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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?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the product xy is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

2. What are the properties of a rectangle?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

3. Law of exponents 3
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(b^m)^n = b^mn
An equation that states that two ratios are equivalent. 4/6 = 10/15

4. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
M = (y2 - y1)/(x2 - x1)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

5. What is the square root of a number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
B^m/b^n = b^m-n
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

6. What is the ratio of similitude?
For any right triangle - a^2 + b^2 = c^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.

7. How do you find the y-intercept of a graph?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Set x = 0 - and solve.
A^m*b^m = (ab)^m

8. How do you find a percent of a number?
Their sum is 90°.
(x + y)(x - y) = x^2 - y^2
An integer greater than one that is not prime.
Write the percent as a decimal - and multiply.

9. What is a ratio?

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10. Properties of zero 5
(b^m)^n = b^mn
For any number b: b = -b if and only if b = 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An integer greater than one that is not prime.

11. 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.
M = (y2 - y1)/(x2 - x1)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

12. How do you find the x-intercept of a graph?
[(x1 + x2)/2] -[(y1 + y2)/2]
Set y = 0 - and solve.
0 is a multiple of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

13. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
360°
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

14. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
(x + y)(x - y) = x^2 - y^2

15. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
In the expression x^b - x is the base and b is the exponent.
A^m/b^m = (a/b)^m
The product of their slopes is -1 (negative reciprocal).

16. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
An angle formed by extending the side of the polygon.

17. What is a negative exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
(n - 2)(180°)
For any number n: x^-n means 1/x^n.

18. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
Equal slopes.
0 is a multiple of every integer.

19. What is the formula for the volume of a cylinder?
A^m*b^m = (ab)^m
At least one of the factors is 0.
D = 2r
V = pr^2h

20. What important property do similar triangles have?
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.
Corresponding sides of similar triangles are in proportion.
Equal slopes.
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°.

21. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.

22. If the product of two or more numbers is 0 - what do you know about the numbers?
In the expression x^b - x is the base and b is the exponent.
(n - 2)(180°)
At least one of the factors is 0.
A = [(s^2*v3)/4]

23. What is the formula for the area of a triangle?
In the expression x^b - x is the base and b is the exponent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = (1/2)bh.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

24. Properties of zero 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

25. What is a function?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Arc = (x°/360)(2pr) where x is the central angle.
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

26. Properties of zero 2
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.
If a is negative and b is positive - then a < 0 < b.
V = lwh

27. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.
Equal slopes.
360°

28. What is true about the slopes of parallel lines?
Area = (x°/360)(pr^2) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
Equal slopes.
For any integer n: 1^n = 1.

29. What is true about the measures of the two acute angles in a right triangle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

30. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = lw
Write the percent over 100 and reduce.
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°.
Shifted right 2 units.

31. What is p?
The two pairs of opposite angles formed are equal to each other.
A = pr^2
A = 2(lw + lh + hw)
(Circumference/diameter) of a circle - or approximately 3.14.

32. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)

33. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number n: x^-n means 1/x^n.

34. Properties of one 3
(b^m)^n = b^mn
1 is a divisor (or factor) of every integer.
In the expression x^b - x is the base and b is the exponent.
Set y = 0 - and solve.

35. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An angle formed by extending the side of the polygon.

36. What are similar triangles?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
[(x1 + x2)/2] -[(y1 + y2)/2]

37. What formula is used for an average?
Then the quotient y/x is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n

38. In a circle of radius r - what is the formula for the circumference?
C = p2r
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
A = bh

39. What is a divisor and a factor of an integer?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.

40. Law of exponents 5
V = pr^2h
A^m/b^m = (a/b)^m
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = s^2 or A =d^2/2 where d is the diagonal

41. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Write the percent over 100 and reduce.
All positive and negative whole numbers - and zero.
Cannot is 0 - must is 1 - all others are in between.
Shifted left 2 units.

42. How do you find the slope of a line?
Arc = (x°/360)(2pr) where x is the central angle.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
M = (y2 - y1)/(x2 - x1)
Their sum is 90°.

43. Properties of one 4
(n - 2)(180°)
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
Even numbers are divisible by 2 and odd numbers are not.

44. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.
The product of their slopes is -1 (negative reciprocal).
A = lw

45. Properties of one 2
A = [(s^2*v3)/4]
For any integer n: 1^n = 1.
Their sum is 90°.
(b^m)^n = b^mn

46. What is the sum of the measures of the n angles of a polygon with n sides?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
(n - 2)(180°)
Divide - then multiply by 100.

47. What is an integer?
All positive and negative whole numbers - and zero.
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.
At least one of the factors is 0.

48. What is the sum of the measures of all angles around a point?
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The two pairs of opposite angles formed are equal to each other.
No matter how many angles there are - the sum around the point is 360°.

49. What is the sum of the measures of the four angles in a quadrilateral?
(b^m)^n = b^mn
V = l^3
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°

50. Properties of zero 3
A = pr^2
(n - 2)(180°)
An integer greater than one that is not prime.
0 is a multiple of every integer.