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Test your basic knowledge |
GRE Math: All In One
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. a(b+c)
Ab+ac
3/2 - 5/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90°
2. What are complementary angles?
Two angles whose sum is 90.
Triangles with same measure and same side lengths.
x²+2xy+y²
12! / 5!7! = 792
3. Ø is a multiple of
1 & 37/132
Two (Ø×2=Ø)
53 - 59
Ø
4. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
90
2 & 3/7
53 - 59
Even
5. What is a subset?
A grouping of the members within a set based on a shared characteristic.
A subset.
x^(2(4)) =x^8 = (x^4)^2
61 - 67
6. Pi is a ratio of what to what?
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7. Pythagorean theorem
A²+b²=c²
The steeper the slope.
x²-2xy+y²
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
8. A number is divisible by 6 if...
Its divisible by 2 and by 3.
Right
x^(4+7) = x^11
Straight Angle
9. (x-y)²
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
x²-2xy+y²
The second graph is less steep.
... the square of the ratios of the corresponding sides.
10. If a lamp increases from $80 to $100 - what is the percent increase?
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Right
x²-y²
11. 5/8 in percent?
12! / 5!7! = 792
Move the decimal point to the right x places
62.5%
Be Zero!
12. Write 10 -843 X 10^7 in scientific notation
1/x
1.0843 X 10^11
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
180
13. Ø is
A-b is negative
1.0843 X 10^11
... the square of the ratios of the corresponding sides.
A multiple of every integer
14. Time
(n-2) x 180
(distance)/(rate) d/r
x²-y²
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
15. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
(n-2) x 180
EVEN
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
16. 30 60 90
Yes - like radicals can be added/subtracted.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x - x(SR3) - 2x
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
17. Which is greater? 27^(-4) or 9^(-8)
(a + b)^2
Diameter(Pi)
3
27^(-4)
18. What is the order of operations?
Undefined
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
A-b is positive
x(x - y + 1)
19. How to find the circumference of a circle which circumscribes a square?
B?b?b (where b is used as a factor n times)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Undefined - because we can'T divide by 0.
A-b is positive
20. What is the side length of an equilateral triangle with altitude 6?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a - b)(a + b)
Infinite.
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
21. When dividing exponential #s with the same base - you do this to the exponents...
A<-b
Indeterminable.
12sqrt2
Subtract them. i.e (5^7)/(5^3)= 5^4
22. 1/8 in percent?
12.5%
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
67 - 71 - 73
(base*height) / 2
23. Define an 'expression'.
A natural number greater than 1 that has no positive divisors other than 1 and itself
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Sector area = (n/360) X (pi)r^2
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
24. 70 < all primes< 80
71 - 73 - 79
M= (Y1-Y2)/(X1-X2)
180
180°
25. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
61 - 67
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
P=4s (s=side)
26. x^2 = 9. What is the value of x?
Move the decimal point to the right x places
3 - -3
Smallest positive integer
Ø=P(E)=1
27. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
C = (pi)d
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Every number
28. To increase a number by x%
x²-y²
x²+2xy+y²
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
75:11
29. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
The objects within a set.
75:11
1 & 37/132
Can be negative - zero - or positive
30. 25^(1/2) or sqrt. 25 =
Ø
x(x - y + 1)
Reciprocal
5 OR -5
31. What is the slope of a vertical line?
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32. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
Positive
y2-y1/x2-x1
1
33. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
3
10! / 3!(10-3)! = 120
The two xes after factoring.
34. The reciprocal of any non-zero #x is
Subtract them. i.e (5^7)/(5^3)= 5^4
1/x
Two (Ø×2=Ø)
3
35. How to determine percent decrease?
Cd
72
2.592 kg
(amount of decrease/original price) x 100%
36. -3³
(amount of decrease/original price) x 100%
4725
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
27
37. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
x - x(SR3) - 2x
Two (Ø×2=Ø)
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
1
38. What is the 'Solution' for a system of linear equations?
$11 -448
The point of intersection of the systems.
The objects within a set.
x²+2xy+y²
39. 10^6 has how many zeroes?
F(x) + c
The set of elements found in both A and B.
6
x^(2(4)) =x^8 = (x^4)^2
40. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
x²-y²
An isosceles right triangle.
P(E) = number of favorable outcomes/total number of possible outcomes
N! / (n-k)!
41. Reduce: 4.8 : 0.8 : 1.6
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
(distance)/(rate) d/r
Ø
6 : 1 : 2
42. Ø Is neither
Positive or Negative
13
Right
1:1:sqrt2
43. If Event is impossible
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Ø Ø=Ø
P(E) = ø
130pi
44. For any number x
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)
Can be negative - zero - or positive
180
The set of elements found in both A and B.
45. How many multiples does a given number have?
(a + b)^2
Infinite.
$11 -448
x - x+1 - x+2
46. One is (a prime or not?)
The direction of the inequality is reversed.
x^(2(4)) =x^8 = (x^4)^2
NOT A PRIME
4.25 - 6 - 22
47. 1/Ø=null If a>b then
(length)(width)(height)
P(E) = 1/1 = 1
A<-b
All numbers multiples of 1.
48. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
y = 2x^2 - 3
$3 -500 in the 9% and $2 -500 in the 7%.
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
49. Define a 'Term' -
A = pi(r^2)
0
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
x²-2xy+y²
50. 1/6 in percent?
9
16.6666%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
27^(-4)