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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 a ratio?

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2. 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.
If a is negative and b is positive - then a < 0 < b.
All positive and negative whole numbers - and zero.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

3. What is p?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Area = (x°/360)(pr^2) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(Circumference/diameter) of a circle - or approximately 3.14.

4. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

5. What is a negative exponent?
(x + y)(x - y) = x^2 - y^2
B^m*b^n = b^m+n
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. Properties of square roots
Shifted left 2 units.
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

7. Important binomial 2
An angle formed by extending the side of the polygon.
D = 2r
Shifted up 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

8. How do you find the area of a sector of a circle?
Write the percent as a decimal - and multiply.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Corresponding sides of similar triangles are in proportion.
Area = (x°/360)(pr^2) where x is the central angle.

9. What is true about the areas of similar triangles?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
B^m*b^n = b^m+n
The product of their slopes is -1 (negative reciprocal).

10. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
An equation that states that two ratios are equivalent. 4/6 = 10/15
M = (y2 - y1)/(x2 - x1)
A = bh

11. 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.
1 is a divisor (or factor) of every integer.
B^m/b^n = b^m-n
A = s^2 or A =d^2/2 where d is the diagonal

12. What is the sum of the measures of the n angles of a polygon with n sides?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction whose denominator is 100 i.e. 17% = 17/100
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(n - 2)(180°)

13. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

14. What is the probability of an event that cannot occur? That must occur?
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.
Cannot is 0 - must is 1 - all others are in between.

15. What is a proportion?
Corresponding sides of similar triangles are in proportion.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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

16. What is the volume of a cube?
V = l^3
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = [(s^2*v3)/4]
For any integer n: 1^n = 1.

17. What is the formula for the surface area of a cube?
A = 6(l^2)
D = 2r
Arc = (x°/360)(2pr) where x is the central angle.
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.

18. What are the quotient and the remainder?

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19. What are the sum - difference - products - and quotient of two numbers?
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
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.

20. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
In the expression x^b - x is the base and b is the exponent.
A = bh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

21. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m
If a is negative and b is positive - then a < 0 < b.

22. What is the distributive law?
V = lwh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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

23. What is the formula for the volume of a cylinder?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = pr^2h
The ratio of corresponding sides of similar triangles.
How steep the line is. Horizontal line = 0 - vertical has no slope.

24. Properties of zero 1
Write the percent as a decimal - and multiply.
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

25. Law of exponents 2
B^m/b^n = b^m-n
V = pr^2h
No matter how many angles there are - the sum around the point is 360°.
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°.

26. What is a divisor and a factor of an integer?
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.
360°
They are both the same. A divisor or factor of an integer leaves no remainder.

27. Properties of one 2
Area = (x°/360)(pr^2) where x is the central angle.
Then the quotient y/x is a constant.
For any integer n: 1^n = 1.
Shifted left 2 units.

28. Properties of zero 5
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

29. What is true about the measures of the three angles in a triangle?
For any number b: b = -b if and only if b = 0.
1 is the smallest positive odd integer.
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.
Their sum is 180°.

30. How do you find a percent of a number?
For any number n: x^-n means 1/x^n.
Shifted down 2 units.
Write the percent as a decimal - and multiply.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

31. Properties of zero 3
At least one of the factors is 0.
B^m/b^n = b^m-n
A = 2(lw + lh + hw)
0 is a multiple of every integer.

32. 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.
0 is the only number that is neither positive nor negative.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.

33. What are the median and the mode of a set of data?
A = s^2 or A =d^2/2 where d is the diagonal
0 is the only number that is neither positive nor negative.
180°. If two or more angles form a straight angle - their sum is 180°.
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.

34. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Cannot is 0 - must is 1 - all others are in between.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted left 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

35. What is an exterior angle of a triangle?
0 is the only number that is neither positive nor negative.
A = pr^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

36. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted down 2 units.
(n - 2)(180°)

37. How you convert a fraction or a decimal to a percent?
1 is a divisor (or factor) of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Divide - then multiply by 100.
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.

38. Important binomial 1
1 is the smallest positive odd integer.
(x + y)(x - y) = x^2 - y^2
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.

39. What is a composite number?
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any right triangle - a^2 + b^2 = c^2.

40. Properties of one 4
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is the smallest positive odd integer.
D = 2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

41. What is a Venn diagram?
Cannot is 0 - must is 1 - all others are in between.
D = 2r
In the expression x^b - x is the base and b is the exponent.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

42. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number b: b = -b if and only if b = 0.
The product of their slopes is -1 (negative reciprocal).

43. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.
(b^m)^n = b^mn
They are both the same. A divisor or factor of an integer leaves no remainder.

44. What is true about the measures of the two acute angles in a right triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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°.
Their sum is 90°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

45. Properties of one 3
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
Shifted up 2 units.
The ratio of corresponding sides of similar triangles.

46. Law of exponents 4
0 is the only number that is neither positive nor negative.
A^m*b^m = (ab)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = lwh

47. What is an even and an odd 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.
(x + y)(x - y) = x^2 - y^2
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.
Even numbers are divisible by 2 and odd numbers are not.

48. What is the distance formula?
A = bh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Then the product xy is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

49. 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.
180°. If two or more angles form a straight angle - their sum is 180°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Even numbers are divisible by 2 and odd numbers are not.

50. What is a fractional exponent?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted right 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.