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. What is a percent?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
1 is a divisor (or factor) of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100

2. What is a ratio?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

3. Properties of zero 1
0 is the only number that is neither positive nor negative.
Shifted up 2 units.
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.

4. What is the distance formula?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
Write the percent as a decimal - and multiply.

5. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Divide - then multiply by 100.
Shifted down 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°

6. How do you calculate percent increases and decreases?
(n - 2)(180°)
Shifted right 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. What is the sum of the measures of the n angles of a polygon with n sides?
A = (1/2)bh.
Shifted left 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(n - 2)(180°)

8. What formula is used for an average?
Avg = sum of n numbers/n
A = s^2 or A =d^2/2 where d is the diagonal
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.

9. In a circle of radius r - what is the formula for the circumference?
C = p2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
(Circumference/diameter) of a circle - or approximately 3.14.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

10. How do you find the slope of a line?
Divide - then multiply by 100.
M = (y2 - y1)/(x2 - x1)
No matter how many angles there are - the sum around the point is 360°.
An angle formed by extending the side of the polygon.

11. What is the volume of a cube?
Shifted left 2 units.
Corresponding sides of similar triangles are in proportion.
If a is negative and b is positive - then a < 0 < b.
V = l^3

12. What are the properties of a square?
180°. If two or more angles form a straight angle - their sum is 180°.
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 - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If a is negative and b is positive - then a < 0 < b.

13. 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°.
Avg = sum of n numbers/n
For any right triangle - a^2 + b^2 = c^2.
They are both the same. A divisor or factor of an integer leaves no remainder.

14. 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.
Avg = sum of n numbers/n
Divide - then multiply by 100.
Set x = 0 - and solve.

15. What is the area of a square?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = (1/2)bh.
A = s^2 or A =d^2/2 where d is the diagonal
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

16. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.
For any right triangle - a^2 + b^2 = c^2.

17. Law of exponents 5
Set y = 0 - and solve.
A^m/b^m = (a/b)^m
Set x = 0 - and solve.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

18. What is the formula for the area of a triangle?
A = (1/2)bh.
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.
The set of all ordered pairs (x -y) such that y = f(x).

19. What are the properties of a rectangle?
Equal slopes.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

20. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
D = 2r
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted down 2 units.

21. Properties of zero 3
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.
0 is a multiple of every integer.
If a is negative and b is positive - then a < 0 < b.

22. Properties of one 3
1 is a divisor (or factor) of every integer.
360°
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = l^3

23. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

24. What is the probability of an event that cannot occur? That must occur?
(Circumference/diameter) of a circle - or approximately 3.14.
At least one of the factors is 0.
A = [(s^2*v3)/4]
Cannot is 0 - must is 1 - all others are in between.

25. Important binomial 3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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
Area = (x°/360)(pr^2) where x is the central angle.

26. What is true about the slopes of perpendicular lines?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The product of their slopes is -1 (negative reciprocal).
Divide - then multiply by 100.
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.

27. What are the median and the mode of a set of data?
Is a right triangle with a ratio of sides x:xv3:2x.
All positive and negative whole numbers - and zero.
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.
A = [(s^2*v3)/4]

28. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is a divisor (or factor) of every integer.

29. What is the sum of the measures of the four angles in a quadrilateral?
(n - 2)(180°)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Then the quotient y/x is a constant.
360°

30. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
Shifted left 2 units.
Write the percent as a decimal - and multiply.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

31. What is the square root of a number?
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
360°
For any number n: x^-n means 1/x^n.

32. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
D = 2r
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r

33. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
0 is the only number that is neither positive nor negative.
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n
Shifted left 2 units.

34. How do you find the y-intercept of a graph?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set x = 0 - and solve.
The set of all ordered pairs (x -y) such that y = f(x).

35. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Even numbers are divisible by 2 and odd numbers are not.

36. How do you find the area of a sector of a circle?
In the expression x^b - x is the base and b is the exponent.
Area = (x°/360)(pr^2) where x is the central angle.
V = l^3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

37. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
360°
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = pr^2h

38. What is an integer?
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.
For any integer n: 1^n = 1.

39. How you convert a fraction or a decimal to a percent?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = [(s^2*v3)/4]
V = l^3
Divide - then multiply by 100.

40. What is the formula for the area of a rectangle?
A = lw
If a is negative and b is positive - then a < 0 < b.
A = 2(lw + lh + hw)
Then the product xy is a constant.

41. What is a negative exponent?
For any number n: x^-n means 1/x^n.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted left 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.

42. If you were given the graph of y = f(x) - what does f(a) represent?
The ratio of corresponding sides of similar triangles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
Cannot is 0 - must is 1 - all others are in between.

43. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
For any right triangle - a^2 + b^2 = c^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15

44. Properties of zero 4
Shifted left 2 units.
360°
The set of all ordered pairs (x -y) such that y = f(x).
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

45. What are the quotient and the remainder?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

46. How do you find a percent of a number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent as a decimal - and multiply.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(b^m)^n = b^mn

47. Law of exponents 3
(b^m)^n = b^mn
V = pr^2h
For any number n: x^-n means 1/x^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.

48. What is the formula for the volume of a cylinder?
V = pr^2h
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.
Equal slopes.

49. Law of exponents 1
360°
B^m*b^n = b^m+n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
M = (y2 - y1)/(x2 - x1)

50. How do you convert a percent to a fraction or a decimal?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Write the percent over 100 and reduce.
All positive and negative whole numbers - and zero.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.