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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 the probability of an event that cannot occur? That must occur?
Their sum is 90°.
Shifted up 2 units.
Cannot is 0 - must is 1 - all others are in between.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

2. What is special formula for the area of an equilateral triangle?
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
360°
A = [(s^2*v3)/4]

3. What is the formula for the surface area of a rectangular solid?
V = l^3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 180°.
A = 2(lw + lh + hw)

4. In a circle of radius r - what is the formula for the diameter?
1 is the smallest positive odd integer.
D = 2r
A = lw
An equation that states that two ratios are equivalent. 4/6 = 10/15

5. 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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted left 2 units.
Then the product xy is a constant.

6. What is a function?
A = bh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = [(s^2*v3)/4]

7. How do you find the x-intercept of a graph?
V = pr^2h
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
C = p2r
Set y = 0 - and solve.

8. How do we write the equation of a line?
Write the percent over 100 and reduce.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Even numbers are divisible by 2 and odd numbers are not.

9. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 2(lw + lh + hw)
Then the product xy is a constant.

10. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

11. What is a proportion?
Set y = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

12. What is a negative exponent?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number n: x^-n means 1/x^n.
Area = (x°/360)(pr^2) where x is the central angle.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

13. What are the properties of a rectangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
All positive and negative whole numbers - and zero.
Arc = (x°/360)(2pr) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

14. What is true about the measures of the two acute angles in a right triangle?
Area = (x°/360)(pr^2) where x is the central angle.
A = [(s^2*v3)/4]
Cannot is 0 - must is 1 - all others are in between.
Their sum is 90°.

15. What is an exterior angle of a triangle?
V = pr^2h
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

16. What is the ratio of similitude?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
A fraction whose denominator is 100 i.e. 17% = 17/100

17. What is the volume of a cube?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An angle formed by extending the side of the polygon.
Write the percent over 100 and reduce.
V = l^3

18. What are similar triangles?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.

19. In a circle of radius r - what is the formula for the circumference?
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 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°.
The ratio of corresponding sides of similar triangles.
C = p2r

20. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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)^n = b^mn
(n - 2)(180°)

21. What is true about the slopes of parallel lines?
Cannot is 0 - must is 1 - all others are in between.
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.
Equal slopes.

22. If the product of two or more numbers is 0 - what do you know about the numbers?
(n - 2)(180°)
Avg = sum of n numbers/n
At least one of the factors is 0.
D = 2r

23. Properties of one 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number a: a * 1 = a and a / 1 = a.

24. What is the formula for the area of a triangle?
A = (1/2)bh.
For any right triangle - a^2 + b^2 = c^2.
Avg = sum of n numbers/n
If a is negative and b is positive - then a < 0 < b.

25. What are the quotient and the remainder?

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26. Properties of zero 5
Even numbers are divisible by 2 and odd numbers are not.
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.
For any number b: b = -b if and only if b = 0.

27. Important binomial 1
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.
(x + y)(x - y) = x^2 - y^2
A = lw
An integer greater than one that is not prime.

28. What is a composite number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An integer greater than one that is not prime.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = bh

29. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Equal slopes.
An angle formed by extending the side of the polygon.
Shifted right 2 units.

30. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
How steep the line is. Horizontal line = 0 - vertical has no slope.
In the expression x^b - x is the base and b is the exponent.
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.

31. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The set of all ordered pairs (x -y) such that y = f(x).
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.

32. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
Shifted left 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 90°.

33. Properties of one 3
1 is a divisor (or factor) of every integer.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

34. Properties of zero 1
V = lwh
0 is the only number that is neither positive nor negative.
The product of their slopes is -1 (negative reciprocal).
For any number b: b = -b if and only if b = 0.

35. Law of exponents 5
A^m/b^m = (a/b)^m
Write the percent over 100 and reduce.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.

36. Properties of zero 2
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.
If a is negative and b is positive - then a < 0 < b.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

37. What is a ratio?

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38. Properties of zero 4
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

39. If you were given the graph of y = f(x) - what does f(a) represent?
V = pr^2h
Shifted up 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

40. Properties of one 2
In the expression x^b - x is the base and b is the exponent.
Then the product xy is a constant.
For any integer n: 1^n = 1.
360°

41. What does it mean if y is directly proportional to x?
A^m/b^m = (a/b)^m
A = 6(l^2)
(Circumference/diameter) of a circle - or approximately 3.14.
Then the quotient y/x is a constant.

42. Properties of square roots
For any number a: a * 1 = a and a / 1 = a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Then the quotient y/x is a constant.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

43. What is the Pythagorean theorem?
No matter how many angles there are - the sum around the point is 360°.
Divide - then multiply by 100.
For any right triangle - a^2 + b^2 = c^2.
A fraction whose denominator is 100 i.e. 17% = 17/100

44. What is the triangle inequality?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
An integer greater than one that is not prime.
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.
Cannot is 0 - must is 1 - all others are in between.

45. How do you find the probability that an event will occur?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The ratio of corresponding sides of similar triangles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
V = pr^2h

46. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Equal slopes.
360°
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any right triangle - a^2 + b^2 = c^2.

47. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
At least one of the factors is 0.

48. What is the measure of a straight 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°.
Arc = (x°/360)(2pr) where x is the central angle.
1 is a divisor (or factor) of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.

49. What is an integer?
All positive and negative whole numbers - and zero.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Equal slopes.
Write the percent as a decimal - and multiply.

50. Important binomial 2
The two pairs of opposite angles formed are equal to each other.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted down 2 units.
A = bh