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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. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An angle formed by extending the side of the polygon.
Then the product xy is a constant.

2. What is the probability of an event that cannot occur? That must occur?
All positive and negative whole numbers - and zero.
For any number n: x^-n means 1/x^n.
Cannot is 0 - must is 1 - all others are in between.
A = (1/2)bh.

3. What is the sum of the measures of all angles around a point?
A = pr^2
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.
No matter how many angles there are - the sum around the point is 360°.
If a is negative and b is positive - then a < 0 < b.

4. What is a function?
For any right triangle - a^2 + b^2 = c^2.
Arc = (x°/360)(2pr) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.

5. Properties of one 2
All positive and negative whole numbers - and zero.
Shifted left 2 units.
For any number b: b = -b if and only if b = 0.
For any integer n: 1^n = 1.

6. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
They are both the same. A divisor or factor of an integer leaves no remainder.
Avg = sum of n numbers/n

7. Properties of one 4
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Their sum is 180°.
Then the product xy is a constant.
1 is the smallest positive odd integer.

8. What is a composite number?
0 is the only number that is neither positive nor negative.
An integer greater than one that is not prime.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

9. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.
360°
B^m*b^n = b^m+n

10. What is the formula for the area of a parallelogram?
A = bh
V = pr^2h
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

11. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

12. Law of exponents 4
A = (1/2)bh.
A^m*b^m = (ab)^m
V = l^3
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
At least one of the factors is 0.
M = (y2 - y1)/(x2 - x1)
Shifted down 2 units.

14. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any right triangle - a^2 + b^2 = c^2.
Equal slopes.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted up 2 units.

15. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is the smallest positive odd integer.
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.

16. What formula is used for an average?
Arc = (x°/360)(2pr) where x is the central angle.
Avg = sum of n numbers/n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°

17. What are the properties of a parallelogram?
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

18. What is the volume of a cube?
Shifted left 2 units.
V = l^3
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.

19. What is an integer?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = lw
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.

20. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m/b^n = b^m-n
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.

21. What is the ratio of similitude?
0 is the only number that is neither positive nor negative.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The ratio of corresponding sides of similar triangles.
Is a right triangle with a ratio of sides x:xv3:2x.

22. Law of exponents 2
The product of their slopes is -1 (negative reciprocal).
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.
A = (1/2)bh.

23. Law of exponents 1
B^m*b^n = b^m+n
0 is the only number that is neither positive nor negative.
(x + y)(x - y) = x^2 - y^2
0 is a multiple of every integer.

24. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.

25. What is the formula for the surface area of a cube?
A = 2(lw + lh + hw)
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)
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.

26. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
All positive and negative whole numbers - and zero.
Shifted up 2 units.
No matter how many angles there are - the sum around the point is 360°.
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°.

27. What are the median and the mode of a set of data?
V = lwh
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
D = 2r
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.

28. 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.
Is a right triangle with a ratio of sides x:xv3:2x.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = [(s^2*v3)/4]

29. Properties of one 3
(Circumference/diameter) of a circle - or approximately 3.14.
1 is a divisor (or factor) of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.

30. What are the sum - difference - products - and quotient of two numbers?
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15

31. What is an exponent?
They are both the same. A divisor or factor of an integer leaves no remainder.
In the expression x^b - x is the base and b is the exponent.
1 is the smallest positive odd integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

32. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m/b^n = b^m-n
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 6(l^2)

33. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A = lw
A fraction whose denominator is 100 i.e. 17% = 17/100
Cannot is 0 - must is 1 - all others are in between.

34. How do we write the equation of a line?
(x + y)(x - y) = x^2 - y^2
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
They are both the same. A divisor or factor of an integer leaves no remainder.

35. What is the distributive law?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = bh
P(e) = (# of favorable outcomes)/(# of possible outcomes)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

36. For what values of a function is the function undefined?
B^m*b^n = b^m+n
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Equal slopes.

37. Properties of one 1
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Set x = 0 - and solve.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number a: a * 1 = a and a / 1 = a.

38. Law of exponents 3
For any number n: x^-n means 1/x^n.
Their sum is 90°.
A = [(s^2*v3)/4]
(b^m)^n = b^mn

39. 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.
Set y = 0 - and solve.
B^m/b^n = b^m-n
360°

40. In a circle of radius r - what is the formula for the diameter?
D = 2r
For any number n: x^-n means 1/x^n.
0 is the only number that is neither positive nor negative.
Avg = sum of n numbers/n

41. In a circle of radius r - what is the formula for the circumference?
C = p2r
A = 2(lw + lh + hw)
360°
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

42. What are the properties of a square?
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.
Shifted up 2 units.
A = bh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

43. If you were given the graph of y = f(x) - what does f(a) represent?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = pr^2h
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

44. 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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

45. What is true about the slopes of parallel lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.

46. What is the formula for the area of a triangle?
360°
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = (1/2)bh.
An angle formed by extending the side of the polygon.

47. How do you calculate percent increases and decreases?
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m*b^n = b^m+n

48. How you convert a fraction or a decimal to a percent?
D = 2r
Their sum is 180°.
Even numbers are divisible by 2 and odd numbers are not.
Divide - then multiply by 100.

49. What is the midpoint formula?
For any right triangle - a^2 + b^2 = c^2.
Divide - then multiply by 100.
[(x1 + x2)/2] -[(y1 + y2)/2]
(Circumference/diameter) of a circle - or approximately 3.14.

50. What is an exterior angle of a triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3