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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. Law of exponents 2
B^m/b^n = b^m-n
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.
A = (1/2)bh.

2. What is p?
No matter how many angles there are - the sum around the point is 360°.
For any number a: a * 1 = a and a / 1 = a.
(Circumference/diameter) of a circle - or approximately 3.14.
(n - 2)(180°)

3. What do we mean by the slope of the line?
V = l^3
How steep the line is. Horizontal line = 0 - vertical has no slope.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is the smallest positive odd integer.

4. Properties of zero 3
Set x = 0 - and solve.
At least one of the factors is 0.
Shifted left 2 units.
0 is a multiple of every integer.

5. Important binomial 2
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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°.
Set y = 0 - and solve.

6. 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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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

7. What are the properties of a parallelogram?
(Circumference/diameter) of a circle - or approximately 3.14.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Avg = sum of n numbers/n

8. How do you find the y-intercept of a graph?
Shifted up 2 units.
Set x = 0 - and solve.
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
1 is a divisor (or factor) of every integer.
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.
Divide - then multiply by 100.

10. What is true about the slopes of parallel lines?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(n - 2)(180°)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Equal slopes.

11. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
1 is a divisor (or factor) of every integer.
360°
No matter how many angles there are - the sum around the point is 360°.

12. Law of exponents 4
A^m*b^m = (ab)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = 6(l^2)
The set of all ordered pairs (x -y) such that y = f(x).

13. What are the properties of a rectangle?
(n - 2)(180°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)(x - y) = x^2 - y^2
A = 6(l^2)

14. Properties of one 2
Set y = 0 - and solve.
Write the percent as a decimal - and multiply.
The product of their slopes is -1 (negative reciprocal).
For any integer n: 1^n = 1.

15. What is the formula for the surface area of a rectangular solid?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
M = (y2 - y1)/(x2 - x1)
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.
A = 2(lw + lh + hw)

16. What is an exterior angle of a polygon?
A = 6(l^2)
0 is a multiple of every integer.
An angle formed by extending the side of the polygon.
(x + y)(x - y) = x^2 - y^2

17. What is true about the slopes of perpendicular lines?
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.
Cannot is 0 - must is 1 - all others are in between.
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n

18. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
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^m*b^m = (ab)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

19. What is a percent?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number b: b = -b if and only if b = 0.
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the product xy is a constant.

20. What is the sum of the measures of the n angles of a polygon with n sides?
C = p2r
Shifted down 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(n - 2)(180°)

21. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Their sum is 90°.
A = 2(lw + lh + hw)
Avg = sum of n numbers/n

22. What is a composite number?
An integer greater than one that is not prime.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

23. What is an integer?
C = p2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = [(s^2*v3)/4]
All positive and negative whole numbers - and zero.

24. How do you calculate percent increases and decreases?
B^m/b^n = b^m-n
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Set x = 0 - and solve.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

25. What does it mean if y is directly proportional to x?
A^m*b^m = (ab)^m
Then the quotient y/x is a constant.
V = lwh
A = lw

26. What is the probability of an event that cannot occur? That must occur?
A^m*b^m = (ab)^m
A = [(s^2*v3)/4]
Cannot is 0 - must is 1 - all others are in between.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

27. Law of exponents 5
A = lw
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°.
A^m/b^m = (a/b)^m

28. What is the formula for the area of a parallelogram?
A = bh
Then the product xy is a constant.
For any number b: b = -b if and only if b = 0.
Is a right triangle with a ratio of sides x:xv3:2x.

29. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
0 is a multiple of every integer.
V = lwh
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

30. What is true about the measures of the four angles formed by two intersecting lines?
Write the percent over 100 and reduce.
360°
A^m/b^m = (a/b)^m
The two pairs of opposite angles formed are equal to each other.

31. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Their sum is 90°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
180°. If two or more angles form a straight angle - their sum is 180°.

32. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
360°
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

33. What is the formula for the area of a rectangle?
A = [(s^2*v3)/4]
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 = lw
D = 2r

34. What are the properties of a square?
Then the product xy is a constant.
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 = (1/2)bh.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

35. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.

36. What is the formula for the volume of a cylinder?
D = 2r
V = pr^2h
V = lwh
C = p2r

37. Properties of zero 4
A = (1/2)bh.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number a: a * 1 = a and a / 1 = a.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

38. How do you calculate a weighted average?
The ratio of corresponding sides of similar triangles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

39. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.
For any number n: x^-n means 1/x^n.
360°

40. How you convert a fraction or a decimal to a percent?
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Divide - then multiply by 100.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

41. What are similar triangles?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Then the product xy is a constant.
Their sum is 180°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

42. What is the ratio of similitude?
In the expression x^b - x is the base and b is the exponent.
A = bh
The ratio of corresponding sides of similar triangles.
No matter how many angles there are - the sum around the point is 360°.

43. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m/b^m = (a/b)^m
(n - 2)(180°)
At least one of the factors is 0.

44. 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.
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Cannot is 0 - must is 1 - all others are in between.

45. Law of exponents 3
V = pr^2h
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn

46. How do you find the slope of a line?
A^m*b^m = (ab)^m
M = (y2 - y1)/(x2 - x1)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

47. If the product of two or more numbers is 0 - what do you know about the numbers?
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

48. What formula is used for an average?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = l^3

49. What is the formula for the volume of a rectangular solid?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
Set x = 0 - and solve.
V = lwh

50. What is an exponent?
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.
In the expression x^b - x is the base and b is the exponent.
A fraction whose denominator is 100 i.e. 17% = 17/100
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.