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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 area of a rectangle?
At least one of the factors is 0.
A^m*b^m = (ab)^m
C = p2r
A = lw

2. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(b^m)^n = b^mn
D = 2r

3. Law of exponents 3
B^m*b^n = b^m+n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted down 2 units.
(b^m)^n = b^mn

4. What is a fractional exponent?
Then the quotient y/x is a constant.
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Arc = (x°/360)(2pr) where x is the central angle.

5. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.
M = (y2 - y1)/(x2 - x1)
Even numbers are divisible by 2 and odd numbers are not.

6. What is a Venn diagram?
Corresponding sides of similar triangles are in proportion.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted right 2 units.
360°

7. What is the volume of a cube?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = l^3
Area = (x°/360)(pr^2) where x is the central angle.
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.

8. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.

9. What are the important properties of 30-60-90 triangle?
Area = (x°/360)(pr^2) where x is the central angle.
[(x1 + x2)/2] -[(y1 + y2)/2]
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted up 2 units.

10. What is p?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(Circumference/diameter) of a circle - or approximately 3.14.
An angle formed by extending the side of the polygon.
Their sum is 180°.

11. Properties of square roots
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

12. What is the sum of the measures of all angles around a point?
Divide - then multiply by 100.
360°
A = pr^2
No matter how many angles there are - the sum around the point is 360°.

13. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
All positive and negative whole numbers - and zero.
Avg = sum of n numbers/n
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 = (1/2)bh.

14. What is true about the slopes of perpendicular lines?
For any number a: a * 1 = a and a / 1 = a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The product of their slopes is -1 (negative reciprocal).
Then the quotient y/x is a constant.

15. What is the formula for the area of a parallelogram?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = bh

16. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Equal slopes.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh

17. Law of exponents 5
A^m/b^m = (a/b)^m
A = [(s^2*v3)/4]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

18. What do we mean by the slope of the line?
Is a right triangle with a ratio of sides x:xv3:2x.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
How steep the line is. Horizontal line = 0 - vertical has no slope.

19. What is a composite number?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
An integer greater than one that is not prime.
B^m/b^n = b^m-n
V = l^3

20. Properties of zero 5
For any number b: b = -b if and only if b = 0.
(b^m)^n = b^mn
V = lwh
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.

21. How you convert a fraction or a decimal to a percent?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Divide - then multiply by 100.
A = 2(lw + lh + hw)
Shifted down 2 units.

22. What is a percent?
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.
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m

23. Law of exponents 2
B^m/b^n = b^m-n
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 90°.
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.

24. Properties of zero 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
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°.
0 is a multiple of every integer.

25. What is the measure of a straight angle?
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°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

26. How do we write the equation of a line?
Their sum is 180°.
1 is a divisor (or factor) of every integer.
M = (y2 - y1)/(x2 - x1)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

27. What is a ratio?

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28. What is an integer?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted down 2 units.
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.
All positive and negative whole numbers - and zero.

29. What is the sum of the measures of the four angles in a quadrilateral?
Arc = (x°/360)(2pr) where x is the central angle.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°
A = [(s^2*v3)/4]

30. What is the formula for the area of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)
A = (1/2)bh.

31. What is the sum of the measures of the n angles of a polygon with n sides?
1 is the smallest positive odd integer.
(n - 2)(180°)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set y = 0 - and solve.

32. What is the formula for the volume of a cylinder?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
1 is the smallest positive odd integer.
V = l^3
V = pr^2h

33. In a circle of radius r - what is the formula for the area?
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = pr^2

34. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^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.
Set y = 0 - and solve.

35. What are similar triangles?
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.
A^m/b^m = (a/b)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

36. Law of exponents 1
B^m*b^n = b^m+n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted right 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

37. What are the properties of a parallelogram?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
No matter how many angles there are - the sum around the point is 360°.

38. What is the formula for the surface area of a rectangular solid?
An equation that states that two ratios are equivalent. 4/6 = 10/15
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
0 is the only number that is neither positive nor negative.
A = 2(lw + lh + hw)

39. What is the distance formula?
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 = 2(lw + lh + hw)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Even numbers are divisible by 2 and odd numbers are not.

40. Properties of zero 2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
360°

41. Law of exponents 4
360°
A^m*b^m = (ab)^m
An integer greater than one that is not prime.
V = lwh

42. What is the ratio of similitude?
Set x = 0 - and solve.
The ratio of corresponding sides of similar triangles.
Shifted up 2 units.
A = s^2 or A =d^2/2 where d is the diagonal

43. What is special formula for the area of an equilateral triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = [(s^2*v3)/4]

44. For what values of a function is the function undefined?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = pr^2h
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

45. What formula is used for an average?
V = pr^2h
Avg = sum of n numbers/n
All positive and negative whole numbers - and zero.
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.

46. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Arc = (x°/360)(2pr) where x is the central angle.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
The ratio of corresponding sides of similar triangles.

47. Important binomial 2
A^m/b^m = (a/b)^m
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
P(e) = (# of favorable outcomes)/(# of possible outcomes)

48. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 90°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = [(s^2*v3)/4]

49. What is a negative exponent?
B^m*b^n = b^m+n
For any number n: x^-n means 1/x^n.
No matter how many angles there are - the sum around the point is 360°.
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.

50. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Equal slopes.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.