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 one 3
1 is a divisor (or factor) of every integer.
For any right triangle - a^2 + b^2 = c^2.
If a is negative and b is positive - then a < 0 < b.
B^m*b^n = b^m+n

2. What is true about the slopes of parallel lines?
Equal slopes.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Write the percent over 100 and reduce.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. What is a ratio?

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

4. What is the formula for the volume of a rectangular solid?
V = lwh
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent over 100 and reduce.
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.

5. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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 = (1/2)bh.
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°.

6. What is a composite number?
B^m*b^n = b^m+n
Their sum is 90°.
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.
An integer greater than one that is not prime.

7. What is the formula for the volume of a cylinder?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = pr^2h
A^m*b^m = (ab)^m
C = p2r

8. What is the Pythagorean theorem?
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.
(n - 2)(180°)
For any right triangle - a^2 + b^2 = c^2.
A = 2(lw + lh + hw)

9. What is the distributive law?
V = pr^2h
No matter how many angles there are - the sum around the point is 360°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

10. What is the midpoint formula?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number n: x^-n means 1/x^n.

11. Properties of one 4
360°
Shifted down 2 units.
Then the quotient y/x is a constant.
1 is the smallest positive odd integer.

12. What is a prime number?
Shifted down 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.
All positive and negative whole numbers - and zero.
Even numbers are divisible by 2 and odd numbers are not.

13. What is the volume of a cube?
V = l^3
For any right triangle - a^2 + b^2 = c^2.
Shifted down 2 units.
For any number a: a * 1 = a and a / 1 = a.

14. What is the graph of a function?
For any integer n: 1^n = 1.
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100
The product of their slopes is -1 (negative reciprocal).

15. What are the median and the mode of a set of data?
C = p2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

16. How you convert a fraction or a decimal to a percent?
Shifted down 2 units.
Divide - then multiply by 100.
360°
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.

17. What is an exponent?
Corresponding sides of similar triangles are in proportion.
Avg = sum of n numbers/n
A = 2(lw + lh + hw)
In the expression x^b - x is the base and b is the exponent.

18. Law of exponents 3
(b^m)^n = b^mn
Even numbers are divisible by 2 and odd numbers are not.
Corresponding sides of similar triangles are in proportion.
At least one of the factors is 0.

19. What is the measure of a straight angle?
For any number n: x^-n means 1/x^n.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

20. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
C = p2r
Is a right triangle with a ratio of sides x:xv3:2x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

21. Properties of zero 5
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.
At least one of the factors is 0.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

22. 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.
Shifted right 2 units.
1 is the smallest positive odd integer.
180°. If two or more angles form a straight angle - their sum is 180°.

23. What formula is used for an average?
360°
The two pairs of opposite angles formed are equal to each other.
Avg = sum of n numbers/n
360°

24. What are the important properties of 30-60-90 triangle?
Shifted right 2 units.
A = (1/2)bh.
Shifted up 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.

25. What is the sum of the measures of the four angles in a quadrilateral?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = [(s^2*v3)/4]
360°
P(e) = (# of favorable outcomes)/(# of possible outcomes)

26. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Is a right triangle with a ratio of sides x:xv3:2x.
Then the quotient y/x is a constant.
360°
A = [(s^2*v3)/4]

27. How do you find the probability that an event will occur?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.
At least one of the factors is 0.

28. What is the formula for the surface area of a cube?
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.
V = pr^2h
A = 6(l^2)
A = s^2 or A =d^2/2 where d is the diagonal

29. What is a negative exponent?
For any number n: x^-n means 1/x^n.
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.
Corresponding sides of similar triangles are in proportion.

30. What is a Venn diagram?
Write the percent over 100 and reduce.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2
Cannot is 0 - must is 1 - all others are in between.

31. How do you find the x-intercept of a graph?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Set y = 0 - and solve.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
1 is a divisor (or factor) of every integer.

32. How do you find a percent of a number?
Equal slopes.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent as a decimal - and multiply.
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.

33. How do you calculate a weighted average?
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.
For any number a: a * 1 = a and a / 1 = a.
0 is a multiple of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

34. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).
Shifted down 2 units.
No matter how many angles there are - the sum around the point is 360°.

35. Properties of square roots
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

36. Law of exponents 5
A^m/b^m = (a/b)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
All positive and negative whole numbers - and zero.

37. Law of exponents 2
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Their sum is 90°.
M = (y2 - y1)/(x2 - x1)

38. Important binomial 3
B^m/b^n = b^m-n
An angle formed by extending the side of the polygon.
(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.

39. How do you calculate percent increases and decreases?
A = pr^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.
Shifted up 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

40. If you were given the graph of y = f(x) - what does f(a) represent?
Equal slopes.
V = lwh
For any number b: b = -b if and only if b = 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

41. What is the formula for the area of a triangle?
A = (1/2)bh.
In the expression x^b - x is the base and b is the exponent.
The product of their slopes is -1 (negative reciprocal).
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

42. What is 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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

43. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
0 is the only number that is neither positive nor negative.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted up 2 units.

44. In a circle of radius r - what is the formula for the area?
0 is the only number that is neither positive nor negative.
For any number a: a * 1 = a and a / 1 = a.
V = pr^2h
A = pr^2

45. Properties of zero 3
0 is a multiple of every integer.
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2
Set x = 0 - and solve.

46. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Set x = 0 - and solve.
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

47. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
V = l^3
All positive and negative whole numbers - and zero.

48. What are the important properties of a 45-45 - 90 triangle?
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Divide - then multiply by 100.

49. In a circle of radius r - what is the formula for the circumference?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.
C = p2r
For any integer n: 1^n = 1.

50. What are the properties of a parallelogram?
An equation that states that two ratios are equivalent. 4/6 = 10/15
An integer greater than one that is not prime.
For any number n: x^-n means 1/x^n.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.