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. In a circle of radius r - what is the formula for the area?
Avg = sum of n numbers/n
Set y = 0 - and solve.
Equal slopes.
A = pr^2

2. What is the formula for the area of a triangle?
0 is the only number that is neither positive nor negative.
An angle formed by extending the side of the polygon.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = (1/2)bh.

3. Properties of one 4
1 is the smallest positive odd integer.
1 is a divisor (or factor) of every integer.
B^m/b^n = b^m-n
V = lwh

4. What is a prime number?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = s^2 or A =d^2/2 where d is the diagonal

5. What does it mean if y is directly proportional to x?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. Law of exponents 3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = pr^2h
(b^m)^n = b^mn
(Circumference/diameter) of a circle - or approximately 3.14.

7. What formula is used for an average?
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n
A = s^2 or A =d^2/2 where d is the diagonal
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

8. How do you find a percent of a number?
For any number n: x^-n means 1/x^n.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Write the percent as a decimal - and multiply.

9. Important binomial 2
No matter how many angles there are - the sum around the point is 360°.
Then the quotient y/x is a constant.
In the expression x^b - x is the base and b is the exponent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

10. What is the triangle inequality?
A = 6(l^2)
A = s^2 or A =d^2/2 where d is the diagonal
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.

11. What is a ratio?

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

12. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Shifted down 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)(x - y) = x^2 - y^2

13. What is an exterior angle of a triangle?
A = 2(lw + lh + hw)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

14. What are the important properties of 30-60-90 triangle?
Shifted up 2 units.
Equal slopes.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Is a right triangle with a ratio of sides x:xv3:2x.

15. What is the formula for the area of a parallelogram?
1 is a divisor (or factor) of every integer.
Corresponding sides of similar triangles are in proportion.
A = bh
At least one of the factors is 0.

16. How do you find the x-intercept of a graph?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Set y = 0 - and solve.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
M = (y2 - y1)/(x2 - x1)

17. What are the properties of a square?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number b: b = -b if and only if b = 0.
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.

18. What is true about the slopes of perpendicular lines?
(b^m)^n = b^mn
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).

19. Law of exponents 2
Then the quotient y/x is a constant.
A^m*b^m = (ab)^m
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
B^m/b^n = b^m-n

20. How do you find the slope of a line?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
M = (y2 - y1)/(x2 - x1)
No matter how many angles there are - the sum around the point is 360°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

21. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Avg = sum of n numbers/n
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

22. What are the properties of a rectangle?
Then the product xy is a constant.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Write the percent over 100 and reduce.
Divide - then multiply by 100.

23. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted left 2 units.
Divide - then multiply by 100.
Shifted down 2 units.

24. What is the formula for the area of a rectangle?
For any integer n: 1^n = 1.
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.
A = lw
They are both the same. A divisor or factor of an integer leaves no remainder.

25. How do you find the y-intercept of a graph?
Shifted up 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Then the quotient y/x is a constant.
Set x = 0 - and solve.

26. What is the formula for the surface area of a rectangular solid?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(n - 2)(180°)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = 2(lw + lh + hw)

27. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
0 is a multiple of every integer.
In the expression x^b - x is the base and b is the exponent.
[(x1 + x2)/2] -[(y1 + y2)/2]

28. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A^m/b^m = (a/b)^m
Shifted down 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = 2(lw + lh + hw)

29. 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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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 quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

30. How you convert a fraction or a decimal to a percent?
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Divide - then multiply by 100.

31. Properties of zero 4
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

32. Law of exponents 1
All positive and negative whole numbers - and zero.
(n - 2)(180°)
B^m*b^n = b^m+n
Divide - then multiply by 100.

33. Properties of one 3
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is a divisor (or factor) of every integer.
In the expression x^b - x is the base and b is the exponent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

34. What are the properties of a parallelogram?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

35. What is the sum of the measures of the n angles of a polygon with n sides?
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(n - 2)(180°)
Set y = 0 - and solve.

36. What is the formula for the surface area of a cube?
A = 6(l^2)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number a: a * 1 = a and a / 1 = a.
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.

37. How do you find the area of a sector of a circle?
The ratio of corresponding sides of similar triangles.
1 is a divisor (or factor) of every integer.
Area = (x°/360)(pr^2) where x is the central angle.
M = (y2 - y1)/(x2 - x1)

38. What is the measure of a straight angle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted up 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
180°. If two or more angles form a straight angle - their sum is 180°.

39. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.

40. How do you convert a percent to a fraction or a decimal?
Their sum is 90°.
Write the percent over 100 and reduce.
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.
A^m*b^m = (ab)^m

41. What is the square root of a number?
D = 2r
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
[(x1 + x2)/2] -[(y1 + y2)/2]

42. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.
A = bh
180°. If two or more angles form a straight angle - their sum is 180°.

43. What is a fractional exponent?
In the expression x^b - x is the base and b is the exponent.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

44. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(b^m)^n = b^mn
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

45. What is true about the measures of the three angles in a triangle?
Arc = (x°/360)(2pr) where x is the central angle.
Their sum is 180°.
Avg = sum of n numbers/n
A^m/b^m = (a/b)^m

46. What is true about the measures of the two acute angles in a right triangle?
Shifted up 2 units.
Write the percent over 100 and reduce.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 90°.

47. Properties of one 1
At least one of the factors is 0.
Equal slopes.
For any number a: a * 1 = a and a / 1 = a.
Avg = sum of n numbers/n

48. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
They are both the same. A divisor or factor of an integer leaves no remainder.
The ratio of corresponding sides of similar triangles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

49. What is the sum of the measures of the four angles in a quadrilateral?
360°
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 90°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

50. What are the sum - difference - products - and quotient of two numbers?
For any right triangle - a^2 + b^2 = c^2.
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = l^3