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 the volume of a cube?
Avg = sum of n numbers/n
M = (y2 - y1)/(x2 - x1)
A = lw
V = l^3

2. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Arc = (x°/360)(2pr) where x is the central angle.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. What is an exterior angle of a triangle?
A = 2(lw + lh + hw)
V = lwh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Area = (x°/360)(pr^2) where x is the central angle.

4. What is a prime number?
For any number n: x^-n means 1/x^n.
A^m/b^m = (a/b)^m
A = s^2 or A =d^2/2 where d is the diagonal
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.

5. What is a fractional exponent?
V = l^3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set y = 0 - and solve.
Their sum is 180°.

6. If you were given the graph of y = f(x) - what does f(a) represent?
Area = (x°/360)(pr^2) where x is the central angle.
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Set y = 0 - and solve.

7. Properties of one 3
V = l^3
1 is a divisor (or factor) of every integer.
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

8. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
A = pr^2
A fraction whose denominator is 100 i.e. 17% = 17/100
In the expression x^b - x is the base and b is the exponent.

9. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For any number n: x^-n means 1/x^n.
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°.
At least one of the factors is 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

10. For what values of a function is the function undefined?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Shifted up 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = (1/2)bh.

11. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.

12. Law of exponents 2
B^m/b^n = b^m-n
1 is the smallest positive odd integer.
The set of all ordered pairs (x -y) such that y = f(x).
[(x1 + x2)/2] -[(y1 + y2)/2]

13. What is the formula for the surface area of a cube?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 6(l^2)
For any number b: b = -b if and only if b = 0.
For any right triangle - a^2 + b^2 = c^2.

14. What is the triangle inequality?
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^m/b^m = (a/b)^m
Avg = sum of n numbers/n

15. What is the formula for the area of a rectangle?
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.
(n - 2)(180°)
A = lw
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

16. How you convert a fraction or a decimal to a percent?
An angle formed by extending the side of the polygon.
Write the percent as a decimal - and multiply.
Divide - then multiply by 100.
A = 6(l^2)

17. What is true about the slopes of perpendicular lines?
Area = (x°/360)(pr^2) where x is the central angle.
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
A = bh

18. What is the graph of a function?
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.
A = (1/2)bh.
The set of all ordered pairs (x -y) such that y = f(x).
For any right triangle - a^2 + b^2 = c^2.

19. What is a composite number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh
A = (1/2)bh.
An integer greater than one that is not prime.

20. How do you find a percent of a number?
An angle formed by extending the side of the polygon.
Then the product xy is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
Write the percent as a decimal - and multiply.

21. 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

22. Properties of one 1
For any number n: x^-n means 1/x^n.
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.
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.

23. What is the formula for the volume of a rectangular solid?
The ratio of corresponding sides of similar triangles.
For any integer n: 1^n = 1.
V = lwh
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.

24. What is true about the measures of the four angles formed by two intersecting lines?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any right triangle - a^2 + b^2 = c^2.
A fraction whose denominator is 100 i.e. 17% = 17/100
The two pairs of opposite angles formed are equal to each other.

25. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
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.
360°
Shifted down 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

26. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.
B^m/b^n = b^m-n
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.

27. What is the sum of the measures of the n angles of a polygon with n sides?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(n - 2)(180°)
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°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

28. How do you find the probability that an event will occur?
How steep the line is. Horizontal line = 0 - vertical has no slope.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

29. Important binomial 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.
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. What is an integer?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Then the product xy is a constant.
360°
All positive and negative whole numbers - and zero.

31. In a circle of radius r - what is the formula for the circumference?
Avg = sum of n numbers/n
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = pr^2h

32. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. 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°.
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.
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.
1 is a divisor (or factor) of every integer.

34. What is the formula for the volume of a cylinder?
V = pr^2h
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Even numbers are divisible by 2 and odd numbers are not.
A fraction whose denominator is 100 i.e. 17% = 17/100

35. What is p?
1 is a divisor (or factor) of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Set x = 0 - and solve.

36. How do you find the x-intercept of a graph?
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.

37. What is the area of a square?
The two pairs of opposite angles formed are equal to each other.
A = s^2 or A =d^2/2 where d is the diagonal
For any right triangle - a^2 + b^2 = c^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.

38. 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.
A = lw
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

39. Properties of zero 1
0 is the only number that is neither positive nor negative.
Their sum is 180°.
360°
The product of their slopes is -1 (negative reciprocal).

40. What is the formula for the area of a triangle?
A = (1/2)bh.
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.
For any integer n: 1^n = 1.
A = 2(lw + lh + hw)

41. If the product of two or more numbers is 0 - what do you know about the numbers?
A = pr^2
At least one of the factors is 0.
For any integer n: 1^n = 1.
A = s^2 or A =d^2/2 where d is the diagonal

42. What formula is used for an average?
A = bh
Equal slopes.
Avg = sum of n numbers/n
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

43. Law of exponents 5
A^m/b^m = (a/b)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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 = l^3

44. What are the median and the mode of a set of data?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set y = 0 - and solve.
Equal slopes.
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.

45. What are the sum - difference - products - and quotient of two numbers?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Area = (x°/360)(pr^2) where x is the central angle.
All positive and negative whole numbers - and zero.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

46. What is true about the slopes of parallel lines?
Avg = sum of n numbers/n
Equal slopes.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

47. What are the properties of a parallelogram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = (1/2)bh.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

48. What is the formula for the surface area of a rectangular solid?
A = 6(l^2)
A = 2(lw + lh + hw)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = (1/2)bh.

49. What is the square root of a number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted up 2 units.
V = pr^2h

50. Properties of zero 4
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent as a decimal - and multiply.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]