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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 is the formula for the surface area of a cube?
(b^m)^n = b^mn
A = 6(l^2)
Shifted up 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

2. What is special formula for the area of an equilateral triangle?
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = [(s^2*v3)/4]

3. Properties of one 2
1 is the smallest positive odd integer.
For any integer n: 1^n = 1.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

4. Properties of zero 4
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Then the quotient y/x is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

5. What is p?
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.
(Circumference/diameter) of a circle - or approximately 3.14.
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.

6. If you were given the graph of y = f(x) - what does f(a) represent?
360°
A^m/b^m = (a/b)^m
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
At least one of the factors is 0.

7. In a circle of radius r - what is the formula for the area?
V = l^3
A = pr^2
[(x1 + x2)/2] -[(y1 + y2)/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.

8. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Divide - then multiply by 100.
A = [(s^2*v3)/4]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set y = 0 - and solve.

9. Properties of one 4
1 is the smallest positive odd integer.
360°
Corresponding sides of similar triangles are in proportion.
1 is a divisor (or factor) of every integer.

10. How do you find the x-intercept of a graph?
0 is the only number that is neither positive nor negative.
Set y = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
B^m/b^n = b^m-n

11. What is the probability of an event that cannot occur? That must occur?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Cannot is 0 - must is 1 - all others are in between.
An angle formed by extending the side of the polygon.
The set of all ordered pairs (x -y) such that y = f(x).

12. How do you convert a percent to a fraction or a decimal?
A = 6(l^2)
Write the percent over 100 and reduce.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Their sum is 180°.

13. What is the distributive law?
A = 2(lw + lh + hw)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
M = (y2 - y1)/(x2 - x1)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

14. In a circle of radius r - what is the formula for the circumference?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.
C = p2r
A = 2(lw + lh + hw)

15. Important binomial 2
(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.
360°
0 is the only number that is neither positive nor negative.

16. How you convert a fraction or a decimal to a percent?
An integer greater than one that is not prime.
For any number n: x^-n means 1/x^n.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Divide - then multiply by 100.

17. 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.
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100

18. Properties of zero 2
D = 2r
[(x1 + x2)/2] -[(y1 + y2)/2]
If a is negative and b is positive - then a < 0 < b.
A = 2(lw + lh + hw)

19. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted right 2 units.
A = bh
Even numbers are divisible by 2 and odd numbers are not.
Shifted down 2 units.

20. What is a proportion?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An equation that states that two ratios are equivalent. 4/6 = 10/15
How steep the line is. Horizontal line = 0 - vertical has no slope.
Write the percent over 100 and reduce.

21. What is the graph of a function?
For any number a: a * 1 = a and a / 1 = a.
The set of all ordered pairs (x -y) such that y = f(x).
V = l^3
0 is the only number that is neither positive nor negative.

22. How do we write the equation of a line?
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = s^2 or A =d^2/2 where d is the diagonal
Set x = 0 - and solve.

23. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is a divisor (or factor) of every integer.

24. What are the properties of a parallelogram?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
Is a right triangle with a ratio of sides x:xv3:2x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

25. What is a divisor and a factor of an integer?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = s^2 or A =d^2/2 where d is the diagonal

26. What is a Venn diagram?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 2(lw + lh + hw)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A fraction whose denominator is 100 i.e. 17% = 17/100

27. What is a multiple of an integer?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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 = 6(l^2)

28. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.

29. What is a prime number?
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.
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is the only number that is neither positive nor negative.

30. Properties of zero 1
0 is the only number that is neither positive nor negative.
An integer greater than one that is not prime.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = s^2 or A =d^2/2 where d is the diagonal

31. What does it mean if y is directly proportional to x?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Then the quotient y/x is a constant.
Set y = 0 - and solve.
M = (y2 - y1)/(x2 - x1)

32. What is true about the slopes of parallel lines?
Equal slopes.
[(x1 + x2)/2] -[(y1 + y2)/2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any number b: b = -b if and only if b = 0.

33. Properties of square roots
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh

34. What is the distance formula?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Even numbers are divisible by 2 and odd numbers are not.
A^m*b^m = (ab)^m
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

35. What is the ratio of similitude?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The ratio of corresponding sides of similar triangles.

36. What are the sum - difference - products - and quotient of two numbers?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = lw
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted left 2 units.

37. What important property do similar triangles have?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number b: b = -b if and only if b = 0.
Corresponding sides of similar triangles are in proportion.
M = (y2 - y1)/(x2 - x1)

38. Law of exponents 2
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any number n: x^-n means 1/x^n.
B^m/b^n = b^m-n
Then the product xy is a constant.

39. What is an integer?
A^m*b^m = (ab)^m
All positive and negative whole numbers - and zero.
The ratio of corresponding sides of similar triangles.
For any number b: b = -b if and only if b = 0.

40. What are the important properties of a 45-45 - 90 triangle?
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(b^m)^n = b^mn

41. What are the important properties of 30-60-90 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°.
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.

42. How do you find a percent of a number?
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.
Write the percent as a decimal - and multiply.
At least one of the factors is 0.
(Circumference/diameter) of a circle - or approximately 3.14.

43. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 90°.

44. What is the sum of the measures of the four angles in a quadrilateral?
1 is the smallest positive odd integer.
In the expression x^b - x is the base and b is the exponent.
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

45. Law of exponents 1
The set of all ordered pairs (x -y) such that y = f(x).
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m*b^n = b^m+n
Their sum is 180°.

46. What is the square root of a number?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = bh
For any integer n: 1^n = 1.

47. If the product of two or more numbers is 0 - what do you know about the numbers?
Their sum is 90°.
At least one of the factors is 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(Circumference/diameter) of a circle - or approximately 3.14.

48. What is true about the slopes of perpendicular lines?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x + y)(x - y) = x^2 - y^2
For any number a: a * 1 = a and a / 1 = a.
The product of their slopes is -1 (negative reciprocal).

49. What is a percent?
Is a right triangle with a ratio of sides x:xv3:2x.
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

50. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.