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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?
Is a right triangle with a ratio of sides x:xv3:2x.
Then the product xy is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = 2(lw + lh + hw)

2. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Their sum is 90°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
They are both the same. A divisor or factor of an integer leaves no remainder.

3. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Write the percent as a decimal - and multiply.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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 = s^2 or A =d^2/2 where d is the diagonal

4. What is true about the measures of the two acute angles in a right triangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = 6(l^2)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 90°.

5. What is true about the measures of the three angles in a triangle?
A = bh
Their sum is 180°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is a divisor (or factor) of every integer.

6. How do you find the y-intercept of a graph?
Divide - then multiply by 100.
Set x = 0 - and solve.
A = lw
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

7. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).
(x + y)(x - y) = x^2 - y^2

8. What is an exterior angle of a triangle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

9. Properties of zero 2
How steep the line is. Horizontal line = 0 - vertical has no slope.
M = (y2 - y1)/(x2 - x1)
If a is negative and b is positive - then a < 0 < b.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

10. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
360°
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°.
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2

11. What is a prime number?
V = l^3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent as a decimal - and multiply.
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.

12. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
In the expression x^b - x is the base and b is the exponent.

13. What are the sum - difference - products - and quotient of two numbers?
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Their sum is 180°.
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.

14. Law of exponents 4
The set of all ordered pairs (x -y) such that y = f(x).
Arc = (x°/360)(2pr) where x is the central angle.
Their sum is 90°.
A^m*b^m = (ab)^m

15. Properties of zero 4
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

16. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted down 2 units.
Shifted right 2 units.
0 is a multiple of every integer.
Avg = sum of n numbers/n

17. How do you calculate a weighted average?
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = 2(lw + lh + hw)

18. What is the formula for the area of a rectangle?
A = [(s^2*v3)/4]
Shifted up 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = lw

19. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. What is the formula for the surface area of a rectangular solid?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 2(lw + lh + hw)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number a: a * 1 = a and a / 1 = a.

21. 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.
All positive and negative whole numbers - and zero.
180°. If two or more angles form a straight angle - their sum is 180°.
Write the percent as a decimal - and multiply.

22. What is the sum of the measures of the n angles of a polygon with n sides?
For any number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.
(n - 2)(180°)
An integer greater than one that is not prime.

23. What is a multiple of an integer?
Is a right triangle with a ratio of sides x:xv3:2x.
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.
An angle formed by extending the side of the polygon.
C = p2r

24. Properties of square roots
Area = (x°/360)(pr^2) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

25. What is the formula for the area of a parallelogram?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = bh
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

26. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Shifted right 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x + y)(x - y) = x^2 - y^2

27. Law of exponents 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
B^m/b^n = b^m-n
The set of all ordered pairs (x -y) such that y = f(x).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

28. How do you find the length of an arc of a circle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Arc = (x°/360)(2pr) where x is the central angle.

29. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
360°
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 a is negative and b is positive - then a < 0 < b.

30. How do you find a percent of a number?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Write the percent as a decimal - and multiply.
180°. If two or more angles form a straight angle - their sum is 180°.
The ratio of corresponding sides of similar triangles.

31. What are the properties of a square?
Arc = (x°/360)(2pr) where x is the central angle.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
Equal slopes.

32. What is a fractional exponent?
A fraction whose denominator is 100 i.e. 17% = 17/100
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The two pairs of opposite angles formed are equal to each other.
Then the quotient y/x is a constant.

33. What is an exterior angle of a polygon?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.
If a is negative and b is positive - then a < 0 < b.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

34. What are the quotient and the remainder?

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35. What is an even and an odd number?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Then the product xy is a constant.
Even numbers are divisible by 2 and odd numbers are not.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

36. 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = pr^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

37. Important binomial 2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
0 is the only number that is neither positive nor negative.
(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.

38. For what values of a function is the function undefined?
For any number b: b = -b if and only if b = 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Write the percent as a decimal - and multiply.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

39. What are the properties of a rectangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(b^m)^n = b^mn
A = lw

40. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
If a is negative and b is positive - then a < 0 < b.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

41. How do you convert a percent to a fraction or a decimal?
[(x1 + x2)/2] -[(y1 + y2)/2]
Write the percent over 100 and reduce.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
At least one of the factors is 0.

42. What is the volume of a cube?
An angle formed by extending the side of the polygon.
V = l^3
For any integer n: 1^n = 1.
No matter how many angles there are - the sum around the point is 360°.

43. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
C = p2r
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

44. What is an integer?
360°
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)
In the expression x^b - x is the base and b is the exponent.

45. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
A = lw
0 is a multiple of every integer.
At least one of the factors is 0.

46. What is a percent?
Area = (x°/360)(pr^2) where x is the central angle.
Then the quotient y/x is a constant.
C = p2r
A fraction whose denominator is 100 i.e. 17% = 17/100

47. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
All positive and negative whole numbers - and zero.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

48. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Their sum is 90°.
Then the quotient y/x 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

49. What is the midpoint formula?
0 is the only number that is neither positive nor negative.
A = lw
No matter how many angles there are - the sum around the point is 360°.
[(x1 + x2)/2] -[(y1 + y2)/2]

50. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
360°
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.