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?
An integer greater than one that is not prime.
Avg = sum of n numbers/n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh

2. Properties of square roots
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 90°.
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.

3. What do we mean by the slope of the line?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

4. What is an exponent?
For any number b: b = -b if and only if b = 0.
All positive and negative whole numbers - and zero.
Avg = sum of n numbers/n
In the expression x^b - x is the base and b is the exponent.

5. What is the midpoint formula?
For any number a: a * 1 = a and a / 1 = a.
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.

6. What is true about the slopes of parallel lines?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Equal slopes.

7. What is a composite number?
An integer greater than one that is not prime.
For any number n: x^-n means 1/x^n.
The set of all ordered pairs (x -y) such that y = f(x).
V = lwh

8. Properties of zero 5
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted up 2 units.
The two pairs of opposite angles formed are equal to each other.
For any number b: b = -b if and only if b = 0.

9. What is the graph of a function?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(x + y)(x - y) = x^2 - y^2
The set of all ordered pairs (x -y) such that y = f(x).

10. Law of exponents 1
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

11. What is a negative exponent?
For any number n: x^-n means 1/x^n.
Divide - then multiply by 100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent as a decimal - and multiply.

12. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted up 2 units.
A = pr^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

13. What is the formula for the surface area of a cube?
For any number a: a * 1 = a and a / 1 = a.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = 6(l^2)
A fraction whose denominator is 100 i.e. 17% = 17/100

14. 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.
For any number b: b = -b if and only if b = 0.
B^m*b^n = b^m+n
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

15. Properties of one 3
The product of their slopes is -1 (negative reciprocal).
Then the product xy is a constant.
A = s^2 or A =d^2/2 where d is the diagonal
1 is a divisor (or factor) of every integer.

16. Important binomial 3
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
0 is the only number that is neither positive nor negative.
360°

17. What is a proportion?
Corresponding sides of similar triangles are in proportion.
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number b: b = -b if and only if b = 0.

18. How do you find the area of a sector of a circle?
D = 2r
Shifted left 2 units.
Area = (x°/360)(pr^2) where x is the central angle.
A = s^2 or A =d^2/2 where d is the diagonal

19. In a circle of radius r - what is the formula for the area?
(b^m)^n = b^mn
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = pr^2

20. What is an exterior angle of a triangle?
(Circumference/diameter) of a circle - or approximately 3.14.
B^m*b^n = b^m+n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Cannot is 0 - must is 1 - all others are in between.

21. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is the only number that is neither positive nor negative.
A^m*b^m = (ab)^m

22. How do you calculate percent increases and decreases?
For any number a: a * 1 = a and a / 1 = a.
Divide - then multiply by 100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

23. How do you find a percent of a number?
A^m/b^m = (a/b)^m
Write the percent as a decimal - and multiply.
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.

24. What is the sum of the measures of the four angles in a quadrilateral?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.
If a is negative and b is positive - then a < 0 < b.
360°

25. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = bh
They are both the same. A divisor or factor of an integer leaves no remainder.

26. How do you find the slope of a line?
A fraction whose denominator is 100 i.e. 17% = 17/100
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
At least one of the factors is 0.
M = (y2 - y1)/(x2 - x1)

27. How do we write the equation of a line?
0 is the only number that is neither positive nor negative.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.

28. How do you calculate a weighted average?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

29. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Write the percent as a decimal - and multiply.
Shifted left 2 units.
All positive and negative whole numbers - and zero.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

30. How do you find the x-intercept of a graph?
V = lwh
360°
Set y = 0 - and solve.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

31. What is the square root of a number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

32. If the product of two or more numbers is 0 - what do you know about the numbers?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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°.
At least one of the factors is 0.
360°

33. Important binomial 1
Write the percent over 100 and reduce.
(x + y)(x - y) = x^2 - y^2
A = [(s^2*v3)/4]
Shifted up 2 units.

34. What is a Venn diagram?
A fraction whose denominator is 100 i.e. 17% = 17/100
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(b^m)^n = b^mn
D = 2r

35. What is the distributive law?
Shifted left 2 units.
In the expression x^b - x is the base and b is the exponent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number n: x^-n means 1/x^n.

36. What is the sum of the measures of the n angles of a polygon with n sides?
Write the percent over 100 and reduce.
(n - 2)(180°)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°

37. Law of exponents 2
The product of their slopes is -1 (negative reciprocal).
For any right triangle - a^2 + b^2 = c^2.
For any number n: x^-n means 1/x^n.
B^m/b^n = b^m-n

38. Law of exponents 3
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)^n = b^mn
180°. If two or more angles form a straight angle - their sum is 180°.
360°

39. Properties of zero 2
At least one of the factors is 0.
Then the quotient y/x is a constant.
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)

40. What is a ratio?

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

41. What is an even and an odd number?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Even numbers are divisible by 2 and odd numbers are not.
1 is a divisor (or factor) of every integer.
They are both the same. A divisor or factor of an integer leaves no remainder.

42. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
A = lw
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
At least one of the factors is 0.

43. What is true about the measures of the three angles in a triangle?
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°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 180°.
D = 2r

44. What formula is used for an average?
An angle formed by extending the side of the polygon.
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.
Avg = sum of n numbers/n

45. What is the formula for the volume of a rectangular solid?
The two pairs of opposite angles formed are equal to each other.
B^m/b^n = b^m-n
V = lwh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

46. 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.
A = 2(lw + lh + hw)
A = pr^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

47. What is a prime number?
A^m*b^m = (ab)^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.
Shifted right 2 units.
A = 6(l^2)

48. Law of exponents 5
Equal slopes.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A^m/b^m = (a/b)^m
For any integer n: 1^n = 1.

49. What is true about the slopes of perpendicular lines?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

50. What is the measure of a straight angle?
No matter how many angles there are - the sum around the point is 360°.
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m
180°. If two or more angles form a straight angle - their sum is 180°.