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 Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
1 is a divisor (or factor) of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Cannot is 0 - must is 1 - all others are in between.

2. In a circle of radius r - what is the formula for the circumference?
A = [(s^2*v3)/4]
M = (y2 - y1)/(x2 - x1)
C = p2r
1 is the smallest positive odd integer.

3. What are the sum - difference - products - and quotient of two numbers?
Set y = 0 - and solve.
A^m*b^m = (ab)^m
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

4. What is true about the measures of the two acute angles in a right triangle?
Avg = sum of n numbers/n
Their sum is 90°.
No matter how many angles there are - the sum around the point is 360°.
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.

5. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
No matter how many angles there are - the sum around the point is 360°.

6. What is the probability of an event that cannot occur? That must occur?
For any integer n: 1^n = 1.
Cannot is 0 - must is 1 - all others are in between.
(b^m)^n = b^mn
A = bh

7. How do you find the slope of a line?
A = [(s^2*v3)/4]
M = (y2 - y1)/(x2 - x1)
V = l^3
1 is a divisor (or factor) of every integer.

8. 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 up 2 units.
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.

9. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
V = pr^2h
(Circumference/diameter) of a circle - or approximately 3.14.
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°.
An equation that states that two ratios are equivalent. 4/6 = 10/15

10. Properties of square roots
A = lw
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = 6(l^2)
(b^m)^n = b^mn

11. What does it mean if y is directly proportional to x?
Shifted down 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°
Then the quotient y/x is a constant.

12. What is the area of a square?
A = 2(lw + lh + hw)
A = s^2 or A =d^2/2 where d is the diagonal
180°. If two or more angles form a straight angle - their sum is 180°.
D = 2r

13. What is an exponent?
Corresponding sides of similar triangles are in proportion.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
In the expression x^b - x is the base and b is the exponent.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

14. Law of exponents 1
B^m*b^n = b^m+n
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.
(x + y)(x - y) = x^2 - y^2
360°

15. Law of exponents 4
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
C = p2r
A^m*b^m = (ab)^m
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

16. What is the graph of a function?
Then the quotient y/x is a constant.
A = lw
Is a right triangle with a ratio of sides x:xv3:2x.
The set of all ordered pairs (x -y) such that y = f(x).

17. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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 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.
Arc = (x°/360)(2pr) where x is the central angle.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

18. How do you find the length of an arc of a circle?
(x + y)(x - y) = x^2 - y^2
Arc = (x°/360)(2pr) where x is the central angle.
Avg = sum of n numbers/n
V = lwh

19. What is true about the slopes of parallel lines?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Equal slopes.
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.

20. What is the formula for the surface area of a rectangular solid?
Area = (x°/360)(pr^2) where x is the central angle.
(Circumference/diameter) of a circle - or approximately 3.14.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = 2(lw + lh + hw)

21. Properties of zero 4
For any number b: b = -b if and only if b = 0.
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
B^m*b^n = b^m+n

22. Law of exponents 2
The two pairs of opposite angles formed are equal to each other.
B^m/b^n = b^m-n
Avg = sum of n numbers/n
For any integer n: 1^n = 1.

23. What important property do similar triangles have?
B^m*b^n = b^m+n
Corresponding sides of similar triangles are in proportion.
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.

24. What is true about the measures of the four angles formed by two intersecting lines?
Set x = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The two pairs of opposite angles formed are equal to each other.
Arc = (x°/360)(2pr) where x is the central angle.

25. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Corresponding sides of similar triangles are in proportion.
Then the quotient y/x is a constant.
Shifted down 2 units.

26. What is an integer?
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n
All positive and negative whole numbers - and zero.
Their sum is 90°.

27. What is the distance formula?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Is a right triangle with a ratio of sides x:xv3:2x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

28. How do you find a percent of a number?
No matter how many angles there are - the sum around the point is 360°.
Write the percent as a decimal - and multiply.
The two pairs of opposite angles formed are equal to each other.
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°.

29. How do you find the area of a sector of a circle?
A^m*b^m = (ab)^m
Shifted up 2 units.
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.

30. Properties of zero 2
0 is the only number that is neither positive nor negative.
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

31. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted right 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

32. How do you find the y-intercept of a graph?
The ratio of corresponding sides of similar triangles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set x = 0 - and solve.

33. What is the distributive law?
(x + y)(x - y) = x^2 - y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = 6(l^2)
A = 2(lw + lh + hw)

34. What is a function?
A = (1/2)bh.
A = bh
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)(x - y) = x^2 - y^2

35. Properties of one 2
The product of their slopes is -1 (negative reciprocal).
Arc = (x°/360)(2pr) where x is the central angle.
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°.
For any integer n: 1^n = 1.

36. What is p?
Then the product xy is a constant.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(Circumference/diameter) of a circle - or approximately 3.14.
A = 6(l^2)

37. Properties of one 3
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

38. 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

39. What is the formula for the area of a triangle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = (1/2)bh.
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.
V = l^3

40. What is true about the areas of similar triangles?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

41. 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°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = 2(lw + lh + hw)
The ratio of corresponding sides of similar triangles.

42. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted left 2 units.
For any number a: a * 1 = a and a / 1 = a.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

43. Law of exponents 5
Write the percent over 100 and reduce.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m/b^m = (a/b)^m
A = lw

44. What is a prime number?
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.
Shifted up 2 units.
B^m/b^n = b^m-n
For any right triangle - a^2 + b^2 = c^2.

45. For what values of a function is the function undefined?
(n - 2)(180°)
Divide - then multiply by 100.
360°
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

46. What is the formula for the area of a rectangle?
All positive and negative whole numbers - and zero.
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°.
A = lw

47. Important binomial 1
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted right 2 units.
(x + y)(x - y) = x^2 - y^2
No matter how many angles there are - the sum around the point is 360°.

48. In a circle of radius r - what is the formula for the diameter?
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
D = 2r
Arc = (x°/360)(2pr) where x is the central angle.

49. What are the median and the mode of a set of data?
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
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.
Set y = 0 - and solve.

50. What is a negative exponent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any number n: x^-n means 1/x^n.
A = lw