Test your basic knowledge |

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 4
0 is the only number that is neither positive nor negative.
Set y = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

2. Law of exponents 4
Arc = (x°/360)(2pr) where x is the central angle.
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.
A^m*b^m = (ab)^m
Corresponding sides of similar triangles are in proportion.

3. Properties of square roots
M = (y2 - y1)/(x2 - x1)
0 is a multiple of every integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any number n: x^-n means 1/x^n.

4. Important binomial 1
1 is the smallest positive odd integer.
(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.
0 is the only number that is neither positive nor negative.

5. What are the properties of a square?
Vertical line is x = a - horizontal is y = b - any other is y = mx + 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
No matter how many angles there are - the sum around the point is 360°.

6. Properties of one 1
B^m/b^n = b^m-n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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 number a: a * 1 = a and a / 1 = a.

7. What is an even and an odd number?
Write the percent over 100 and reduce.
A^m*b^m = (ab)^m
Even numbers are divisible by 2 and odd numbers are not.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

8. What is the graph of a function?
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 set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)
A fraction whose denominator is 100 i.e. 17% = 17/100

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
C = p2r
The product of their slopes is -1 (negative reciprocal).
Shifted left 2 units.
In the expression x^b - x is the base and b is the exponent.

10. If you were given the graph of y = f(x) - what does f(a) represent?
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.
(x + y)(x - y) = x^2 - y^2
They are both the same. A divisor or factor of an integer leaves no remainder.

11. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
Their sum is 90°.

12. How do you convert a percent to a fraction or a decimal?
The set of all ordered pairs (x -y) such that y = f(x).
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°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Write the percent over 100 and reduce.

13. Properties of one 2
For any integer n: 1^n = 1.
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°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

14. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
They are both the same. A divisor or factor of an integer leaves no remainder.
Set y = 0 - and solve.
V = pr^2h

15. What is the formula for the surface area of a rectangular solid?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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 = lwh
A = 2(lw + lh + hw)

16. What is a percent?
No matter how many angles there are - the sum around the point is 360°.
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.
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the product xy is a constant.

17. What is an exponent?
Shifted up 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
In the expression x^b - x is the base and b is the exponent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

18. 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.
0 is a multiple of every integer.
M = (y2 - y1)/(x2 - x1)
Shifted left 2 units.

19. What is the sum of the measures of the n angles of a polygon with n sides?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Area = (x°/360)(pr^2) where x is the central angle.
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.
(n - 2)(180°)

20. What is true about the areas of similar triangles?
The set of all ordered pairs (x -y) such that y = f(x).
(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.
0 is a multiple of every integer.

21. Important binomial 3
1 is a divisor (or factor) of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Cannot is 0 - must is 1 - all others are in between.
0 is a multiple of every integer.

22. What is true about the slopes of parallel lines?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Equal slopes.
Their sum is 180°.

23. What does it mean if y is inversely proportional to x?
[(x1 + x2)/2] -[(y1 + y2)/2]
Then the product xy is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
They are both the same. A divisor or factor of an integer leaves no remainder.

24. What are the median and the mode of a set of data?
C = p2r
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
B^m*b^n = b^m+n

25. What does it mean if y is directly proportional to x?
0 is the only number that is neither positive nor negative.
Their sum is 180°.
1 is a divisor (or factor) of every integer.
Then the quotient y/x is a constant.

26. How you convert a fraction or a decimal to a percent?
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
180°. If two or more angles form a straight angle - their sum is 180°.
Divide - then multiply by 100.

27. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Write the percent over 100 and reduce.
A^m/b^m = (a/b)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

28. What is true about the measures of the three angles in a triangle?
A^m*b^m = (ab)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]

29. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
C = p2r
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°
They are both the same. A divisor or factor of an integer leaves no remainder.

30. What is the Pythagorean theorem?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = pr^2h
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°.
For any right triangle - a^2 + b^2 = c^2.

31. How do we write the equation of a line?
M = (y2 - y1)/(x2 - x1)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent as a decimal - and multiply.

32. What is the formula for the volume of a cylinder?
For any right triangle - a^2 + b^2 = c^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set x = 0 - and solve.
V = pr^2h

33. What is the volume of a cube?
A^m*b^m = (ab)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Write the percent as a decimal - and multiply.
V = l^3

34. What is true about the measures of the two acute angles in a right triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number n: x^-n means 1/x^n.
Their sum is 90°.
Corresponding sides of similar triangles are in proportion.

35. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
Shifted right 2 units.
Write the percent as a decimal - and multiply.

36. 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°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
No matter how many angles there are - the sum around the point is 360°.
For any number a: a * 1 = a and a / 1 = a.

37. What are similar triangles?
An integer greater than one that is not prime.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m

38. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Avg = sum of n numbers/n
Shifted right 2 units.
Write the percent over 100 and reduce.

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Then the quotient y/x is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
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.
Shifted up 2 units.

40. What is the sum of the measures of all angles around a point?
At least one of the factors is 0.
A = (1/2)bh.
A = lw
No matter how many angles there are - the sum around the point is 360°.

41. What is a composite number?
An integer greater than one that is not prime.
A = (1/2)bh.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = [(s^2*v3)/4]

42. How do you calculate percent increases and decreases?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

43. Properties of zero 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Corresponding sides of similar triangles are in proportion.
0 is the only number that is neither positive nor negative.

44. What is special formula for the area of an equilateral triangle?
A = (1/2)bh.
A = [(s^2*v3)/4]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = lw

45. Properties of zero 5
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted right 2 units.
For any number b: b = -b if and only if b = 0.

46. For what values of a function is the function undefined?
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]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
No matter how many angles there are - the sum around the point is 360°.

47. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted down 2 units.

48. What is a fractional exponent?
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.
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.

49. What is a multiple of an integer?
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
In the expression x^b - x is the base and b is the exponent.
A = s^2 or A =d^2/2 where d is the diagonal

50. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = (1/2)bh.
A = pr^2