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 parallelogram?
Is a right triangle with a ratio of sides x:xv3:2x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
180°. If two or more angles form a straight angle - their sum is 180°.
A = bh

2. What are similar triangles?
A = s^2 or A =d^2/2 where d is the diagonal
V = lwh
Then the quotient y/x is a constant.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

3. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
No matter how many angles there are - the sum around the point is 360°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
1 is the smallest positive odd integer.

4. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
360°
The ratio of corresponding sides of similar triangles.

5. What is the measure of a straight angle?
Set x = 0 - and solve.
They are both the same. A divisor or factor of an integer leaves no remainder.
360°
180°. If two or more angles form a straight angle - their sum is 180°.

6. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
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°.
Set x = 0 - and solve.

7. What is true about the measures of the three angles in a triangle?
A = [(s^2*v3)/4]
Their sum is 180°.
V = lwh
B^m/b^n = b^m-n

8. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction whose denominator is 100 i.e. 17% = 17/100
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

9. What are the important properties of 30-60-90 triangle?
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)
At least one of the factors is 0.
Is a right triangle with a ratio of sides x:xv3:2x.

10. What is the volume of a cube?
180°. If two or more angles form a straight angle - their sum is 180°.
V = l^3
An integer greater than one that is not prime.
Set y = 0 - and solve.

11. What is the triangle inequality?
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
D = 2r
The set of all ordered pairs (x -y) such that y = f(x).

12. In a circle of radius r - what is the formula for the circumference?
The product of their slopes is -1 (negative reciprocal).
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 set of all ordered pairs (x -y) such that y = f(x).
C = p2r

13. What is a multiple of an 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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°
A = s^2 or A =d^2/2 where d is the diagonal

14. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is a multiple of every integer.
Set y = 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.

15. Law of exponents 2
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.
B^m/b^n = b^m-n
For any right triangle - a^2 + b^2 = c^2.

16. If the product of two or more numbers is 0 - what do you know about the numbers?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
At least one of the factors is 0.
V = lwh
B^m*b^n = b^m+n

17. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted up 2 units.
Then the product xy is a constant.

18. What is the formula for the area of a rectangle?
A = s^2 or A =d^2/2 where d is the diagonal
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = lw
Their sum is 180°.

19. What is true about the slopes of parallel lines?
Equal slopes.
B^m/b^n = b^m-n
Their sum is 180°.
An integer greater than one that is not prime.

20. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Even numbers are divisible by 2 and odd numbers are not.
A = pr^2
(b^m)^n = b^mn

21. What is the ratio of similitude?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.
The ratio of corresponding sides of similar triangles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

22. What is true about the areas of similar triangles?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Equal slopes.
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.

23. How do you calculate a weighted average?
If a is negative and b is positive - then a < 0 < b.
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m*b^n = b^m+n

24. Properties of one 4
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
Then the quotient y/x is a constant.
1 is the smallest positive odd integer.

25. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
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.
Shifted left 2 units.

26. What is the formula for the area of a triangle?
The set of all ordered pairs (x -y) such that y = f(x).
A = (1/2)bh.
Equal slopes.
0 is the only number that is neither positive nor negative.

27. Law of exponents 5
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^m/b^m = (a/b)^m
A = [(s^2*v3)/4]
Shifted right 2 units.

28. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Write the percent as a decimal - and multiply.
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

29. Important binomial 3
A^m/b^m = (a/b)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
B^m/b^n = b^m-n

30. Properties of zero 4
360°
A = pr^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

31. In a circle of radius r - what is the formula for the diameter?
V = pr^2h
At least one of the factors is 0.
D = 2r
Arc = (x°/360)(2pr) where x is the central angle.

32. What is the distributive law?
A = bh
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Then the product xy is a constant.
For any number a: a * 1 = a and a / 1 = a.

33. How you convert a fraction or a decimal to a percent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Divide - then multiply by 100.
Arc = (x°/360)(2pr) where x is the central angle.
A = s^2 or A =d^2/2 where d is the diagonal

34. Properties of zero 5
M = (y2 - y1)/(x2 - x1)
For any number b: b = -b if and only if b = 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.

35. How do you find the length of an arc of a circle?
B^m*b^n = b^m+n
At least one of the factors is 0.
Arc = (x°/360)(2pr) where x is the central angle.
How steep the line is. Horizontal line = 0 - vertical has no slope.

36. Properties of zero 3
Write the percent as a decimal - and multiply.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.
360°

37. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Cannot is 0 - must is 1 - all others are in between.
1 is the smallest positive odd integer.
A = (1/2)bh.

38. Law of exponents 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An angle formed by extending the side of the polygon.
B^m*b^n = b^m+n
For any number n: x^-n means 1/x^n.

39. How do you find the x-intercept of a graph?
A fraction whose denominator is 100 i.e. 17% = 17/100
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Set y = 0 - and solve.

40. What is an integer?
Even numbers are divisible by 2 and odd numbers are not.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
All positive and negative whole numbers - and zero.
A^m/b^m = (a/b)^m

41. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Corresponding sides of similar triangles are in proportion.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted left 2 units.
Set x = 0 - and solve.

42. What is the square root of a number?
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
Shifted up 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

43. What is the distance formula?
V = l^3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An angle formed by extending the side of the polygon.

44. What is true about the measures of the four angles formed by two intersecting lines?
A fraction whose denominator is 100 i.e. 17% = 17/100
Equal slopes.
The two pairs of opposite angles formed are equal to each other.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

45. 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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The set of all ordered pairs (x -y) such that y = f(x).

46. How do you find a percent of a number?
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent as a decimal - and multiply.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh

47. Properties of one 3
Even numbers are divisible by 2 and odd numbers are not.
A fraction whose denominator is 100 i.e. 17% = 17/100
The product of their slopes is -1 (negative reciprocal).
1 is a divisor (or factor) of every integer.

48. 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.
V = lwh
Shifted right 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.

49. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

50. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2