Test your basic knowledge |

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 is a multiple of an integer?
A = 2(lw + lh + hw)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

2. Law of exponents 3
(b^m)^n = b^mn
1 is the smallest positive odd integer.
360°
Avg = sum of n numbers/n

3. What is the triangle inequality?
(b^m)^n = b^mn
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

4. What is a Venn diagram?
V = l^3
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = pr^2

5. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Equal slopes.
Their sum is 180°.
Shifted left 2 units.
For any integer n: 1^n = 1.

6. Law of exponents 1
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted down 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

7. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
A^m/b^m = (a/b)^m
Shifted right 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100

8. What is the square root of a number?
The ratio of corresponding sides of similar triangles.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
No matter how many angles there are - the sum around the point is 360°.
Corresponding sides of similar triangles are in proportion.

9. Properties of one 1
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(b^m)^n = b^mn
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2

10. What is true about the measures of the four angles formed by two intersecting lines?
B^m*b^n = b^m+n
The two pairs of opposite angles formed are equal to each other.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

11. What are the sum - difference - products - and quotient of two numbers?
V = lwh
1 is the smallest positive odd integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The two pairs of opposite angles formed are equal to each other.

12. How do you find the slope of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
M = (y2 - y1)/(x2 - x1)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

13. Properties of one 3
1 is a divisor (or factor) of every integer.
The product of their slopes is -1 (negative reciprocal).
1 is the smallest positive odd integer.
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.

14. What is a composite number?
A = [(s^2*v3)/4]
An integer greater than one that is not prime.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
In the expression x^b - x is the base and b is the exponent.

15. What does it mean if y is directly proportional to x?
If a is negative and b is positive - then a < 0 < b.
They are both the same. A divisor or factor of an integer leaves no remainder.
Then the quotient y/x is a constant.
(b^m)^n = b^mn

16. How do you find the area of a sector of a circle?
Equal slopes.
Cannot is 0 - must is 1 - all others are in between.
Area = (x°/360)(pr^2) where x is the central angle.
Corresponding sides of similar triangles are in proportion.

17. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
360°
All positive and negative whole numbers - and zero.
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°.

18. How do you find the x-intercept of a graph?
All positive and negative whole numbers - and zero.
Set y = 0 - and solve.
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.

19. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
An integer greater than one that is not prime.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted up 2 units.

20. Law of exponents 4
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m
360°
A = bh

21. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
The product of their slopes is -1 (negative reciprocal).
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted up 2 units.

22. 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.
A = (1/2)bh.
1 is a divisor (or factor) of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

23. Important binomial 2
Shifted down 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
D = 2r
Write the percent as a decimal - and multiply.

24. What is an exponent?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
In the expression x^b - x is the base and b is the exponent.
Write the percent as a decimal - and multiply.
1 is the smallest positive odd integer.

25. What is an integer?
Is a right triangle with a ratio of sides x:xv3:2x.
A^m*b^m = (ab)^m
All positive and negative whole numbers - and zero.
Then the product xy is a constant.

26. What is a prime number?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

27. What is the ratio of similitude?
A = s^2 or A =d^2/2 where d is the diagonal
Their sum is 180°.
V = pr^2h
The ratio of corresponding sides of similar triangles.

28. What is an exterior angle of a triangle?
Even numbers are divisible by 2 and odd numbers are not.
The two pairs of opposite angles formed are equal to each other.
(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.

29. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
No matter how many angles there are - the sum around the point is 360°.

30. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A^m/b^m = (a/b)^m
B^m*b^n = b^m+n
Shifted down 2 units.

31. What important property do similar triangles have?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
M = (y2 - y1)/(x2 - x1)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Corresponding sides of similar triangles are in proportion.

32. How do you find the length of an arc of a circle?
The product of their slopes is -1 (negative reciprocal).
Area = (x°/360)(pr^2) where x is the central angle.
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. What is true about the measures of the three angles in a triangle?
V = pr^2h
A = pr^2
Write the percent as a decimal - and multiply.
Their sum is 180°.

34. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Their sum is 90°.
Shifted right 2 units.
0 is the only number that is neither positive nor negative.
For any integer n: 1^n = 1.

35. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
The two pairs of opposite angles formed are equal to each other.
Shifted down 2 units.
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.

36. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent over 100 and reduce.

37. What is p?
Write the percent as a decimal - and multiply.
(Circumference/diameter) of a circle - or approximately 3.14.
The two pairs of opposite angles formed are equal to each other.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

38. What are the properties of a square?
C = p2r
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.
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.

39. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Set y = 0 - and solve.
The set of all ordered pairs (x -y) such that y = f(x).
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

40. What are the properties of a rectangle?
A = s^2 or A =d^2/2 where d is the diagonal
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

41. What are similar triangles?
(Circumference/diameter) of a circle - or approximately 3.14.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 6(l^2)
A^m*b^m = (ab)^m

42. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Avg = sum of n numbers/n
M = (y2 - y1)/(x2 - x1)
A = pr^2

43. Important binomial 1
Shifted down 2 units.
(x + y)(x - y) = x^2 - y^2
Area = (x°/360)(pr^2) where x is the central angle.
A = pr^2

44. What is the volume of a cube?
V = l^3
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 = [(s^2*v3)/4]
V = lwh

45. What is the measure of a straight angle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).
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.
180°. If two or more angles form a straight angle - their sum is 180°.

46. How you convert a fraction or a decimal to a percent?
V = pr^2h
Divide - then multiply by 100.
Write the percent as a decimal - and multiply.
180°. If two or more angles form a straight angle - their sum is 180°.

47. What is a negative exponent?
For any number n: x^-n means 1/x^n.
Set y = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m/b^m = (a/b)^m

48. How do we write the equation of a line?
An integer greater than one that is not prime.
1 is a divisor (or factor) of every integer.
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.

49. If you were given the graph of y = f(x) - what does f(a) represent?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Divide - then multiply by 100.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.

50. In a circle of radius r - what is the formula for the circumference?
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.