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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. Important binomial 2
(b^m)^n = b^mn
(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.
360°

2. What is a negative exponent?
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

3. What is the formula for the surface area of a rectangular solid?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = 2(lw + lh + hw)
Equal slopes.
0 is a multiple of every integer.

4. Law of exponents 2
In the expression x^b - x is the base and b is the exponent.
A = 2(lw + lh + hw)
B^m/b^n = b^m-n
1 is a divisor (or factor) of every integer.

5. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
No matter how many angles there are - the sum around the point is 360°.
Shifted right 2 units.
V = l^3
(x + y)(x - y) = x^2 - y^2

6. Important binomial 1
V = pr^2h
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.
(x + y)(x - y) = x^2 - y^2
They are both the same. A divisor or factor of an integer leaves no remainder.

7. What are the important properties of a 45-45 - 90 triangle?
V = lwh
Equal slopes.
A = 6(l^2)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

8. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Set y = 0 - and solve.
A = lw
Shifted left 2 units.

9. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An integer greater than one that is not prime.
If a is negative and b is positive - then a < 0 < b.

10. How do you calculate percent increases and decreases?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A fraction whose denominator is 100 i.e. 17% = 17/100

11. What are the median and the mode of a set of data?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
The ratio of corresponding sides of similar triangles.
A = pr^2

12. What is a composite number?
An integer greater than one that is not prime.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Their sum is 90°.

13. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.
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.

14. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
If a is negative and b is positive - then a < 0 < b.
A = [(s^2*v3)/4]
Their sum is 180°.

15. Properties of one 4
1 is the smallest positive odd integer.
(x + y)(x - y) = x^2 - y^2
Write the percent as a decimal - and multiply.
If a is negative and b is positive - then a < 0 < b.

16. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
V = pr^2h
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

17. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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 = pr^2h
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.

18. Properties of square roots
V = lwh
1 is the smallest positive odd integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

19. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Their sum is 180°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

20. What are similar triangles?
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.
Their sum is 180°.
Then the quotient y/x is a constant.

21. What is the distributive law?
Even numbers are divisible by 2 and odd numbers are not.
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

22. What is the formula for the area of a parallelogram?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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°.
In the expression x^b - x is the base and b is the exponent.
A = bh

23. What is special formula for the area of an equilateral triangle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]

24. What is a fractional exponent?
Equal slopes.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
An angle formed by extending the side of the polygon.
V = l^3

25. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
V = l^3
Divide - then multiply by 100.
M = (y2 - y1)/(x2 - x1)

26. Properties of zero 1
0 is the only number that is neither positive nor negative.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted left 2 units.

27. What are the quotient and the remainder?

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28. What is true about the slopes of parallel lines?
A = bh
Shifted left 2 units.
A = 2(lw + lh + hw)
Equal slopes.

29. What is a prime number?
The ratio of corresponding sides of similar triangles.
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.
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°.
Write the percent as a decimal - and multiply.

30. In a circle of radius r - what is the formula for the area?
B^m/b^n = b^m-n
Shifted left 2 units.
Write the percent over 100 and reduce.
A = pr^2

31. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Write the percent as a decimal - and multiply.
Their sum is 90°.
Avg = sum of n numbers/n

32. What is the measure of a straight angle?
Avg = sum of n numbers/n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
180°. If two or more angles form a straight angle - their sum is 180°.
In the expression x^b - x is the base and b is the exponent.

33. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
0 is the only number that is neither positive nor negative.
No matter how many angles there are - the sum around the point is 360°.
D = 2r

34. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
All positive and negative whole numbers - and zero.
1 is a divisor (or factor) of every integer.
Shifted down 2 units.

35. What are the properties of a rectangle?
The product of their slopes is -1 (negative reciprocal).
The ratio of corresponding sides of similar triangles.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

36. How do we write the equation of a line?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the quotient y/x is a constant.
Divide - then multiply by 100.

37. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

38. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
For any number b: b = -b if and only if b = 0.
For any right triangle - a^2 + b^2 = c^2.
Shifted right 2 units.

39. What formula is used for an average?
Avg = sum of n numbers/n
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.

40. What is a function?
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Write the percent over 100 and reduce.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

41. Properties of one 3
360°
1 is a divisor (or factor) of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

42. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°
A = s^2 or A =d^2/2 where d is the diagonal

43. What is true about the measures of the two acute angles in a right triangle?
Then the quotient y/x is a constant.
Their sum is 90°.
Write the percent over 100 and reduce.
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.

44. What is a Venn diagram?
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.
Shifted left 2 units.
For any number n: x^-n means 1/x^n.

45. What is the volume of a cube?
V = l^3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
M = (y2 - y1)/(x2 - x1)
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.

46. What is the triangle inequality?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The set of all ordered pairs (x -y) such that y = f(x).
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.

47. What is the formula for the surface area of a cube?
V = lwh
A = 6(l^2)
Shifted right 2 units.
Set x = 0 - and solve.

48. What is the formula for the volume of a rectangular solid?
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 = lwh
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the product xy is a constant.

49. What important property do similar triangles have?
For any right triangle - a^2 + b^2 = c^2.
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.
Write the percent over 100 and reduce.

50. What is the sum of the measures of the n angles of a polygon with n sides?
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
(n - 2)(180°)