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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. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Equal slopes.
For any number a: a * 1 = a and a / 1 = a.
A = s^2 or A =d^2/2 where d is the diagonal

2. How do you calculate percent increases and decreases?
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

3. How do you find the length of an arc of a circle?
Shifted right 2 units.
B^m/b^n = b^m-n
A^m/b^m = (a/b)^m
Arc = (x°/360)(2pr) where x is the central angle.

4. What is an integer?
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 any right triangle - a^2 + b^2 = c^2.
All positive and negative whole numbers - and zero.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

5. In a circle of radius r - what is the formula for the area?
A = pr^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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

6. What is a ratio?

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7. How do you find the probability that an event will occur?
D = 2r
V = pr^2h
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

8. Properties of zero 3
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.
0 is a multiple of every integer.
Write the percent as a decimal - and multiply.

9. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted up 2 units.

10. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the quotient y/x is a constant.
D = 2r
Corresponding sides of similar triangles are in proportion.

11. What is the formula for the area of a rectangle?
A = lw
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.

12. What is a percent?
(n - 2)(180°)
A fraction whose denominator is 100 i.e. 17% = 17/100
How steep the line is. Horizontal line = 0 - vertical has no slope.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
The ratio of corresponding sides of similar triangles.
Avg = sum of n numbers/n
The product of their slopes is -1 (negative reciprocal).

14. Properties of zero 4
(Circumference/diameter) of a circle - or approximately 3.14.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The two pairs of opposite angles formed are equal to each other.
M = (y2 - y1)/(x2 - x1)

15. What is an exponent?
Even numbers are divisible by 2 and odd numbers are not.
Write the percent over 100 and reduce.
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.

16. 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.
V = l^3
B^m*b^n = b^m+n
Shifted down 2 units.

17. What are the important properties of 30-60-90 triangle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Is a right triangle with a ratio of sides x:xv3:2x.
0 is the only number that is neither positive nor negative.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

18. What is a proportion?
Write the percent as a decimal - and multiply.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is the only number that is neither positive nor negative.

19. What is a composite number?
The product of their slopes is -1 (negative reciprocal).
An integer greater than one that is not prime.
V = lwh
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

20. What is a Venn diagram?
A = 2(lw + lh + hw)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
They are both the same. A divisor or factor of an integer leaves no remainder.

21. Law of exponents 3
C = p2r
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(b^m)^n = b^mn

22. What is the graph of a function?
Then the quotient y/x is a constant.
V = pr^2h
The set of all ordered pairs (x -y) such that y = f(x).
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.

23. What is a divisor and a factor of an integer?
B^m/b^n = b^m-n
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 6(l^2)
A^m*b^m = (ab)^m

24. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.
A = [(s^2*v3)/4]

25. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - 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.

26. Important binomial 2
360°
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m*b^m = (ab)^m
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

27. Law of exponents 4
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.
Their sum is 90°.
A^m*b^m = (ab)^m
Is a right triangle with a ratio of sides x:xv3:2x.

28. What is an even and an odd number?
A = 6(l^2)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.

29. What is the formula for the area of a triangle?
A = (1/2)bh.
An integer greater than one that is not prime.
360°
(Circumference/diameter) of a circle - or approximately 3.14.

30. What is true about the slopes of perpendicular lines?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2
The product of their slopes is -1 (negative reciprocal).

31. What is true about the areas of similar triangles?
A = (1/2)bh.
Shifted left 2 units.
An angle formed by extending the side of the polygon.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

32. 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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)(x - y) = x^2 - y^2

33. What is the ratio of similitude?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The ratio of corresponding sides of similar triangles.

34. What are similar triangles?
Then the product xy is a constant.
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.
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.

35. What is the triangle inequality?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
(x + y)(x - y) = x^2 - y^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

36. How do you convert a percent to a fraction or a decimal?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent over 100 and reduce.

37. What is the formula for the volume of a cylinder?
For any integer n: 1^n = 1.
An integer greater than one that is not prime.
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.

38. Properties of square roots
C = p2r
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
They are both the same. A divisor or factor of an integer leaves no remainder.

39. If the product of two or more numbers is 0 - what do you know about the numbers?
Shifted left 2 units.
M = (y2 - y1)/(x2 - x1)
At least one of the factors is 0.
D = 2r

40. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Cannot is 0 - must is 1 - all others are in between.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.

41. Properties of one 1
Avg = sum of n numbers/n
V = lwh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any number a: a * 1 = a and a / 1 = a.

42. What is special formula for the area of an equilateral triangle?
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = s^2 or A =d^2/2 where d is the diagonal

43. What is the probability of an event that cannot occur? That must occur?
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.
Corresponding sides of similar triangles are in proportion.
An integer greater than one that is not prime.

44. What is true about the measures of the three angles in a triangle?
Then the quotient y/x is a constant.
Then the product xy is a constant.
Their sum is 180°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

45. Properties of one 3
1 is a divisor (or factor) of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.
360°
B^m*b^n = b^m+n

46. What is the formula for the volume of a rectangular solid?
V = lwh
A = 6(l^2)
Shifted down 2 units.
The ratio of corresponding sides of similar triangles.

47. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted down 2 units.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

48. What important property do similar triangles have?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m/b^m = (a/b)^m
Corresponding sides of similar triangles are in proportion.
A = (1/2)bh.

49. What is the formula for the area of a parallelogram?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = bh
Set y = 0 - and solve.
V = l^3

50. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
If a is negative and b is positive - then a < 0 < b.
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°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(Circumference/diameter) of a circle - or approximately 3.14.