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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. Law of exponents 4
For any number n: x^-n means 1/x^n.
A^m*b^m = (ab)^m
The ratio of corresponding sides of similar triangles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

2. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

3. What is the formula for the volume of a rectangular solid?
Shifted right 2 units.
V = lwh
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh

4. What are the median and the mode of a set of data?
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.
The set of all ordered pairs (x -y) such that y = f(x).
1 is the smallest positive odd integer.
Shifted right 2 units.

5. What is true about the measures of the four angles formed by two intersecting lines?
Their sum is 90°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The two pairs of opposite angles formed are equal to each other.

6. What is the volume of a cube?
Write the percent over 100 and reduce.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = l^3
(b^m)^n = b^mn

7. What is the formula for the volume of a cylinder?
V = lwh
An integer greater than one that is not prime.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = pr^2h

8. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An integer greater than one that is not prime.
Their sum is 180°.

9. What is the formula for the area of a parallelogram?
A = bh
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.

10. What is a prime number?
A = (1/2)bh.
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.
Shifted down 2 units.
A^m*b^m = (ab)^m

11. What is p?
Set y = 0 - and solve.
Shifted right 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.

12. What is an exterior angle of a polygon?
A = pr^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An angle formed by extending the side of the polygon.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

13. What important property do similar triangles have?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
C = p2r
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.
Corresponding sides of similar triangles are in proportion.

14. What do we mean by the slope of the line?
M = (y2 - y1)/(x2 - x1)
How steep the line is. Horizontal line = 0 - vertical has no slope.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

15. How do you find the slope of a line?
Write the percent over 100 and reduce.
The ratio of corresponding sides of similar triangles.
(x + y)(x - y) = x^2 - y^2
M = (y2 - y1)/(x2 - x1)

16. How you convert a fraction or a decimal to a percent?
A^m/b^m = (a/b)^m
Shifted up 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Divide - then multiply by 100.

17. 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.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

18. How do you convert a percent to a fraction or a decimal?
The ratio of corresponding sides of similar triangles.
Write the percent over 100 and reduce.
Their sum is 90°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

19. What is the ratio of similitude?
An angle formed by extending the side of the polygon.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The ratio of corresponding sides of similar triangles.
The product of their slopes is -1 (negative reciprocal).

20. What are similar triangles?
A^m*b^m = (ab)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

21. How do you find the x-intercept of a graph?
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.
Set y = 0 - and solve.
Shifted right 2 units.

22. If the product of two or more numbers is 0 - what do you know about the numbers?
A fraction whose denominator is 100 i.e. 17% = 17/100
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
At least one of the factors is 0.
For any integer n: 1^n = 1.

23. What is the probability of an event that cannot occur? That must occur?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = pr^2
V = l^3
Cannot is 0 - must is 1 - all others are in between.

24. What are the important properties of 30-60-90 triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2

25. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
No matter how many angles there are - the sum around the point is 360°.
(n - 2)(180°)

26. What is a percent?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction whose denominator is 100 i.e. 17% = 17/100
In the expression x^b - x is the base and b is the exponent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

27. What are the properties of a parallelogram?
The set of all ordered pairs (x -y) such that y = f(x).
V = lwh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
[(x1 + x2)/2] -[(y1 + y2)/2]

28. What is a Venn diagram?
For any right triangle - a^2 + b^2 = c^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Even numbers are divisible by 2 and odd numbers are not.
Avg = sum of n numbers/n

29. What is true about the measures of the two acute angles in a right triangle?
V = lwh
Shifted right 2 units.
Then the quotient y/x is a constant.
Their sum is 90°.

30. What is an integer?
All positive and negative whole numbers - and zero.
Shifted right 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

31. What is the square root of a number?
At least one of the factors is 0.
(n - 2)(180°)
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

32. What is a multiple of an integer?
An equation that states that two ratios are equivalent. 4/6 = 10/15
An angle formed by extending the side of the polygon.
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.
The product of their slopes is -1 (negative reciprocal).

33. How do you find a percent of a number?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent over 100 and reduce.

34. What is true about the slopes of parallel lines?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Equal slopes.
Shifted right 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

35. Properties of one 4
At least one of the factors is 0.
For any number b: b = -b if and only if b = 0.
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.
1 is the smallest positive odd integer.

36. What are the sum - difference - products - and quotient of two numbers?
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent over 100 and reduce.
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

37. Important binomial 3
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

38. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
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.
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.

39. Properties of one 1
A = pr^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.

40. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 6(l^2)

41. What is the sum of the measures of the four angles in a quadrilateral?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°
Is a right triangle with a ratio of sides x:xv3:2x.
A fraction whose denominator is 100 i.e. 17% = 17/100

42. 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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).

43. If you were given the graph of y = f(x) - what does f(a) represent?
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
V = pr^2h
All positive and negative whole numbers - and zero.

44. Properties of one 3
They are both the same. A divisor or factor of an integer leaves no remainder.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is a divisor (or factor) of every integer.
For any number n: x^-n means 1/x^n.

45. Properties of square roots
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is a multiple of every integer.

46. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.
(n - 2)(180°)

47. What is the relationship between a radius of a circle and a line that is tangent to the circle?
V = lwh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

48. What is the triangle inequality?
Then the product xy is a constant.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

49. What formula is used for an average?
An integer greater than one that is not prime.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Avg = sum of n numbers/n

50. 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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 180°.