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Test your basic knowledge |
GRE Math: Facts
Start Test
Study First
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 are the properties of a square?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any number n: x^-n means 1/x^n.
Arc = (x°/360)(2pr) where x is the central angle.
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.
2. What are the important properties of 30-60-90 triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Is a right triangle with a ratio of sides x:xv3:2x.
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
3. What is an integer?
Shifted up 2 units.
Shifted left 2 units.
All positive and negative whole numbers - and zero.
1 is the smallest positive odd integer.
4. How do you convert a percent to a fraction or a decimal?
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Write the percent over 100 and reduce.
180°. If two or more angles form a straight angle - their sum is 180°.
5. 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 over 100 and reduce.
Their sum is 180°.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
6. What is a Venn diagram?
A = (1/2)bh.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted right 2 units.
For any number a: a * 1 = a and a / 1 = a.
7. What is the formula for the area of a parallelogram?
A = 6(l^2)
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
Cannot is 0 - must is 1 - all others are in between.
8. What is a negative exponent?
0 is the only number that is neither positive nor negative.
(x + y)(x - y) = x^2 - y^2
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.
9. What are the important properties of a 45-45 - 90 triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
They are both the same. A divisor or factor of an integer leaves no remainder.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
10. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The set of all ordered pairs (x -y) such that y = f(x).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
11. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
The product of their slopes is -1 (negative reciprocal).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Equal slopes.
12. What is the midpoint formula?
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.
360°
[(x1 + x2)/2] -[(y1 + y2)/2]
The product of their slopes is -1 (negative reciprocal).
13. 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.
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.
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
14. What is the Pythagorean theorem?
Shifted down 2 units.
A = 2(lw + lh + hw)
Equal slopes.
For any right triangle - a^2 + b^2 = c^2.
15. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Avg = sum of n numbers/n
16. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.
A = 2(lw + lh + hw)
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
17. What is the formula for the surface area of a cube?
Their sum is 90°.
At least one of the factors is 0.
Shifted right 2 units.
A = 6(l^2)
18. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.
Write the percent over 100 and reduce.
19. What is a percent?
360°
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)(x - y) = x^2 - y^2
20. 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
V = l^3
A = 2(lw + lh + hw)
21. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
Shifted up 2 units.
Avg = sum of n numbers/n
Their sum is 180°.
22. What is an exponent?
Cannot is 0 - must is 1 - all others are in between.
A = 2(lw + lh + hw)
Write the percent as a decimal - and multiply.
In the expression x^b - x is the base and b is the exponent.
23. What are the properties of a rectangle?
B^m/b^n = b^m-n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
24. What is the ratio of similitude?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Arc = (x°/360)(2pr) where x is the central angle.
The ratio of corresponding sides of similar triangles.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
25. Properties of square roots
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = bh
26. What are the sum - difference - products - and quotient of two numbers?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(b^m)^n = b^mn
Write the percent over 100 and reduce.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
27. In a circle of radius r - what is the formula for the area?
M = (y2 - y1)/(x2 - x1)
A = pr^2
For any number a: a * 1 = a and a / 1 = a.
A^m*b^m = (ab)^m
28. Important binomial 3
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
29. Properties of zero 3
360°
0 is a multiple 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.
They are both the same. A divisor or factor of an integer leaves no remainder.
30. What is an exterior angle of a polygon?
In the expression x^b - x is the base and b is the exponent.
Arc = (x°/360)(2pr) where x is the central angle.
A = pr^2
An angle formed by extending the side of the polygon.
31. What is true about the measures of the two acute angles in a right triangle?
Then the product xy is a constant.
Their sum is 90°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = 2(lw + lh + hw)
32. Properties of zero 4
For any number n: x^-n means 1/x^n.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
An equation that states that two ratios are equivalent. 4/6 = 10/15
No matter how many angles there are - the sum around the point is 360°.
33. What is the formula for the volume of a rectangular solid?
A = pr^2
At least one of the factors is 0.
V = lwh
Write the percent over 100 and reduce.
34. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
35. What is the formula for the area of a rectangle?
(Circumference/diameter) of a circle - or approximately 3.14.
A^m/b^m = (a/b)^m
A = lw
(n - 2)(180°)
36. Law of exponents 3
(b^m)^n = b^mn
No matter how many angles there are - the sum around the point is 360°.
Write the percent as a decimal - and multiply.
A fraction whose denominator is 100 i.e. 17% = 17/100
37. What formula is used for an average?
B^m*b^n = b^m+n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
38. What is the volume of a cube?
The two pairs of opposite angles formed are equal to each other.
V = l^3
Set y = 0 - and solve.
All positive and negative whole numbers - and zero.
39. Important binomial 1
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
If a is negative and b is positive - then a < 0 < b.
(x + y)(x - y) = x^2 - y^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
40. What does it mean if y is inversely proportional to x?
Write the percent as a decimal - and multiply.
Shifted down 2 units.
Then the product xy is a constant.
A = 6(l^2)
41. How do you calculate percent increases and decreases?
Cannot is 0 - must is 1 - all others are in between.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m
42. If you were given the graph of y = f(x) - what does f(a) represent?
V = l^3
Then the quotient y/x is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A^m/b^m = (a/b)^m
43. How do we write the equation of a line?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the quotient y/x is a constant.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = pr^2
44. What is true about the slopes of perpendicular lines?
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)
45. What is a proportion?
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Shifted up 2 units.
46. What is a composite number?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An integer greater than one that is not prime.
(Circumference/diameter) of a circle - or approximately 3.14.
M = (y2 - y1)/(x2 - x1)
47. Properties of one 2
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
48. What is the distributive law?
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The ratio of corresponding sides of similar triangles.
49. What is the formula for the volume of a cylinder?
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn
V = pr^2h
How steep the line is. Horizontal line = 0 - vertical has no slope.
50. How you convert a fraction or a decimal to a percent?
B^m*b^n = b^m+n
Divide - then multiply by 100.
Cannot is 0 - must is 1 - all others are in between.
V = l^3