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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 are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted down 2 units.

2. What is the midpoint formula?
Shifted down 2 units.
If a is negative and b is positive - then a < 0 < b.
[(x1 + x2)/2] -[(y1 + y2)/2]
In the expression x^b - x is the base and b is the exponent.

3. How do you calculate a weighted average?
In the expression x^b - x is the base and b is the exponent.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Their sum is 90°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

4. Properties of one 4
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.
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.

5. What is a ratio?

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6. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

7. What is true about the areas of similar triangles?
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.
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 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.

8. Important binomial 1
M = (y2 - y1)/(x2 - x1)
(b^m)^n = b^mn
The ratio of corresponding sides of similar triangles.
(x + y)(x - y) = x^2 - y^2

9. How do we write the equation of a line?
180°. If two or more angles form a straight angle - their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any right triangle - a^2 + b^2 = c^2.
Divide - then multiply by 100.

10. What is the measure of a straight angle?
(x + y)(x - y) = x^2 - y^2
180°. If two or more angles form a straight angle - their sum is 180°.
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m

11. What is the formula for the surface area of a cube?
Shifted left 2 units.
For any right triangle - a^2 + b^2 = c^2.
For any number n: x^-n means 1/x^n.
A = 6(l^2)

12. What is true about the measures of the four angles formed by two intersecting lines?
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.
Is a right triangle with a ratio of sides x:xv3:2x.
The two pairs of opposite angles formed are equal to each other.
Set x = 0 - and solve.

13. What is true about the slopes of parallel lines?
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.
Equal slopes.
An angle formed by extending the side of the polygon.
For any number a: a * 1 = a and a / 1 = a.

14. How do you calculate percent increases and decreases?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

15. What is the graph of a function?
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.
M = (y2 - y1)/(x2 - x1)
The set of all ordered pairs (x -y) such that y = f(x).

16. What is the sum of the measures of the n angles of a polygon with n sides?
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.
(n - 2)(180°)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = [(s^2*v3)/4]

17. What is the relationship between a radius of a circle and a line that is tangent to the circle?
[(x1 + x2)/2] -[(y1 + y2)/2]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = pr^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

18. What is the triangle inequality?
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 = 2(lw + lh + hw)
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.

19. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is the smallest positive odd integer.
D = 2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

20. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
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.
Cannot is 0 - must is 1 - all others are in between.

21. Law of exponents 4
No matter how many angles there are - the sum around the point is 360°.
C = p2r
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

22. What is p?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = lwh
(Circumference/diameter) of a circle - or approximately 3.14.

23. Important binomial 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.
For any number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

24. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
C = p2r
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
360°

25. What is the ratio of similitude?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The ratio of corresponding sides of similar triangles.
The product of their slopes is -1 (negative reciprocal).
B^m/b^n = b^m-n

26. In a circle of radius r - what is the formula for the area?
0 is the only number that is neither positive nor negative.
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.
360°
A = pr^2

27. What are the quotient and the remainder?

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28. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For any number n: x^-n means 1/x^n.
(n - 2)(180°)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

29. What is the volume of a cube?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = l^3
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. What are the properties of a square?
C = p2r
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

31. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
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.
D = 2r
V = lwh

32. What is a negative exponent?
For any number n: x^-n means 1/x^n.
0 is the only number that is neither positive nor negative.
Shifted left 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. What do we mean by the slope of the line?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted down 2 units.
The product of their slopes is -1 (negative reciprocal).
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. How do you find the area of a sector of a circle?
[(x1 + x2)/2] -[(y1 + y2)/2]
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.
Area = (x°/360)(pr^2) where x is the central angle.

35. What is a prime number?
Cannot is 0 - must is 1 - all others are in between.
Their sum is 180°.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

36. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
A = lw
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 x = 0 - and solve.

37. What is the formula for the area of a parallelogram?
A = bh
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted down 2 units.

38. What is the distributive law?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

39. What is a composite number?
An integer greater than one that is not prime.
B^m/b^n = b^m-n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
How steep the line is. Horizontal line = 0 - vertical has no slope.

40. What are the properties of a rectangle?
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
[(x1 + x2)/2] -[(y1 + y2)/2]
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

41. Properties of zero 4
1 is the smallest positive odd integer.
The product of their slopes is -1 (negative reciprocal).
A = bh
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

42. 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The product of their slopes is -1 (negative reciprocal).

43. What are the median and the mode of a set of data?
A = bh
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

44. What is a divisor and a factor of an integer?
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 = 6(l^2)
They are both the same. A divisor or factor of an integer leaves no remainder.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

45. Properties of zero 3
V = l^3
A = (1/2)bh.
0 is a multiple of every integer.
Write the percent over 100 and reduce.

46. In a circle of radius r - what is the formula for the diameter?
D = 2r
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted up 2 units.
Cannot is 0 - must is 1 - all others are in between.

47. What are the important properties of a 45-45 - 90 triangle?
360°
Write the percent as a decimal - and multiply.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Corresponding sides of similar triangles are in proportion.

48. How do you find the y-intercept of a graph?
Divide - then multiply by 100.
A = 6(l^2)
V = l^3
Set x = 0 - and solve.

49. What does it mean if y is directly proportional to x?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
Shifted up 2 units.
Then the quotient y/x is a constant.

50. Law of exponents 2
D = 2r
An integer greater than one that is not prime.
B^m/b^n = b^m-n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.