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 distributive law?
All positive and negative whole numbers - and zero.
Shifted left 2 units.
The product of their slopes is -1 (negative reciprocal).
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

2. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
A = (1/2)bh.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
No matter how many angles there are - the sum around the point is 360°.

3. What is the ratio of similitude?
A = lw
The ratio of corresponding sides of similar triangles.
(n - 2)(180°)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

4. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. What is p?
A = lw
A^m/b^m = (a/b)^m
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(Circumference/diameter) of a circle - or approximately 3.14.

6. How you convert a fraction or a decimal to a percent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Divide - then multiply by 100.
Cannot is 0 - must is 1 - all others are in between.
Area = (x°/360)(pr^2) where x is the central angle.

7. How do you calculate percent increases and decreases?
V = l^3
V = pr^2h
V = lwh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

8. Law of exponents 5
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.
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^m/b^m = (a/b)^m
[(x1 + x2)/2] -[(y1 + y2)/2]

9. What is the sum of the measures of all angles around a point?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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°.
Shifted down 2 units.

10. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number a: a * 1 = a and a / 1 = a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

11. Law of exponents 3
A = 2(lw + lh + hw)
How steep the line is. Horizontal line = 0 - vertical has no slope.
(b^m)^n = b^mn
Divide - then multiply by 100.

12. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = pr^2h
1 is the smallest positive odd integer.

13. What is a fractional exponent?
Their sum is 90°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
An angle formed by extending the side of the polygon.

14. What is the relationship between the graph of f(x) the graph of y = f(x) + 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.
A = s^2 or A =d^2/2 where d is the diagonal
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted up 2 units.

15. Properties of zero 3
The product of their slopes is -1 (negative reciprocal).
0 is a multiple of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 180°.

16. What are the properties of a square?
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

17. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Then the product xy is a constant.
Shifted down 2 units.
All positive and negative whole numbers - and zero.
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.

18. What is the distance formula?
Avg = sum of n numbers/n
A = 6(l^2)
Set x = 0 - and solve.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

19. What does it mean if y is directly proportional to x?
Even numbers are divisible by 2 and odd numbers are not.
Then the quotient y/x is a constant.
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent over 100 and reduce.

20. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.

21. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
1 is the smallest positive odd integer.
C = p2r
The product of their slopes is -1 (negative reciprocal).

22. What is a divisor and a factor of an integer?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is the smallest positive odd integer.

23. What is the formula for the surface area of a cube?
For any integer n: 1^n = 1.
How steep the line is. Horizontal line = 0 - vertical has no slope.
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)

24. What is the volume of a cube?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n
M = (y2 - y1)/(x2 - x1)
V = l^3

25. What is the triangle inequality?
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.
The two pairs of opposite angles formed are equal to each other.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At least one of the factors is 0.

26. What are the important properties of 30-60-90 triangle?
V = lwh
An integer greater than one that is not prime.
A = s^2 or A =d^2/2 where d is the diagonal
Is a right triangle with a ratio of sides x:xv3:2x.

27. What is a negative exponent?
No matter how many angles there are - the sum around the point is 360°.
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 n: x^-n means 1/x^n.
360°

28. Law of exponents 1
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.
Equal slopes.
B^m*b^n = b^m+n

29. What is a function?
For any number a: a * 1 = a and a / 1 = a.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(Circumference/diameter) of a circle - or approximately 3.14.
180°. If two or more angles form a straight angle - their sum is 180°.

30. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
C = p2r
Divide - then multiply by 100.
A fraction whose denominator is 100 i.e. 17% = 17/100

31. 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 b: b = -b if and only if b = 0.
(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°.
A^m/b^m = (a/b)^m

32. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
A^m*b^m = (ab)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

33. Properties of zero 1
0 is the only number that is neither positive nor negative.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = bh
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. What is a proportion?
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15
The ratio of corresponding sides of similar triangles.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

35. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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.
360°
Their sum is 90°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

36. How do you find a percent of a number?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.

37. What is a Venn diagram?
The set of all ordered pairs (x -y) such that y = f(x).
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.

38. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.
A^m*b^m = (ab)^m
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

39. What is the Pythagorean theorem?
Then the product xy is a constant.
[(x1 + x2)/2] -[(y1 + y2)/2]
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.

40. What is the formula for the volume of a rectangular solid?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Write the percent as a decimal - and multiply.
A = s^2 or A =d^2/2 where d is the diagonal
V = lwh

41. What is the formula for the area of a triangle?
1 is a divisor (or factor) of every integer.
Is a right triangle with a ratio of sides x:xv3:2x.
A = (1/2)bh.
Write the percent as a decimal - and multiply.

42. If you were given the graph of y = f(x) - what does f(a) represent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set x = 0 - and solve.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

43. For what values of a function is the function undefined?
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
V = l^3
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

44. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is the smallest positive odd integer.
C = p2r

45. What are similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
C = p2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

46. How do you find the y-intercept of a graph?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is a multiple of every integer.
Set x = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.

47. 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.
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.
V = pr^2h
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

48. Properties of one 4
A = lw
1 is the smallest positive odd integer.
180°. If two or more angles form a straight angle - their sum is 180°.
Their sum is 90°.

49. What is an even and an odd number?
A = 2(lw + lh + hw)
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

50. How do you find the area of a sector of a circle?
Even numbers are divisible by 2 and odd numbers are not.
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.