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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. Which is greater? 64^5 or 16^8
3
An expression with just one term (-6x - 2a^2)
13
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
2. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
F(x) - c
5
A chord is a line segment joining two points on a circle.
3. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
P(E) = 1/1 = 1
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
48
(x+y)(x-y)
4. Can you simplify sqrt72?
The shortest arc between points A and B on a circle'S diameter.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x(x - y + 1)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
5. 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
(b + c)
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...
9
6. What is the intersection of A and B?
The set of elements found in both A and B.
90
The objects within a set.
True
7. The product of any number x and its reciprocal
The empty set - denoted by a circle with a diagonal through it.
90°
D/t (distance)/(time)
1
8. How to recognize if a # is a multiple of 12
28
The interesection of A and B.
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
Its divisible by 2 and by 3.
9. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
x²+2xy+y²
x²-y²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
True
10. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
2(pi)r
62.5%
11. Slope given 2 points
M= (Y1-Y2)/(X1-X2)
20.5
Pi(diameter)
An angle which is supplementary to an interior angle.
12. If a is inversely porportional to b - what does it equal?
The interesection of A and B.
A subset.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Ab=k (k is a constant)
13. X is the opposite of
X
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The sum of its digits is divisible by 3.
2²
14. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
1 & 37/132
Distance=rate×time or d=rt
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
M= (Y1-Y2)/(X1-X2)
15. factored binomial product of (x+y)²
A subset.
x²+2xy+y²
12sqrt2
P=4s (s=side)
16. a<b then a - b is positive or negative?
A+c<b+c
A-b is negative
Every number
11 - 13 - 17 - 19
17. binomial product of (x+y)(x-y)
An arc is a portion of a circumference of a circle.
A set with no members - denoted by a circle with a diagonal through it.
x²-y²
130pi
18. How many multiples does a given number have?
Undefined - because we can'T divide by 0.
A+c<b+c
Infinite.
Every number
19. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
90°
Pi is the ratio of a circle'S circumference to its diameter.
3
2sqrt6
20. Rate
(2x7)³
A tangent is a line that only touches one point on the circumference of a circle.
y/x is a constant
D/t (distance)/(time)
21. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
x(x - y + 1)
2.592 kg
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
3x - 4x - 5x
22. How to recognize a multiple of 6
The set of output values for a function.
13pi / 2
1/a^6
Sum of digits is a multiple of 3 and the last digit is even.
23. Find distance when given time and rate
D=rt so r= d/t and t=d/r
61 - 67
x²+2xy+y²
1
24. a(b+c)
Ab+ac
... the square of the ratios of the corresponding sides.
P=4s (s=side)
Lies opposite the greater angle
25. If a product of two numbers is Ø - one number must be
D=rt so r= d/t and t=d/r
P= 2L + 2w
F(x-c)
Ø
26. 30 60 90
12! / 5!7! = 792
1
x - x(SR3) - 2x
6
27. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
ODD number
Ø=P(E)=1
$11 -448
F(x) + c
28. x^4 + x^7 =
9 : 25
48
F(x-c)
x^(4+7) = x^11
29. What is the maximum value for the function g(x) = (-2x^2) -1?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
2²
Ø
1
30. 2 is the only
67 - 71 - 73
Even prime number
F(x-c)
A=pi*(r^2)
31. Probability of Event all cases
An expression with just one term (-6x - 2a^2)
Ø=P(E)=1
52
ODD number
32. The reciprocal of any non-zero number is
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
6 : 1 : 2
41 - 43 - 47
1/x
33. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Two equal sides and two equal angles.
31 - 37
180
34. The objects in a set are called two names:
V=l×w×h
x²-2xy+y²
Members or elements
C = (pi)d
35. factored binomial product of (x-y)²
2 & 3/7
The direction of the inequality is reversed.
x²-2xy+y²
1 - P(E)
36. Evaluate 3& 2/7 / 1/3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
3
Move the decimal point to the right x places
9 & 6/7
37. A prime number (or a prime)
A natural number greater than 1 that has no positive divisors other than 1 and itself
Its last two digits are divisible by 4.
D/t (distance)/(time)
An isosceles right triangle.
38. Acute Angle
A multiple of every integer
an angle that is less than 90°
31 - 37
A natural number greater than 1 that has no positive divisors other than 1 and itself
39. How to recognize a # as a multiple of 4
The set of output values for a function.
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.)
Ab=k (k is a constant)
Two angles whose sum is 90.
40. -3²
9
P(E) = ø
V=Lwh
A=pi*(r^2)
41. Write 10 -843 X 10^7 in scientific notation
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1.0843 X 10^11
(base*height) / 2
130pi
42. The ratio of the areas of two similar polygons is ...
9
2sqrt6
12.5%
... the square of the ratios of the corresponding sides.
43. The larger the absolute value of the slope...
Do not have slopes!
The steeper the slope.
26
31 - 37
44. ز
52
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Ø
288 (8 9 4)
45. The Perimeter of a rectangle
P=2(l+w)
Ab+ac
y/x is a constant
A-b is negative
46. What is the ratio of the sides of an isosceles right triangle?
1
1:1:sqrt2
10
70
47. What are the members or elements of a set?
Diameter(Pi)
x^(4+7) = x^11
Be Zero!
The objects within a set.
48. 25^(1/2) or sqrt. 25 =
x²-2xy+y²
Members or elements
5 OR -5
1/x
49. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A grouping of the members within a set based on a shared characteristic.
A-b is positive
(amount of decrease/original price) x 100%
50. Factor a^2 + 2ab + b^2
Positive
5
Add them. i.e. (5^7) * (5^3) = 5^10
(a + b)^2