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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 true about the areas of similar triangles?
At least one of the factors is 0.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = pr^2
An equation that states that two ratios are equivalent. 4/6 = 10/15

2. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
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.
(x + y)(x - y) = x^2 - y^2

3. What is true about the measures of the two acute angles in a right triangle?
Shifted up 2 units.
Their sum is 90°.
A fraction whose denominator is 100 i.e. 17% = 17/100
V = pr^2h

4. What are the properties of a rectangle?
Cannot is 0 - must is 1 - all others are in between.
Divide - then multiply by 100.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An equation that states that two ratios are equivalent. 4/6 = 10/15

5. What are similar triangles?
Divide - then multiply by 100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 6(l^2)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

6. In a circle of radius r - what is the formula for the area?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = pr^2

7. What is the Pythagorean theorem?
For any number b: b = -b if and only if b = 0.
For any right triangle - a^2 + b^2 = c^2.
360°
Is a right triangle with a ratio of sides x:xv3:2x.

8. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A^m/b^m = (a/b)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

9. Law of exponents 4
For any number b: b = -b if and only if b = 0.
A = 6(l^2)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A^m*b^m = (ab)^m

10. Properties of zero 1
Shifted left 2 units.
D = 2r
0 is the only number that is neither positive nor negative.
V = lwh

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
180°. If two or more angles form a straight angle - their sum is 180°.
Divide - then multiply by 100.
Shifted left 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

12. What is the sum of the measures of the four angles in a quadrilateral?
In the expression x^b - x is the base and b is the exponent.
The ratio of corresponding sides of similar triangles.
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

13. 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
Is a right triangle with a ratio of sides x:xv3:2x.
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. What is true about the slopes of parallel lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Equal slopes.
Shifted left 2 units.

15. What is a composite number?
An integer greater than one that is not prime.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any right triangle - a^2 + b^2 = c^2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

16. What is a multiple of an integer?
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.
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.

17. What is special formula for the area of an equilateral triangle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Their sum is 180°.
Set x = 0 - and solve.
A = [(s^2*v3)/4]

18. 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 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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
B^m*b^n = b^m+n

19. What is a function?
A = pr^2
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°.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

20. What are the important properties of a 45-45 - 90 triangle?
(Circumference/diameter) of a circle - or approximately 3.14.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

21. Important binomial 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.

22. How do you calculate a weighted average?
0 is a multiple of every integer.
Cannot is 0 - must is 1 - all others are in between.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

23. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
At least one of the factors is 0.
In the expression x^b - x is the base and b is the exponent.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

24. What is the measure of a straight angle?
360°
180°. If two or more angles form a straight angle - their sum is 180°.
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°.
D = 2r

25. What is the formula for the surface area of a cube?
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.
V = lwh
A = 6(l^2)
Shifted left 2 units.

26. Properties of square roots
1 is a divisor (or factor) of every integer.
A = 2(lw + lh + hw)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

27. What is the area of a square?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number n: x^-n means 1/x^n.
Then the quotient y/x is a constant.
A = s^2 or A =d^2/2 where d is the diagonal

28. What is the formula for the volume of a rectangular solid?
V = lwh
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.
Set x = 0 - and solve.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

29. What is a ratio?

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30. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Avg = sum of n numbers/n
Write the percent as a decimal - and multiply.

31. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
C = p2r

32. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A^m*b^m = (ab)^m
1 is the smallest positive odd integer.
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.

33. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
A^m*b^m = (ab)^m
A = pr^2
0 is the only number that is neither positive nor negative.

34. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
The set of all ordered pairs (x -y) such that y = f(x).
A = lw
1 is a divisor (or factor) of every integer.

35. 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.
360°
The two pairs of opposite angles formed are equal to each other.

36. What is true about the measures of the four angles formed by two intersecting lines?
In the expression x^b - x is the base and b is the exponent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The two pairs of opposite angles formed are equal to each other.
A = [(s^2*v3)/4]

37. Law of exponents 2
B^m/b^n = b^m-n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.

38. What does it mean if y is directly proportional to x?
Shifted left 2 units.
(b^m)^n = b^mn
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Then the quotient y/x is a constant.

39. Important binomial 1
Their sum is 180°.
They are both the same. A divisor or factor of an integer leaves no remainder.
(x + y)(x - y) = x^2 - y^2
Divide - then multiply by 100.

40. What is an exterior angle of a triangle?
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.
The product of their slopes is -1 (negative reciprocal).
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

41. What is a negative exponent?
For any number n: x^-n means 1/x^n.
1 is the smallest positive odd integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = [(s^2*v3)/4]

42. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
(b^m)^n = b^mn
For any right triangle - a^2 + b^2 = c^2.
M = (y2 - y1)/(x2 - x1)

43. What is a fractional exponent?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh
Shifted down 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

44. What is the probability of an event that cannot occur? That must occur?
1 is the smallest positive odd integer.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.

45. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number a: a * 1 = a and a / 1 = a.

46. What is a proportion?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Write the percent as a decimal - and multiply.
C = p2r

47. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Then the quotient y/x is a constant.
V = lwh
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°.
B^m*b^n = b^m+n

48. What is a Venn diagram?
(n - 2)(180°)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = lw

49. Properties of one 3
Equal slopes.
Their sum is 180°.
1 is a divisor (or factor) of every integer.
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.

50. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
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.
Their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2