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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 is the formula for the volume of a rectangular solid?
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°.
V = lwh
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.

2. Properties of one 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.
For any integer n: 1^n = 1.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Their sum is 90°.

3. Law of exponents 2
Cannot is 0 - must is 1 - all others are in between.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The ratio of corresponding sides of similar triangles.
B^m/b^n = b^m-n

4. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At least one of the factors is 0.
(x + y)(x - y) = x^2 - y^2

5. If the product of two or more numbers is 0 - what do you know about the numbers?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Set y = 0 - and solve.
At least one of the factors is 0.
If a is negative and b is positive - then a < 0 < b.

6. What is the square root of a number?
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

7. How do you find the length of an arc of a circle?
[(x1 + x2)/2] -[(y1 + y2)/2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
Arc = (x°/360)(2pr) where x is the central angle.

8. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = lw
(x + y)(x - y) = x^2 - y^2
A = 2(lw + lh + hw)
Shifted down 2 units.

9. What formula is used for an average?
A fraction whose denominator is 100 i.e. 17% = 17/100
Avg = sum of n numbers/n
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 = bh

10. What is the volume of a cube?
V = l^3
(Circumference/diameter) of a circle - or approximately 3.14.
Corresponding sides of similar triangles are in proportion.
A = bh

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n
All positive and negative whole numbers - and zero.
Shifted left 2 units.

12. What is special formula for the area of an equilateral triangle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any right triangle - a^2 + b^2 = c^2.
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.

13. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Equal slopes.
No matter how many angles there are - the sum around the point is 360°.
Shifted up 2 units.

14. What is a fractional exponent?
360°
Divide - then multiply by 100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(n - 2)(180°)

15. What is an integer?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
All positive and negative whole numbers - and zero.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Even numbers are divisible by 2 and odd numbers are not.

16. What is the formula for the volume of a cylinder?
Write the percent as a decimal - and multiply.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = pr^2h
Arc = (x°/360)(2pr) where x is the central angle.

17. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.
For any number a: a * 1 = a and a / 1 = a.

18. 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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Then the quotient y/x is a constant.
(b^m)^n = b^mn

19. What is the sum of the measures of all angles around a point?
360°
No matter how many angles there are - the sum around the point is 360°.
At least one of the factors is 0.
(b^m)^n = b^mn

20. What is the ratio of similitude?
A = 6(l^2)
B^m*b^n = b^m+n
The ratio of corresponding sides of similar triangles.
All positive and negative whole numbers - and zero.

21. What is a divisor and a factor of an integer?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn
[(x1 + x2)/2] -[(y1 + y2)/2]
They are both the same. A divisor or factor of an integer leaves no remainder.

22. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
Avg = sum of n numbers/n
V = pr^2h

23. What is the area of a square?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = s^2 or A =d^2/2 where d is the diagonal
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
360°

24. How do you find the slope of a line?
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.
If a is negative and b is positive - then a < 0 < b.
M = (y2 - y1)/(x2 - x1)
A = (1/2)bh.

25. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

26. How do you find the probability that an event will occur?
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

27. What is p?
Set x = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = lwh
(Circumference/diameter) of a circle - or approximately 3.14.

28. In a circle of radius r - what is the formula for the area?
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.
Write the percent as a decimal - and multiply.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = pr^2

29. What is a multiple of an integer?
For any integer n: 1^n = 1.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

30. For what values of a function is the function undefined?
1 is a divisor (or factor) of every integer.
Even numbers are divisible by 2 and odd numbers are not.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
An angle formed by extending the side of the polygon.

31. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An equation that states that two ratios are equivalent. 4/6 = 10/15
An integer greater than one that is not prime.

32. Law of exponents 4
V = lwh
0 is the only number that is neither positive nor negative.
A^m*b^m = (ab)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

33. How you convert a fraction or a decimal to a percent?
B^m/b^n = b^m-n
A = 6(l^2)
Divide - then multiply by 100.
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. What is the sum of the measures of the four angles in a quadrilateral?
Write the percent over 100 and reduce.
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 right triangle - a^2 + b^2 = c^2.
360°

35. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For any number b: b = -b if and only if b = 0.
Shifted right 2 units.
(x + y)(x - y) = x^2 - y^2
0 is a multiple of every integer.

36. What is the measure of a straight angle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
180°. If two or more angles form a straight angle - their sum is 180°.
(n - 2)(180°)

37. What is the formula for the area of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = l^3
Avg = sum of n numbers/n
A = lw

38. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Shifted left 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)(x - y) = x^2 - y^2

39. What is a composite number?
A fraction whose denominator is 100 i.e. 17% = 17/100
Cannot is 0 - must is 1 - all others are in between.
An integer greater than one that is not prime.
Even numbers are divisible by 2 and odd numbers are not.

40. Important binomial 1
For any number b: b = -b if and only if b = 0.
(x + y)(x - y) = x^2 - y^2
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

41. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set y = 0 - and solve.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
D = 2r

42. Properties of one 3
All positive and negative whole numbers - and zero.
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.
In the expression x^b - x is the base and b is the exponent.

43. What is an exponent?
Divide - then multiply by 100.
In the expression x^b - x is the base and b is the exponent.
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.
Set y = 0 - and solve.

44. What is the formula for the surface area of a cube?
(Circumference/diameter) of a circle - or approximately 3.14.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any number b: b = -b if and only if b = 0.
A = 6(l^2)

45. How do you convert a percent to a fraction or a decimal?
A = lw
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.
(x + y)(x - y) = x^2 - y^2
Write the percent over 100 and reduce.

46. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
0 is a multiple of every integer.
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m

47. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set y = 0 - and solve.

48. 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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

49. Properties of zero 3
Shifted left 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
Then the product xy is a constant.
0 is a multiple of every integer.

50. How do you calculate percent increases and decreases?
A^m*b^m = (ab)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.