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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 does it mean if y is inversely proportional to x?
Then the product xy is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Corresponding sides of similar triangles are in proportion.

2. How do you find the x-intercept of a graph?
D = 2r
Set y = 0 - and solve.
A^m/b^m = (a/b)^m
A = 6(l^2)

3. What is an even and an odd number?
C = p2r
Even numbers are divisible by 2 and odd numbers are not.
A^m*b^m = (ab)^m
Divide - then multiply by 100.

4. Properties of one 2
Write the percent as a decimal - and multiply.
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°.
C = p2r
For any integer n: 1^n = 1.

5. 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.
Set x = 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.
360°

6. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
No matter how many angles there are - the sum around the point is 360°.
Arc = (x°/360)(2pr) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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°.

7. What is a composite number?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An integer greater than one that is not prime.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted left 2 units.

8. What are the median and the mode of a set of data?
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 = 2(lw + lh + hw)
Write the percent as a decimal - and multiply.
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.

9. How do you calculate percent increases and decreases?
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.
180°. If two or more angles form a straight angle - their sum is 180°.
For any number a: a * 1 = a and a / 1 = a.

10. Law of exponents 2
180°. If two or more angles form a straight angle - their sum is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The two pairs of opposite angles formed are equal to each other.
B^m/b^n = b^m-n

11. What is the ratio of similitude?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The ratio of corresponding sides of similar triangles.
1 is the smallest positive odd integer.
Is a right triangle with a ratio of sides x:xv3:2x.

12. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.

13. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
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.
Write the percent as a decimal - and multiply.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

14. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
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.
(b^m)^n = b^mn
Shifted right 2 units.

15. Law of exponents 3
(b^m)^n = b^mn
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An angle formed by extending the side of the polygon.
For any number n: x^-n means 1/x^n.

16. How do you find the area of a sector of a circle?
Set y = 0 - and solve.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = [(s^2*v3)/4]
Area = (x°/360)(pr^2) where x is the central angle.

17. Important binomial 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°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
1 is the smallest positive odd integer.

18. How you convert a fraction or a decimal to a percent?
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted right 2 units.
Divide - then multiply by 100.
Shifted down 2 units.

19. What is a proportion?
Set x = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The product of their slopes is -1 (negative reciprocal).
A = 2(lw + lh + hw)

20. What are the quotient and the remainder?

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21. Properties of square roots
Shifted right 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Area = (x°/360)(pr^2) where x is the central angle.

22. What are similar triangles?
The ratio of corresponding sides 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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = pr^2h

23. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
(n - 2)(180°)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted down 2 units.
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.

24. What are the properties of a square?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m*b^n = b^m+n
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.

25. What are the properties of a rectangle?
B^m*b^n = b^m+n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = lwh

26. What do we mean by the slope of the line?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.

27. What is the measure of a straight angle?
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°.
Write the percent over 100 and reduce.
A = [(s^2*v3)/4]
180°. If two or more angles form a straight angle - their sum is 180°.

28. What is the formula for the volume of a rectangular solid?
V = lwh
An integer greater than one that is not prime.
A = 2(lw + lh + hw)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

29. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The product of their slopes is -1 (negative reciprocal).

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.
If a is negative and b is positive - then a < 0 < b.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Arc = (x°/360)(2pr) where x is the central angle.

31. What is true about the measures of the three angles in a triangle?
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 180°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

32. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m*b^m = (ab)^m
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.

33. What is true about the slopes of parallel lines?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.
Equal slopes.

34. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
The ratio of corresponding sides of similar triangles.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

35. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
C = p2r
V = pr^2h
Their sum is 180°.

36. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
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.
An angle formed by extending the side of the polygon.

37. What is the Pythagorean theorem?
The product of their slopes is -1 (negative reciprocal).
B^m/b^n = b^m-n
For any number b: b = -b if and only if b = 0.
For any right triangle - a^2 + b^2 = c^2.

38. If you were given the graph of y = f(x) - what does f(a) represent?
For any number n: x^-n means 1/x^n.
Equal slopes.
For any integer n: 1^n = 1.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

39. What is true about the areas of similar triangles?
A = pr^2
Shifted up 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.

40. Properties of zero 5
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number b: b = -b if and only if b = 0.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(x + y)(x - y) = x^2 - y^2

41. What are the important properties of 30-60-90 triangle?
360°
Is a right triangle with a ratio of sides x:xv3:2x.
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.

42. 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.
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 = [(s^2*v3)/4]
For any right triangle - a^2 + b^2 = c^2.

43. How do you find the slope of a line?
B^m/b^n = b^m-n
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
M = (y2 - y1)/(x2 - x1)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

44. What is a percent?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is the smallest positive odd integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction whose denominator is 100 i.e. 17% = 17/100

45. What is the formula for the volume of a cylinder?
At least one of the factors is 0.
V = lwh
A = 6(l^2)
V = pr^2h

46. Properties of zero 3
A = 2(lw + lh + hw)
0 is a multiple of every integer.
Write the percent over 100 and reduce.
A = pr^2

47. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = pr^2
A = [(s^2*v3)/4]

48. What is a prime number?
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.
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 = (1/2)bh.
The set of all ordered pairs (x -y) such that y = f(x).

49. Properties of zero 1
0 is the only number that is neither positive nor negative.
Is a right triangle with a ratio of sides x:xv3:2x.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A^m/b^m = (a/b)^m

50. What is a negative exponent?
Write the percent as a decimal - and multiply.
360°
A = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.