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 the formula for the area of a rectangle?
A = lw
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn
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.

2. What is a negative exponent?
V = lwh
A = (1/2)bh.
For any number n: x^-n means 1/x^n.
A = s^2 or A =d^2/2 where d is the diagonal

3. What is the sum of the measures of the four angles in a quadrilateral?
At least one of the factors is 0.
360°
For any number b: b = -b if and only if b = 0.
Divide - then multiply by 100.

4. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
For any number b: b = -b if and only if b = 0.
At least one of the factors is 0.
Equal slopes.

5. Law of exponents 5
The product of their slopes is -1 (negative reciprocal).
V = pr^2h
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

6. What are the quotient and the remainder?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

7. 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 = [(s^2*v3)/4]
[(x1 + x2)/2] -[(y1 + y2)/2]
An equation that states that two ratios are equivalent. 4/6 = 10/15

8. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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°.
Equal slopes.

9. Properties of zero 1
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = pr^2
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

10. Law of exponents 4
A^m*b^m = (ab)^m
For any number b: b = -b if and only if b = 0.
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

11. What are the important properties of 30-60-90 triangle?
If a is negative and b is positive - then a < 0 < b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Is a right triangle with a ratio of sides x:xv3:2x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

12. What is the distributive law?
V = lwh
If a is negative and b is positive - then a < 0 < b.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°

13. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
An integer greater than one that is not prime.
Set y = 0 - and solve.
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.

14. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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.
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°.
A = pr^2

15. What is true about the slopes of parallel lines?
For any right triangle - a^2 + b^2 = c^2.
(n - 2)(180°)
[(x1 + x2)/2] -[(y1 + y2)/2]
Equal slopes.

16. 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.
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.
If a is negative and b is positive - then a < 0 < b.
(b^m)^n = b^mn

17. What is the volume of a cube?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = l^3
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted down 2 units.

18. What is the midpoint formula?
In the expression x^b - x is the base and b is the exponent.
D = 2r
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
[(x1 + x2)/2] -[(y1 + y2)/2]

19. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The set of all ordered pairs (x -y) such that y = f(x).
Equal slopes.

20. Properties of one 4
1 is the smallest positive odd integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Even numbers are divisible by 2 and odd numbers are not.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

21. What is the formula for the area of a parallelogram?
(Circumference/diameter) of a circle - or approximately 3.14.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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.
A = bh

22. What is the Pythagorean theorem?
No matter how many angles there are - the sum around the point is 360°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Divide - then multiply by 100.
For any right triangle - a^2 + b^2 = c^2.

23. Properties of zero 3
0 is a multiple of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

24. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
B^m/b^n = b^m-n
Their sum is 90°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

25. What is the formula for the area of a triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Avg = sum of n numbers/n
A = (1/2)bh.

26. What is the triangle inequality?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

27. What is a ratio?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

28. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = lwh
0 is the only number that is neither positive nor negative.
360°

29. What is the measure of a straight angle?
In the expression x^b - x is the base and b is the exponent.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m
180°. If two or more angles form a straight angle - their sum is 180°.

30. What is a Venn diagram?
Shifted up 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted left 2 units.
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.

31. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
At least one of the factors is 0.
Shifted up 2 units.
V = pr^2h
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.

32. Important binomial 2
Divide - then multiply by 100.
Corresponding sides of similar triangles are in proportion.
For any right triangle - a^2 + b^2 = c^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

33. What important property do similar triangles have?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Corresponding sides of similar triangles are in proportion.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
180°. If two or more angles form a straight angle - their sum is 180°.

34. In a circle of radius r - what is the formula for the circumference?
(b^m)^n = b^mn
C = p2r
Avg = sum of n numbers/n
The ratio of corresponding sides of similar triangles.

35. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = (1/2)bh.
All positive and negative whole numbers - and zero.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

36. What is a function?
A^m/b^m = (a/b)^m
Shifted up 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

37. What is the area of a square?
Arc = (x°/360)(2pr) where x is the central angle.
C = p2r
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 or A =d^2/2 where d is the diagonal

38. What is true about the measures of the three angles in a triangle?
A = 6(l^2)
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set y = 0 - and solve.
Their sum is 180°.

39. Law of exponents 2
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m/b^n = b^m-n

40. What is a proportion?
M = (y2 - y1)/(x2 - x1)
The set of all ordered pairs (x -y) such that y = f(x).
The two pairs of opposite angles formed are equal to each other.
An equation that states that two ratios are equivalent. 4/6 = 10/15

41. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

42. 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.
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.
1 is the smallest positive odd integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. What is a multiple of an integer?
For any number a: a * 1 = a and a / 1 = a.
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 n: x^-n means 1/x^n.

44. Properties of one 2
For any integer n: 1^n = 1.
The ratio of corresponding sides of similar triangles.
Set y = 0 - and solve.
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.

45. How do you calculate a weighted average?
Set y = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

46. How do you find the y-intercept of a graph?
The product of their slopes is -1 (negative reciprocal).
V = l^3
0 is the only number that is neither positive nor negative.
Set x = 0 - and solve.

47. What is the ratio of similitude?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = s^2 or A =d^2/2 where d is the diagonal
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.

48. 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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A^m/b^m = (a/b)^m
V = l^3

49. Important binomial 1
(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.
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2

50. Law of exponents 3
A = pr^2
(b^m)^n = b^mn
Is a right triangle with a ratio of sides x:xv3:2x.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.