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. Law of exponents 2
The two pairs of opposite angles formed are equal to each other.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
B^m/b^n = b^m-n
An angle formed by extending the side of the polygon.

2. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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 = 6(l^2)

3. What are the properties of a parallelogram?
360°
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted down 2 units.

4. Important binomial 2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.

5. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The set of all ordered pairs (x -y) such that y = f(x).
(b^m)^n = b^mn
C = p2r

6. Properties of one 2
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.
360°

7. How do you find the probability that an event will occur?
Avg = sum of n numbers/n
Even numbers are divisible by 2 and odd numbers are not.
A = pr^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

8. Properties of square roots
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

9. What is the relationship between the graph of f(x) the graph of y = f(x + 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.
(b^m)^n = b^mn
Shifted left 2 units.
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.

10. Properties of zero 5
For any number b: b = -b if and only if b = 0.
V = l^3
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.

11. In a circle of radius r - what is the formula for the area?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = pr^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Is a right triangle with a ratio of sides x:xv3:2x.

12. What do we mean by the slope of the line?
A = pr^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
180°. If two or more angles form a straight angle - their sum is 180°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

13. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is a multiple of every integer.
Even numbers are divisible by 2 and odd numbers are not.

14. What are the important properties of 30-60-90 triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.
Set y = 0 - and solve.
If a is negative and b is positive - then a < 0 < b.

15. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
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 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.
Shifted right 2 units.
360°

16. What are the quotient and the remainder?

17. How do you find the slope of a line?
A = s^2 or A =d^2/2 where d is the diagonal
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
Shifted left 2 units.

18. Law of exponents 1
0 is the only number that is neither positive nor negative.
(Circumference/diameter) of a circle - or approximately 3.14.
B^m*b^n = b^m+n
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. What is an 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.
1 is a divisor (or factor) of every integer.
All positive and negative whole numbers - and zero.
A = s^2 or A =d^2/2 where d is the diagonal

20. What is special formula for the area of an equilateral triangle?
0 is the only number that is neither positive nor negative.
A = [(s^2*v3)/4]
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 = (1/2)bh.

21. What is the sum of the measures of all angles around a point?
For any number n: x^-n means 1/x^n.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
No matter how many angles there are - the sum around the point is 360°.
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.

22. How do you find the length of an arc of a circle?
The two pairs of opposite angles formed are equal to each other.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Arc = (x°/360)(2pr) where x is the central angle.
Area = (x°/360)(pr^2) where x is the central angle.

23. What is the ratio of similitude?
Shifted right 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The ratio of corresponding sides of similar triangles.
B^m/b^n = b^m-n

24. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Even numbers are divisible by 2 and odd numbers are not.
A = 2(lw + lh + hw)
Shifted down 2 units.

25. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
A = 2(lw + lh + hw)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

26. What are similar triangles?
D = 2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(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.

27. What is the formula for the area of a triangle?
Set x = 0 - and solve.
1 is a divisor (or factor) of every integer.
A = (1/2)bh.
(Circumference/diameter) of a circle - or approximately 3.14.

28. How you convert a fraction or a decimal to a percent?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Divide - then multiply by 100.
Is a right triangle with a ratio of sides x:xv3:2x.
A = lw

29. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Even numbers are divisible by 2 and odd numbers are not.
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°.

30. Properties of one 1
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 two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.
For any number a: a * 1 = a and a / 1 = a.

31. How do you calculate a weighted average?
360°
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

32. What is a composite number?
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
[(x1 + x2)/2] -[(y1 + y2)/2]
A^m*b^m = (ab)^m

33. What is an exponent?
For any number a: a * 1 = a and a / 1 = a.
All positive and negative whole numbers - and zero.
Set y = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.

34. What is a prime number?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An integer greater than one that is not prime.
Divide - then multiply by 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.

35. 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.
Shifted right 2 units.
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.
C = p2r

36. What is the square root of a number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Set y = 0 - and solve.

37. What is a Venn diagram?
0 is the only number that is neither positive nor negative.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal

38. What is the triangle inequality?
Corresponding sides of similar triangles are in proportion.
Avg = sum of n numbers/n
Cannot is 0 - must is 1 - all others are in between.
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.

39. What are the sum - difference - products - and quotient of two numbers?
0 is a multiple of every integer.
For any number a: a * 1 = a and a / 1 = a.
Their sum is 90°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

40. Law of exponents 4
Then the product xy is a constant.
A^m*b^m = (ab)^m
C = p2r
M = (y2 - y1)/(x2 - x1)

41. What is true about the measures of the two acute angles in a right triangle?
Write the percent over 100 and reduce.
C = p2r
Their sum is 90°.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

42. What is true about the measures of the three angles in a triangle?
All positive and negative whole numbers - and zero.
Their sum is 180°.
Write the percent over 100 and reduce.
Avg = sum of n numbers/n

43. What is a negative exponent?
Shifted down 2 units.
A = 6(l^2)
A = lw
For any number n: x^-n means 1/x^n.

44. If the product of two or more numbers is 0 - what do you know about the numbers?
How steep the line is. Horizontal line = 0 - vertical has no slope.
(Circumference/diameter) of a circle - or approximately 3.14.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At least one of the factors is 0.

45. What is the measure of a straight angle?
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°.
For any right triangle - a^2 + b^2 = c^2.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

46. Law of exponents 3
(b^m)^n = b^mn
Area = (x°/360)(pr^2) where x is the central angle.
Avg = sum of n numbers/n
Equal slopes.

47. What is a ratio?

48. Properties of one 4
V = pr^2h
A^m*b^m = (ab)^m
1 is the smallest positive odd integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

49. What is true about the slopes of parallel lines?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Equal slopes.
A = lw
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.

50. What is a fractional exponent?
All positive and negative whole numbers - and zero.
0 is the only number that is neither positive nor negative.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
B^m/b^n = b^m-n