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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 properties of a square?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any integer n: 1^n = 1.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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. What important property do similar triangles have?
B^m/b^n = b^m-n
A = s^2 or A =d^2/2 where d is the diagonal
360°
Corresponding sides of similar triangles are in proportion.

3. What is true about the slopes of parallel lines?
A = [(s^2*v3)/4]
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.
Equal slopes.
C = p2r

4. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Corresponding sides of similar triangles are in proportion.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

5. What is a function?
A^m/b^m = (a/b)^m
At least one of the factors is 0.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Avg = sum of n numbers/n

6. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = lw
At least one of the factors is 0.
(n - 2)(180°)

7. How do you calculate percent increases and decreases?
D = 2r
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

8. What is the formula for the area of a triangle?
A = (1/2)bh.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The product of their slopes is -1 (negative reciprocal).
Set y = 0 - and solve.

9. What is true about the measures of the three angles in a triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
No matter how many angles there are - the sum around the point is 360°.
Their sum is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.

10. What formula is used for an average?
Arc = (x°/360)(2pr) where x is the central angle.
0 is a multiple of every integer.
Avg = sum of n numbers/n
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.

11. What is the probability of an event that cannot occur? That must occur?
For any number n: x^-n means 1/x^n.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Cannot is 0 - must is 1 - all others are in between.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

12. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
The ratio of corresponding sides of similar triangles.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted left 2 units.

13. What are the median and the mode of a set of data?
Shifted right 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any integer n: 1^n = 1.
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.

14. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.
If a is negative and b is positive - then a < 0 < b.

15. What is the square root of a number?
360°
A = 2(lw + lh + hw)
For any number n: x^-n means 1/x^n.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

16. How do you find the area of a sector of a circle?
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.
A = [(s^2*v3)/4]
They are both the same. A divisor or factor of an integer leaves no remainder.
Area = (x°/360)(pr^2) where x is the central angle.

17. Properties of one 3
Shifted left 2 units.
1 is a divisor (or factor) of every integer.
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.

18. What is a prime number?
0 is a multiple of every integer.
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.
Corresponding sides of similar triangles are in proportion.
Area = (x°/360)(pr^2) where x is the central angle.

19. What is a ratio?

20. 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.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
Set y = 0 - and solve.

21. What is an exterior angle of a polygon?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted right 2 units.
An angle formed by extending the side of the polygon.

22. In a circle of radius r - what is the formula for the area?
A = pr^2
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

23. Law of exponents 3
The ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = (1/2)bh.
(b^m)^n = b^mn

24. What do we mean by the slope of the line?
A = pr^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.

25. What does it mean if y is directly proportional to x?
(b^m)^n = b^mn
Then the quotient y/x is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

26. What is a composite number?
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = pr^2h

27. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
No matter how many angles there are - the sum around the point is 360°.
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.
Shifted up 2 units.

28. 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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = lwh

29. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
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.
The ratio of corresponding sides of similar triangles.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

30. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.
D = 2r
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

31. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted left 2 units.
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.

32. Important binomial 3
An integer greater than one that is not prime.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is a divisor (or factor) of every integer.
A^m*b^m = (ab)^m

33. 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.
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.
Set y = 0 - and solve.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

34. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
D = 2r
Is a right triangle with a ratio of sides x:xv3:2x.
For any number n: x^-n means 1/x^n.

35. Properties of zero 1
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A fraction whose denominator is 100 i.e. 17% = 17/100
0 is the only number that is neither positive nor negative.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

36. What is true about the slopes of perpendicular lines?
For any integer n: 1^n = 1.
The product of their slopes is -1 (negative reciprocal).
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.

37. Law of exponents 1
Set x = 0 - and solve.
B^m*b^n = b^m+n
For any right triangle - a^2 + b^2 = c^2.
Write the percent as a decimal - and multiply.

38. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
180°. If two or more angles form a straight angle - their sum is 180°.
A = 6(l^2)
In the expression x^b - x is the base and b is the exponent.

39. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
Then the quotient y/x is a constant.
Cannot is 0 - must is 1 - all others are in between.
The two pairs of opposite angles formed are equal to each other.

40. Properties of one 4
Set y = 0 - and solve.
An angle formed by extending the side of the polygon.
1 is the smallest positive odd integer.
In the expression x^b - x is the base and b is the exponent.

41. What is a percent?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
They are both the same. A divisor or factor of an integer leaves no remainder.
Set y = 0 - and solve.
A fraction whose denominator is 100 i.e. 17% = 17/100

42. How do you find a percent of a number?
(x + y)(x - y) = x^2 - y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
C = p2r
Write the percent as a decimal - and multiply.

43. What are the important properties of a 45-45 - 90 triangle?
0 is a multiple of every integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Equal slopes.
For any right triangle - a^2 + b^2 = c^2.

44. What is the ratio of similitude?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

45. What is the formula for the volume of a cylinder?
An integer greater than one that is not prime.
V = pr^2h
1 is a divisor (or factor) of every integer.
A = 6(l^2)

46. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Set y = 0 - and solve.
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.
B^m*b^n = b^m+n

47. What is the distance formula?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The set of all ordered pairs (x -y) such that y = f(x).
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

48. What is the formula for the volume of a rectangular solid?
V = lwh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
D = 2r

49. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Shifted right 2 units.
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.
Their sum is 90°.

50. How do you find the y-intercept of a graph?
The set of all ordered pairs (x -y) such that y = f(x).
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Set x = 0 - and solve.