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 sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360°.
0 is a multiple of every integer.
1 is the smallest positive odd integer.
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.

2. What is the formula for the area of a parallelogram?
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.
Even numbers are divisible by 2 and odd numbers are not.
A = bh

3. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted up 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

4. What is true about the measures of the four angles formed by two intersecting lines?
For any number b: b = -b if and only if b = 0.
Set x = 0 - and solve.
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.
The two pairs of opposite angles formed are equal to each other.

5. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°

6. How do you find the slope of a line?
At least one of the factors is 0.
D = 2r
M = (y2 - y1)/(x2 - x1)
The set of all ordered pairs (x -y) such that y = f(x).

7. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
For any number n: x^-n means 1/x^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.
Avg = sum of n numbers/n
V = lwh

8. What is the distance formula?
(n - 2)(180°)
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.

9. What is special formula for the area of an equilateral triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At least one of the factors is 0.
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.

10. What are similar triangles?
(b^m)^n = b^mn
If a is negative and b is positive - then a < 0 < b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer greater than one that is not prime.

11. What is a multiple of an integer?
C = p2r
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is a multiple of every integer.
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.

12. What is the probability of an event that cannot occur? That must occur?
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.
All positive and negative whole numbers - and zero.
Equal slopes.
Cannot is 0 - must is 1 - all others are in between.

13. In a circle of radius r - what is the formula for the circumference?
C = p2r
180°. If two or more angles form a straight angle - their sum is 180°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = l^3

14. What is the formula for the volume of a cylinder?
V = pr^2h
V = l^3
Write the percent as a decimal - and multiply.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

15. If the product of two or more numbers is 0 - what do you know about the numbers?
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
Shifted up 2 units.
At least one of the factors is 0.

16. Law of exponents 2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted down 2 units.
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.
B^m/b^n = b^m-n

17. 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°.
Then the quotient y/x is a constant.
A = bh

18. What is the distributive law?
Cannot is 0 - must is 1 - all others are in between.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted up 2 units.
(x + y)(x - y) = x^2 - y^2

19. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
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 = s^2 or A =d^2/2 where d is the diagonal
Shifted right 2 units.

20. What is p?
An equation that states that two ratios are equivalent. 4/6 = 10/15
(Circumference/diameter) of a circle - or approximately 3.14.
1 is a divisor (or factor) of every integer.
For any right triangle - a^2 + b^2 = c^2.

21. What is a percent?
Cannot is 0 - must is 1 - all others are in between.
For any number n: x^-n means 1/x^n.
C = p2r
A fraction whose denominator is 100 i.e. 17% = 17/100

22. What is the formula for the surface area of a cube?
Set y = 0 - and solve.
A = 6(l^2)
Their sum is 90°.
How steep the line is. Horizontal line = 0 - vertical has no slope.

23. Law of exponents 3
(b^m)^n = b^mn
A = pr^2
A = bh
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

24. What is an exterior angle of a polygon?
Set x = 0 - and solve.
360°
An angle formed by extending the side of the polygon.
180°. If two or more angles form a straight angle - their sum is 180°.

25. How do you find the probability that an event will occur?
A^m/b^m = (a/b)^m
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
An integer greater than one that is not prime.

26. Important binomial 2
The product of their slopes is -1 (negative reciprocal).
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
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

27. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
(b^m)^n = b^mn
Shifted right 2 units.
Then the product xy is a constant.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

28. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted left 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

29. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
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.
If a is negative and b is positive - then a < 0 < b.

30. What is an integer?
For any number b: b = -b if and only if b = 0.
No matter how many angles there are - the sum around the point is 360°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
All positive and negative whole numbers - and zero.

31. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m/b^m = (a/b)^m
The ratio of corresponding sides of similar triangles.
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.

32. What is a prime number?
M = (y2 - y1)/(x2 - x1)
A^m/b^m = (a/b)^m
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 any number n: x^-n means 1/x^n.

33. Properties of zero 1
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

34. How do we write the equation of a line?
D = 2r
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

35. What do we mean by the slope of the line?
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°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any integer n: 1^n = 1.

36. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
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.
A = 6(l^2)

37. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
B^m/b^n = b^m-n
Shifted down 2 units.
Write the percent as a decimal - and multiply.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

38. Properties of zero 5
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number b: b = -b if and only if b = 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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

39. For what values of a function is the function undefined?
Set y = 0 - and solve.
Equal slopes.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

40. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An angle formed by extending the side of the polygon.
For any number b: b = -b if and only if b = 0.
Corresponding sides of similar triangles are in proportion.

41. What is the area of a square?
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.
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

42. In a circle of radius r - what is the formula for the area?
A = pr^2
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 x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

43. What are the properties of a parallelogram?
The ratio of corresponding sides of similar triangles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Then the quotient y/x is a constant.

44. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh

45. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
360°
A = 6(l^2)

46. What is the measure of a straight angle?
Then the quotient y/x is a constant.
180°. If two or more angles form a straight angle - their sum is 180°.
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.
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.

47. What is the midpoint formula?
Shifted right 2 units.
Cannot is 0 - must is 1 - all others are in between.
[(x1 + x2)/2] -[(y1 + y2)/2]
The set of all ordered pairs (x -y) such that y = f(x).

48. What is true about the slopes of perpendicular lines?
Shifted right 2 units.
360°
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.

49. How do you calculate percent increases and decreases?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted up 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

50. What is a ratio?

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