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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 are the properties of a square?
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.
360°
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

2. What is an exterior angle of a polygon?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°
An angle formed by extending the side of the polygon.
Then the quotient y/x is a constant.

3. What is true about the slopes of parallel lines?
V = pr^2h
Equal slopes.
C = p2r
Cannot is 0 - must is 1 - all others are in between.

4. What is a ratio?

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5. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

6. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted left 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15

7. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = lwh
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

8. What is an integer?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
Area = (x°/360)(pr^2) where x is the central angle.
All positive and negative whole numbers - and zero.

9. Important binomial 2
A = (1/2)bh.
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

10. What is the triangle inequality?
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.
V = pr^2h
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 = pr^2

11. What is the measure of a straight angle?
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
The ratio of corresponding sides of similar triangles.

12. In a circle of radius r - what is the formula for the circumference?
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 = (ab)^m
C = p2r
360°

13. How you convert a fraction or a decimal to a percent?
Cannot is 0 - must is 1 - all others are in between.
A = lw
The two pairs of opposite angles formed are equal to each other.
Divide - then multiply by 100.

14. Properties of one 2
In the expression x^b - x is the base and b is the exponent.
The ratio of corresponding sides of similar triangles.
D = 2r
For any integer n: 1^n = 1.

15. What is the graph of a function?
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.
0 is a multiple of every integer.
V = lwh
The set of all ordered pairs (x -y) such that y = f(x).

16. What is a Venn diagram?
Then the quotient y/x is a constant.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh

17. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is 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.
[(x1 + x2)/2] -[(y1 + y2)/2]
A fraction whose denominator is 100 i.e. 17% = 17/100

18. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = lwh

19. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
360°
Shifted right 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If a is negative and b is positive - then a < 0 < b.

20. What is the formula for the surface area of a rectangular solid?
Set x = 0 - and solve.
V = lwh
A = 2(lw + lh + hw)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

21. Properties of one 4
1 is the smallest positive odd integer.
Area = (x°/360)(pr^2) where x is the central angle.
Set x = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

22. What does it mean if y is directly proportional to x?
Their sum is 90°.
Then the quotient y/x is a constant.
V = l^3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

23. What is the midpoint formula?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Divide - then multiply by 100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
[(x1 + x2)/2] -[(y1 + y2)/2]

24. What is the formula for the area of a rectangle?
360°
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = [(s^2*v3)/4]

25. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = lw
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

26. Properties of zero 5
An angle formed by extending the side of the polygon.
For any number b: b = -b if and only if b = 0.
For any right triangle - a^2 + b^2 = c^2.
D = 2r

27. Properties of zero 1
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An integer greater than one that is not prime.
0 is the only number that is neither positive nor negative.
B^m/b^n = b^m-n

28. Law of exponents 3
A^m*b^m = (ab)^m
Divide - then multiply by 100.
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn

29. What are the important properties of 30-60-90 triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.

30. 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.
B^m*b^n = b^m+n
A = pr^2
(n - 2)(180°)

31. What is the distance formula?
V = pr^2h
1 is the smallest positive odd integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
P(e) = (# of favorable outcomes)/(# of possible outcomes)

32. How do you find the slope of a line?
360°
0 is the only number that is neither positive nor negative.
M = (y2 - y1)/(x2 - x1)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

33. What is an exponent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An integer greater than one that is not prime.
In the expression x^b - x is the base and b is the exponent.
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.

34. Properties of one 3
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.
1 is a divisor (or factor) of every integer.
(n - 2)(180°)
Set y = 0 - and solve.

35. Law of exponents 4
Then the quotient y/x is a constant.
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m

36. What is the formula for the volume of a cylinder?
A = bh
V = pr^2h
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°.
Then the quotient y/x is a constant.

37. How do you find a percent of a number?
Shifted up 2 units.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent as a decimal - and multiply.

38. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

39. What is the square root of a number?
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.
An integer greater than one that is not prime.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

40. What are the quotient and the remainder?

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41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
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 = bh
Then the quotient y/x is a constant.

42. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15

43. If the product of two or more numbers is 0 - what do you know about the numbers?
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.
180°. If two or more angles form a straight angle - their sum is 180°.
At least one of the factors is 0.
An integer greater than one that is not prime.

44. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A fraction whose denominator is 100 i.e. 17% = 17/100
Arc = (x°/360)(2pr) where x is the central angle.
A = [(s^2*v3)/4]

45. How do you convert a percent to a fraction or a decimal?
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.
(x + y)(x - y) = x^2 - y^2

46. What are the properties of a parallelogram?
No matter how many angles there are - the sum around the point is 360°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)

47. In a circle of radius r - what is the formula for the area?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
In the expression x^b - x is the base and b is the exponent.
For any right triangle - a^2 + b^2 = c^2.
A = pr^2

48. What is a composite number?
Their sum is 180°.
All positive and negative whole numbers - and zero.
Their sum is 90°.
An integer greater than one that is not prime.

49. 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.
(b^m)^n = b^mn
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

50. What are the important properties of a 45-45 - 90 triangle?
An integer greater than one that is not prime.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.