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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 2
V = lwh
For any integer n: 1^n = 1.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The product of their slopes is -1 (negative reciprocal).

2. What is a multiple of an integer?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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 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.
For any number a: a * 1 = a and a / 1 = a.

3. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m*b^n = b^m+n
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°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

4. What is the sum of the measures of the four angles in a quadrilateral?
A^m/b^m = (a/b)^m
360°
Shifted right 2 units.
C = p2r

5. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Write the percent over 100 and reduce.
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°.
Shifted left 2 units.
A = bh

6. What is the formula for the surface area of a rectangular solid?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(b^m)^n = b^mn
A = [(s^2*v3)/4]
A = 2(lw + lh + hw)

7. How do we write the equation of a line?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number b: b = -b if and only if b = 0.
B^m*b^n = b^m+n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

8. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
For any number a: a * 1 = a and a / 1 = a.
The set of all ordered pairs (x -y) such that y = f(x).
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°.

9. What is a ratio?

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10. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
360°
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.

11. What is true about the slopes of parallel lines?
Equal slopes.
Their sum is 90°.
B^m/b^n = b^m-n
B^m*b^n = b^m+n

12. How do you calculate percent increases and decreases?
Shifted down 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

13. What is a proportion?
The set of all ordered pairs (x -y) such that y = f(x).
An equation that states that two ratios are equivalent. 4/6 = 10/15
V = lwh
0 is the only number that is neither positive nor negative.

14. Important binomial 3
Write the percent over 100 and reduce.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)
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.

15. How do you convert a percent to a fraction or a decimal?
M = (y2 - y1)/(x2 - x1)
V = pr^2h
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent over 100 and reduce.

16. What are the properties of a parallelogram?
Set x = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

17. What is an exponent?
(Circumference/diameter) of a circle - or approximately 3.14.
In the expression x^b - x is the base and b is the exponent.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted up 2 units.

18. What is the formula for the area of a triangle?
Then the quotient y/x is a constant.
If a is negative and b is positive - then a < 0 < b.
All positive and negative whole numbers - and zero.
A = (1/2)bh.

19. 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.
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal
Their sum is 90°.

20. What is the volume of a cube?
If a is negative and b is positive - then a < 0 < b.
V = l^3
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

21. What is the measure of a straight angle?
Equal slopes.
How steep the line is. Horizontal line = 0 - vertical has no slope.
180°. If two or more angles form a straight angle - their sum is 180°.
M = (y2 - y1)/(x2 - x1)

22. What are the properties of a rectangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
360°
Set x = 0 - and solve.

23. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. What is the sum of the measures of the n angles of a polygon with n sides?
No matter how many angles there are - the sum around the point is 360°.
A = pr^2
(n - 2)(180°)
Shifted down 2 units.

25. What are similar triangles?
B^m*b^n = b^m+n
(n - 2)(180°)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

26. What is the midpoint formula?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
[(x1 + x2)/2] -[(y1 + y2)/2]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m*b^n = b^m+n

27. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
C = p2r
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 = l^3

28. What is the formula for the volume of a cylinder?
V = pr^2h
Divide - then multiply by 100.
At least one of the factors is 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

29. Properties of zero 5
B^m*b^n = b^m+n
An integer greater than one that is not prime.
For any number b: b = -b if and only if b = 0.
(Circumference/diameter) of a circle - or approximately 3.14.

30. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The set of all ordered pairs (x -y) such that y = f(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.
Write the percent as a decimal - and multiply.

31. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
All positive and negative whole numbers - and zero.
If a is negative and b is positive - then a < 0 < b.

32. What is the distributive law?
For any right triangle - a^2 + b^2 = c^2.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(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.

33. What is true about the measures of the four angles formed by two intersecting lines?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The two pairs of opposite angles formed are equal to each other.
The ratio of corresponding sides of similar triangles.
At least one of the factors is 0.

34. What important property do similar triangles have?
For any right triangle - a^2 + b^2 = c^2.
Corresponding sides of similar triangles are in proportion.
Arc = (x°/360)(2pr) where x is the central angle.
B^m/b^n = b^m-n

35. What do we mean by the slope of the line?
All positive and negative whole numbers - and zero.
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
A = lw

36. How you convert a fraction or a decimal to a percent?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For any right triangle - a^2 + b^2 = c^2.
Divide - then multiply by 100.
(Circumference/diameter) of a circle - or approximately 3.14.

37. In a circle of radius r - what is the formula for the diameter?
D = 2r
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.
Equal slopes.

38. For what values of a function is the function undefined?
If a is negative and b is positive - then a < 0 < b.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number n: x^-n means 1/x^n.
Shifted down 2 units.

39. How do you find the length of an arc of a circle?
V = lwh
Arc = (x°/360)(2pr) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Then the quotient y/x is a constant.

40. What is the graph of a function?
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any integer n: 1^n = 1.
The set of all ordered pairs (x -y) such that y = f(x).

41. What is special formula for the area of an equilateral triangle?
For any number b: b = -b if and only if b = 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = [(s^2*v3)/4]

42. Properties of one 4
1 is the smallest positive odd integer.
An angle formed by extending the side of the polygon.
Divide - then multiply by 100.
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.

43. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set x = 0 - and solve.
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.
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.

44. 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 down 2 units.
Avg = sum of n numbers/n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

45. What are the important properties of a 45-45 - 90 triangle?
A^m/b^m = (a/b)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

46. What are the median and the mode of a set of data?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted left 2 units.
0 is the only number that is neither positive nor negative.
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.

47. Important binomial 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
[(x1 + x2)/2] -[(y1 + y2)/2]
(x + y)(x - y) = x^2 - y^2

48. What are the sum - difference - products - and quotient of two numbers?
Set y = 0 - and solve.
A = lw
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.

49. Law of exponents 1
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Cannot is 0 - must is 1 - all others are in between.
0 is the only number that is neither positive nor negative.
B^m*b^n = b^m+n

50. Properties of zero 2
Avg = sum of n numbers/n
Shifted down 2 units.
If a is negative and b is positive - then a < 0 < b.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.