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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. How do we write the equation of a line?
In the expression x^b - x is the base and b is the exponent.
Shifted down 2 units.
Corresponding sides of similar triangles are in proportion.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

2. What is the formula for the surface area of a rectangular solid?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = 2(lw + lh + hw)
At least one of the factors is 0.
Their sum is 90°.

3. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
A = bh
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
No matter how many angles there are - the sum around the point is 360°.

4. Properties of one 4
At least one of the factors is 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted right 2 units.
1 is the smallest positive odd integer.

5. What is special formula for the area of an equilateral triangle?
No matter how many angles there are - the sum around the point is 360°.
A = [(s^2*v3)/4]
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

6. How do you calculate percent increases and decreases?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
A = pr^2

7. How do you find the length of an arc of a circle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Arc = (x°/360)(2pr) where x is the central angle.
Corresponding sides of similar triangles are in proportion.

8. What is the formula for the area of a triangle?
A = (1/2)bh.
V = l^3
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

9. What does it mean if y is directly proportional to x?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Corresponding sides of similar triangles are in proportion.
Arc = (x°/360)(2pr) where x is the central angle.
Then the quotient y/x is a constant.

10. What is the formula for the area of a rectangle?
A = lw
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.
Then the product xy is a constant.

11. What is a Venn diagram?
V = lwh
D = 2r
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Their sum is 90°.

12. Law of exponents 4
A^m*b^m = (ab)^m
Shifted right 2 units.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)(x - y) = x^2 - y^2

13. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
360°
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

14. What is the sum of the measures of the four angles in a quadrilateral?
360°
The ratio of corresponding sides of similar triangles.
Then the product xy is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.

15. What is the square root of a 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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.

16. Law of exponents 3
(b^m)^n = b^mn
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.
For any number n: x^-n means 1/x^n.
V = lwh

17. What is an even and an odd number?
At least one of the factors is 0.
Equal slopes.
Write the percent over 100 and reduce.
Even numbers are divisible by 2 and odd numbers are not.

18. What is the measure of a straight angle?
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
180°. If two or more angles form a straight angle - their sum is 180°.

19. What is a fractional exponent?
Avg = sum of n numbers/n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = lwh

20. In a circle of radius r - what is the formula for the area?
C = p2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any integer n: 1^n = 1.
A = pr^2

21. Law of exponents 5
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^m/b^m = (a/b)^m
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

22. Law of exponents 2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360°
B^m/b^n = b^m-n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

23. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
Shifted down 2 units.

24. What is a function?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

25. Properties of square roots
(Circumference/diameter) of a circle - or approximately 3.14.
Equal slopes.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Write the percent over 100 and reduce.

26. What does it mean if y is inversely proportional to x?
For any number b: b = -b if and only if b = 0.
A = bh
Then the product xy is a constant.
V = lwh

27. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Then the product xy is a constant.
Shifted down 2 units.
D = 2r

28. What important property do similar triangles have?
A = [(s^2*v3)/4]
How steep the line is. Horizontal line = 0 - vertical has no slope.
M = (y2 - y1)/(x2 - x1)
Corresponding sides of similar triangles are in proportion.

29. Properties of zero 5
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
At least one of the factors is 0.
For any number b: b = -b if and only if b = 0.

30. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If a is negative and b is positive - then a < 0 < b.
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.
360°

31. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).

32. What do we mean by the slope of the line?
A = bh
[(x1 + x2)/2] -[(y1 + y2)/2]
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.

33. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
(n - 2)(180°)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A^m*b^m = (ab)^m
Shifted right 2 units.

34. What is a percent?
(Circumference/diameter) of a circle - or approximately 3.14.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

35. How you convert a fraction or a decimal to a percent?
If a is negative and b is positive - then a < 0 < b.
Divide - then multiply by 100.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

36. What is an integer?
All positive and negative whole numbers - and zero.
A = 6(l^2)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = pr^2

37. Properties of one 2
If a is negative and b is positive - then a < 0 < b.
Write the percent over 100 and reduce.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any integer n: 1^n = 1.

38. Important binomial 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is the smallest positive odd integer.
Set x = 0 - and solve.

39. What is the relationship between a radius of a circle and a line that is tangent to the circle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is a multiple of every integer.
A^m/b^m = (a/b)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

40. What is an exterior angle of a triangle?
V = lwh
Cannot is 0 - must is 1 - all others are in between.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Then the product xy is a constant.

41. What is a multiple of an integer?
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.
D = 2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is a divisor (or factor) of every integer.

42. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = bh
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

43. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = s^2 or A =d^2/2 where d is the diagonal
(n - 2)(180°)

44. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
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.
Shifted left 2 units.
Avg = sum of n numbers/n

45. What is true about the areas of similar triangles?
The set of all ordered pairs (x -y) such that y = f(x).
1 is the smallest positive odd integer.
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

46. Properties of zero 4
For any right triangle - a^2 + b^2 = c^2.
Equal slopes.
Write the percent over 100 and reduce.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

47. What is the volume of a cube?
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m/b^n = b^m-n
V = l^3

48. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Divide - then multiply by 100.
An angle formed by extending the side of the polygon.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

49. What is the sum of the measures of the n angles of a polygon with n sides?
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.
(b^m)^n = b^mn
(n - 2)(180°)

50. Important binomial 3
Is a right triangle with a ratio of sides x:xv3:2x.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Cannot is 0 - must is 1 - all others are in between.
For any number n: x^-n means 1/x^n.