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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. Properties of zero 2
Shifted right 2 units.
M = (y2 - y1)/(x2 - x1)
If a is negative and b is positive - then a < 0 < b.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

2. What formula is used for an average?
A = s^2 or A =d^2/2 where d is the diagonal
An equation that states that two ratios are equivalent. 4/6 = 10/15
Avg = sum of n numbers/n
(b^m)^n = b^mn

3. What is true about the slopes of parallel lines?
A = lw
A = s^2 or A =d^2/2 where d is the diagonal
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Equal slopes.

4. What is the formula for the volume of a rectangular solid?
At least one of the factors is 0.
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.
Shifted right 2 units.

5. What are the important properties of 30-60-90 triangle?
1 is a divisor (or factor) of every integer.
Divide - then multiply by 100.
An integer greater than one that is not prime.
Is a right triangle with a ratio of sides x:xv3:2x.

6. 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.
For any integer n: 1^n = 1.
A = pr^2
360°

7. What is the formula for the volume of a cylinder?
V = pr^2h
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number a: a * 1 = a and a / 1 = a.
Arc = (x°/360)(2pr) where x is the central angle.

8. Properties of zero 1
Is a right triangle with a ratio of sides x:xv3:2x.
M = (y2 - y1)/(x2 - x1)
0 is the only number that is neither positive nor negative.
(n - 2)(180°)

9. What are the properties of a rectangle?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m*b^m = (ab)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

10. What is true about the measures of the two acute angles in a right triangle?
Then the product xy is a constant.
A = 6(l^2)
Their sum is 90°.
A = lw

11. 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.
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(b^m)^n = b^mn

12. Important binomial 2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Corresponding sides of similar triangles are in proportion.
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

13. What is the formula for the area of a rectangle?
A = lw
180°. If two or more angles form a straight angle - their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
If a is negative and b is positive - then a < 0 < b.

14. What is the formula for the surface area of a cube?
For any number a: a * 1 = a and a / 1 = a.
B^m/b^n = b^m-n
A = 6(l^2)
In the expression x^b - x is the base and b is the exponent.

15. In a circle of radius r - what is the formula for the circumference?
Avg = sum of n numbers/n
C = p2r
Corresponding sides of similar triangles are in proportion.
Shifted up 2 units.

16. What is the area of a square?
180°. If two or more angles form a straight angle - their sum is 180°.
0 is a multiple of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = s^2 or A =d^2/2 where d is the diagonal

17. Properties of one 2
Their sum is 90°.
(b^m)^n = b^mn
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any integer n: 1^n = 1.

18. What is a Venn diagram?
1 is the smallest positive odd integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The two pairs of opposite angles formed are equal to each other.
360°

19. What is a proportion?
A = s^2 or A =d^2/2 where d is the diagonal
Corresponding sides of similar triangles are in proportion.
An equation that states that two ratios are equivalent. 4/6 = 10/15
1 is a divisor (or factor) of every integer.

20. What is the formula for the area of a parallelogram?
A = bh
C = p2r
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A^m*b^m = (ab)^m

21. What do we mean by the slope of the line?
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.
At least one of the factors is 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°

22. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
360°
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(b^m)^n = b^mn

23. What is the midpoint formula?
How steep the line is. Horizontal line = 0 - vertical has no slope.
[(x1 + x2)/2] -[(y1 + y2)/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.
Cannot is 0 - must is 1 - all others are in between.

24. How do you calculate a weighted average?
1 is the smallest positive odd integer.
A = (1/2)bh.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = s^2 or A =d^2/2 where d is the diagonal

25. What does it mean if y is inversely proportional to x?
No matter how many angles there are - the sum around the point is 360°.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the product xy is a constant.
(x + y)(x - y) = x^2 - y^2

26. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Avg = sum of n numbers/n

27. What is true about the slopes of perpendicular lines?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The product of their slopes is -1 (negative reciprocal).
Set y = 0 - and solve.
Even numbers are divisible by 2 and odd numbers are not.

28. What are the median and the mode of a set of data?
C = p2r
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.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

29. What important property do similar triangles have?
A = bh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.

30. Properties of square roots
360°
Then the quotient y/x is a constant.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
They are both the same. A divisor or factor of an integer leaves no remainder.

31. How do you find a percent of a number?
Even numbers are divisible by 2 and odd numbers are not.
Write the percent as a decimal - and multiply.
D = 2r
In the expression x^b - x is the base and b is the exponent.

32. What is a function?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An angle formed by extending the side of the polygon.
For any right triangle - a^2 + b^2 = c^2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

33. What is the ratio of similitude?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted left 2 units.
The ratio of corresponding sides of similar triangles.

34. What are the properties of a square?
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.
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 = lw

35. What is a negative exponent?
An angle formed by extending the side of the polygon.
V = lwh
For any number n: x^-n means 1/x^n.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

36. How do we write the equation of a line?
180°. If two or more angles form a straight angle - their sum is 180°.
360°
A^m*b^m = (ab)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

37. What is a prime number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
1 is the smallest positive odd 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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

38. If the product of two or more numbers is 0 - what do you know about the numbers?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
At least one of the factors is 0.
The two pairs of opposite angles formed are equal to each other.

39. Law of exponents 2
B^m/b^n = b^m-n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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°.

40. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

41. What are the quotient and the remainder?

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42. What are similar triangles?
Divide - then multiply by 100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted down 2 units.
(b^m)^n = b^mn

43. What is the sum of the measures of all angles around a point?
D = 2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
No matter how many angles there are - the sum around the point is 360°.

44. What is the sum of the measures of the four angles in a quadrilateral?
A^m*b^m = (ab)^m
360°
The product of their slopes is -1 (negative reciprocal).
1 is a divisor (or factor) of every integer.

45. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
In the expression x^b - x is the base and b is the exponent.
Corresponding sides of similar triangles are in proportion.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

46. What is p?
Corresponding sides of similar triangles are in proportion.
(Circumference/diameter) of a circle - or approximately 3.14.
Their sum is 90°.
A = 2(lw + lh + hw)

47. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
All positive and negative whole numbers - and zero.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

48. In a circle of radius r - what is the formula for the area?
A = pr^2
360°
Arc = (x°/360)(2pr) where x is the central angle.
Their sum is 180°.

49. If you were given the graph of y = f(x) - what does f(a) represent?
(n - 2)(180°)
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.
0 is the only number that is neither positive nor negative.

50. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = 6(l^2)
A = (1/2)bh.
A = pr^2
Shifted down 2 units.