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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 the relationship between the graph of f(x) the graph of y = f(x + 2)?
Set x = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted left 2 units.
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°.

2. What is the graph of a function?
Arc = (x°/360)(2pr) where x is the central angle.
The product of their slopes is -1 (negative reciprocal).
The two pairs of opposite angles formed are equal to each other.
The set of all ordered pairs (x -y) such that y = f(x).

3. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
For any number a: a * 1 = a and a / 1 = a.
In the expression x^b - x is the base and b is the exponent.
360°
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

4. What is a ratio?

5. What is true about the measures of the two acute angles in a right triangle?
Even numbers are divisible by 2 and odd numbers are not.
Shifted up 2 units.
Their sum is 90°.
The two pairs of opposite angles formed are equal to each other.

6. What is special formula for the area of an equilateral triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
A = [(s^2*v3)/4]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

7. Properties of zero 1
C = p2r
(x + y)(x - y) = x^2 - y^2
Equal slopes.
0 is the only number that is neither positive nor negative.

8. 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.
B^m/b^n = b^m-n
Set x = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

9. How do we write the equation of a line?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m/b^m = (a/b)^m
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.

10. What is true about the measures of the three angles in a triangle?
The product of their slopes is -1 (negative reciprocal).
Their sum is 180°.
All positive and negative whole numbers - and zero.
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.

11. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted left 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
In the expression x^b - x is the base and b is the exponent.

12. Law of exponents 2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An angle formed by extending the side of the polygon.
360°
B^m/b^n = b^m-n

13. Properties of zero 5
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any number b: b = -b if and only if b = 0.
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.

14. What is the formula for the volume of a cylinder?
The set of all ordered pairs (x -y) such that y = f(x).
V = l^3
V = pr^2h
Arc = (x°/360)(2pr) where x is the central angle.

15. What is the square root of a number?
The ratio of corresponding sides of similar triangles.
Equal slopes.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

16. What is a prime number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted down 2 units.
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.
V = lwh

17. What are the sum - difference - products - and quotient of two numbers?
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.
Shifted right 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Divide - then multiply by 100.

18. How do you calculate percent increases and decreases?
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = pr^2
0 is the only number that is neither positive nor negative.

19. What is the sum of the measures of all angles around a point?
The product of their slopes is -1 (negative reciprocal).
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
No matter how many angles there are - the sum around the point is 360°.

20. What are the important properties of a 45-45 - 90 triangle?
(x + y)(x - y) = x^2 - y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(Circumference/diameter) of a circle - or approximately 3.14.

21. What is a negative exponent?
A = (1/2)bh.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number n: x^-n means 1/x^n.
V = pr^2h

22. How do you find the area of a sector of a circle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent as a decimal - and multiply.
Area = (x°/360)(pr^2) where x is the central angle.
Shifted left 2 units.

23. Law of exponents 3
(b^m)^n = b^mn
An angle formed by extending the side of the polygon.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = bh

24. What is a function?
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°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

25. What is the formula for the area of a rectangle?
A = lw
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
V = l^3

26. What are the properties of a parallelogram?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = bh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

27. In a circle of radius r - what is the formula for the circumference?
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.
C = p2r
A^m/b^m = (a/b)^m
Corresponding sides of similar triangles are in proportion.

28. Properties of zero 3
0 is a multiple of every integer.
A = 6(l^2)
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

29. What is the formula for the area of a parallelogram?
A = pr^2
B^m*b^n = b^m+n
A^m/b^m = (a/b)^m
A = bh

30. How do you find the length of an arc of a circle?
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.
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.
For any right triangle - a^2 + b^2 = c^2.

31. 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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = (1/2)bh.
Shifted left 2 units.

32. What is the ratio of similitude?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
[(x1 + x2)/2] -[(y1 + y2)/2]
The ratio of corresponding sides of similar triangles.
Set y = 0 - and solve.

33. What is the midpoint formula?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A^m*b^m = (ab)^m
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]

34. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
0 is the only number that is neither positive nor negative.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If a is negative and b is positive - then a < 0 < b.

35. What is an exterior angle of a polygon?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
B^m/b^n = b^m-n
V = lwh
An angle formed by extending the side of the polygon.

36. Important binomial 3
A^m*b^m = (ab)^m
At least one of the factors is 0.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

37. What is the area of a square?
Write the percent over 100 and reduce.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = s^2 or A =d^2/2 where d is the diagonal
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

38. What does it mean if y is directly proportional to x?
(n - 2)(180°)
A = [(s^2*v3)/4]
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 quotient y/x is a constant.

39. What is the formula for the surface area of a cube?
(n - 2)(180°)
A = 6(l^2)
360°
Write the percent over 100 and reduce.

40. What is a fractional exponent?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A fraction whose denominator is 100 i.e. 17% = 17/100
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

41. What is true about the measures of the four angles formed by two intersecting lines?
(Circumference/diameter) of a circle - or approximately 3.14.
A = [(s^2*v3)/4]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The two pairs of opposite angles formed are equal to each other.

42. If you were given the graph of y = f(x) - what does f(a) represent?
Avg = sum of n numbers/n
0 is a multiple of every integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

43. In a circle of radius r - what is the formula for the area?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 90°.
(x + y)(x - y) = x^2 - y^2
A = pr^2

44. Law of exponents 1
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The product of their slopes is -1 (negative reciprocal).
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
B^m*b^n = b^m+n

45. 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°.
For any integer n: 1^n = 1.
A = 2(lw + lh + hw)
1 is a divisor (or factor) of every integer.

46. How you convert a fraction or a decimal to a percent?
Shifted left 2 units.
Divide - then multiply by 100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.

47. For what values of a function is the function undefined?
A = pr^2
For any right triangle - a^2 + b^2 = c^2.
At least one of the factors is 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

48. What is an exterior angle of a triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Write the percent over 100 and reduce.

49. Properties of zero 4
For any right triangle - a^2 + b^2 = c^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An angle formed by extending the side of the polygon.
The product of their slopes is -1 (negative reciprocal).

50. 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.
Shifted down 2 units.
All positive and negative whole numbers - and zero.
A = [(s^2*v3)/4]