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.

8. How do we write the equation of a line?
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set x = 0 - and solve.
Write the percent as a decimal - and multiply.

9. What are the quotient and the remainder?

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10. What is the graph of a function?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The set of all ordered pairs (x -y) such that y = f(x).
Shifted left 2 units.
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.

11. Properties of zero 5
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n
For any number b: b = -b if and only if b = 0.
They are both the same. A divisor or factor of an integer leaves no remainder.

12. What are the properties of a square?
Shifted right 2 units.
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.
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

13. What is the volume of a cube?
V = l^3
V = lwh
A = bh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

14. What is the distance formula?
All positive and negative whole numbers - and zero.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The set of all ordered pairs (x -y) such that y = f(x).

15. If you were given the graph of y = f(x) - what does f(a) represent?
Shifted right 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
0 is a multiple of every integer.
If a is negative and b is positive - then a < 0 < b.

16. Properties of zero 2
(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.
Corresponding sides of similar triangles are in proportion.

17. What are similar triangles?
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.
For any integer n: 1^n = 1.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = (1/2)bh.

18. What is true about the slopes of parallel lines?
Shifted left 2 units.
If a is negative and b is positive - then a < 0 < b.
[(x1 + x2)/2] -[(y1 + y2)/2]
Equal slopes.

19. What is the ratio of similitude?
V = pr^2h
The ratio of corresponding sides of similar triangles.
B^m*b^n = b^m+n
D = 2r

20. What is special formula for the area of an equilateral triangle?
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = [(s^2*v3)/4]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

21. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A fraction whose denominator is 100 i.e. 17% = 17/100

22. What is an exterior angle of a polygon?
Avg = sum of n numbers/n
For any number a: a * 1 = a and a / 1 = a.
An angle formed by extending the side of the polygon.
A = bh

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

24. How do you find the y-intercept of a graph?
Their sum is 180°.
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°.
Set x = 0 - and solve.

25. What is a ratio?

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26. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Equal slopes.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
360°

27. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
1 is the smallest positive odd integer.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Corresponding sides of similar triangles are in proportion.

28. What is the formula for the area of a triangle?
A = (1/2)bh.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Equal slopes.
The ratio of corresponding sides of similar triangles.

29. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
D = 2r

30. What is the sum of the measures of the n angles of a polygon with n sides?
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.
(n - 2)(180°)
[(x1 + x2)/2] -[(y1 + y2)/2]

31. Law of exponents 3
(b^m)^n = b^mn
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The ratio of corresponding sides of similar triangles.
Shifted up 2 units.

32. In a circle of radius r - what is the formula for the area?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = pr^2
360°
M = (y2 - y1)/(x2 - x1)

33. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
1 is the smallest positive odd integer.
All positive and negative whole numbers - and zero.
V = pr^2h

34. What important property do similar triangles have?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Corresponding sides of similar triangles are in proportion.
All positive and negative whole numbers - and zero.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

35. What is a composite number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.
For any right triangle - a^2 + b^2 = c^2.

36. Properties of one 4
Avg = sum of n numbers/n
1 is the smallest positive odd integer.
B^m*b^n = b^m+n
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.

37. What is the Pythagorean theorem?
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
All positive and negative whole numbers - and zero.

38. 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.
The two pairs of opposite angles formed are equal to each other.
M = (y2 - y1)/(x2 - x1)
The set of all ordered pairs (x -y) such that y = f(x).

39. What is the midpoint formula?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

40. What is an even and an odd number?
A = lw
(n - 2)(180°)
1 is the smallest positive odd integer.
Even numbers are divisible by 2 and odd numbers are not.

41. What is the probability of an event that cannot occur? That must occur?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = (1/2)bh.
In the expression x^b - x is the base and b is the exponent.
Cannot is 0 - must is 1 - all others are in between.

42. What is the triangle inequality?
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)
(Circumference/diameter) of a circle - or approximately 3.14.
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.

43. Law of exponents 5
(x + y)(x - y) = x^2 - y^2
No matter how many angles there are - the sum around the point is 360°.
A^m/b^m = (a/b)^m
(Circumference/diameter) of a circle - or approximately 3.14.

44. What is a fractional exponent?
At least one of the factors is 0.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
In the expression x^b - x is the base and b is the exponent.
C = p2r

45. What is the measure of a straight 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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

46. What is the sum of the measures of the four angles in a quadrilateral?
B^m*b^n = b^m+n
360°
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If a is negative and b is positive - then a < 0 < b.

47. What is an integer?
An angle formed by extending the side of the polygon.
All positive and negative whole numbers - and zero.
They are both the same. A divisor or factor of an integer leaves no remainder.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

48. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Corresponding sides of similar triangles are in proportion.

49. Important binomial 1
Shifted down 2 units.
Avg = sum of n numbers/n
(x + y)(x - y) = x^2 - y^2
B^m*b^n = b^m+n

50. 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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted up 2 units.
A^m*b^m = (ab)^m