Mathematics Knowledge

Question 1

If 48 is divided by 0.08, the result is

A. 0.06
B. 0.6
C. 60
D. 600

Answer 1

D. 600

A question like this one tests your ability to work with decimals. 48/0.08 is the same as 4,800/8 = 600. D is correct. When dividing by a decimal, be sure to move the decimal place the same number of spaces for both numbers.

Question 2

If the number 9,899,399 is increased by 2,082, the result will be

A. 9,901,481
B. 9,901,471
C. 9,902,481
D. 9,902,471

Answer 2

A. 9,901,481

Be careful with your number crunching here. 9,899,399 + 2,082 = 9,901,481, choice A.

Question 3

The cube of 9 is

A. 27
B. 81
C. 243
D. 729

Answer 3

D. 729

The cube of a number is that number multiplied by itself three times. So the cube of 9 would be 9 x 9 x 9 = 729, choice D.

Question 4

What is the value of (-ab)(a) when a = -2 and b = 3?

A. -12
B. -6
C. 6
D. 12

Answer 4

A. -12

Plug in the values for a and b and remember your order of operations when working through your calculations. When a = -2 and b = 3,

(-ab)(a) = -(-2) x 3
= (-[-6])(-2)
= (6) x (-2) = -12, choice A

Question 5

(x-4)(x-4) =

A. x^2 + 8x - 16
B. x^2 - 8x - 16
C. x^2 - 8x +16
D. x^2 - 16x + 8

Answer 5

C. x^2 - 8x + 16

This is a classic product of two binomials. Remember to FOIL, and you’re good to go.

(x-4)(x-4) = (x)(x) + (x)(-4) + (-4)(x) + (-4)(-4)
= x^2 - 4x - 4x + 16
= x^2 - 8x + 16

Choice C is correct. If you recognized this as one of the classic quadratics, a binomial squared, you could have answered this correctly without using FOIL.

Question 6

0.123 x 10^4 =

A. .0000123
B. .00123
C. 1.23
D. 1,230

Answer 6

D. 1,230

10^4 = 10,000, indicating that you should move the decimal four places to the right.

So 0.123 x 10^4 = 0.123 x 10,000 = 1,230, choice D.

Question 7

√100 - √64 =

A. 2
B. 4
C. 6
D. 8

Answer 7

A. 2

Know your perfect squares. √100=10 and √64=8. So √100 - √64 = 10 - 8, choice A.

Question 8

A circle has a diameter of 6, an area of b square units, and a circumference of c units. What is the value of b + c?

A. 9π
B. 15π
C. 18π
D. 42π

Answer 8

B. 15π

Given a diameter of 6, the radius must equal 1/2 of 6, or 3. Next, the circumference (c) = 2πr = 2π(3) =6π. The area (b) = πr^2 = π(3^2 ) =9π. Add those two: 9π + 6π = 15π.

Question 9

A bag contains 8 white, 4 red, 7 green, and 5 blue marbles. Eight marbles are withdrawn at random. How many of the withdrawn marbles are white if the chance of drawing a white marble is now 1 in 4?

A. 3
B. 4
C. 5
D. 6

Answer 9

B. 4

To find the probability of something occurring, divide the number of desired outcomes by the number of total outcomes. In the example of the bag of marbles, you begin with 8 + 4 + 7 + 5 = 24 marbles, and draw out 8, leaving you with 16 marbles. Out of those 16 marbles, 4 must be white since the chance of drawing a white marble is now 4/16 or 1/4. If you are left with 4 white marbles, you must have already withdrawn 4 white marbles. B is correct.

Question 10

Liza has 40 fewer than 3 times the number of books that Janice has. If B is equal to the number of books that Janice has, which of the following expressions shows the number of books that Liza and Janice have together?

A. 3B - 40
B. 3B + 40
C. 4B - 40
D. 4B + 40

Answer 10

C. 4B - 40

If B is equal to the number of books that Janice has, and you know that Liza has 40 fewer than 3 times the number of books that Janice, Liza has 3B - 40 books, and Janice has B books. Together they have 4B - 40 books, choice C.

Question 11

If the perimeter of a square is 32 meters, then what is the area of the square, in square meters?

A. 16
B. 32
C. 48
D. 64

Answer 11

D. 64

The perimeter of a square is 4s where s is the length of a side. If a square has a perimeter of 32, then it has a side length of 8. The area of the square is s^2 = 8^2 = 64, choice D.

Question 12

If x ≠ 0, then (6x^6)/(2x^2) =

A. 4x^4
B. 4x^3
C. 3x^4
D. 3x^3

Answer 12

C. 3x^4

You can simplify this expression as follows:

(6x^2)/(2x^2) = (6)(x^6)/(2)(x^2) = 3x^4

Remember to subtract exponents when dividing.

Question 13

A number is considered “blue” if the sum of its digits is equal to the product of its digits. Which of the following is “blue”?

A. 111
B. 220
C. 321
D. 422

Answer 13

C. 321

Go through the answer choices one at a time, and select the choice whose digits have a sum and product that are equal.

A. 111 Product = (1)(1)(1) = 1 Sum = 1 + 1 + 1 = 3 Eliminate

B. 220 Product = (2)(2)(0) = 0 Sum = 2 + 2 + 0 = 4 Eliminate

C. 321 Product = (3)(2)(1) = 6 Sum = 3 + 2 + 1 = 6 Choice C is correct

Question 14

If x = 1/8, what is the value of y when 2/x = y/4?

A. 1/4
B. 4
C. 16
D. 64

Answer 14

D. 64

If x = 1/8, and we are asked to solve for y when 2/x = y/4, begin by plugging in 1/8 for x. (2)/(1/8) = y/4. Cross multiply and solve, (1/8)(y) = 8, so y = 64, D.

Question 15

If 3ab = 6, what is the value of a in terms of b?

A. 2/b
B. 2/b^2
C. 2b
D. 2b^2

Answer 15

A. 2/b

If you’re looking for a in terms of b, isolate the a on one side of the equation.

3ab = 6
ab = 2
a = 2/b

Question 16

For what value of y is 4(y - 1) = 2(y + 2)?

A. 0
B. 2
C. 4
D. 6

Answer 16

C. 4

Distribute the numbers outside the parentheses and solve for y.

4(y - 1) = 2(y + 2)
4y - 4 = 2y + 4
2y = 8
y = 4

Question 17

In a triangle RST, if RS = RT, what is the degree measure of angle S if angle R measures 70 degrees?

A. 40
B. 55
C. 70
D. cannot be determined from the information given

Answer 17

B. 55

Since RS and RT are equal, the angles opposite them must be equal. Therefore, angle T = angle S. Since the degree measures of the three interior angles of a triangle sum to 180, 70 + angle measure S + angle measure T = 180, and angle measure S + angle measure T = 110. Since the two angles, S and T, are equal, each must have angle measures half of 110, or 55.

Question 18

When D is divided by 15, the result is 6 with a remainder of 2. What is the remainder when D is divided by 6?

A. 0
B. 2
C. 3
D. 4

Answer 18

B. 2

When D is divided by 15, the result is 6 with a remainder of 2. That means that D = 6(15) + 2 or 92. When 92 is divided by 6, the remainder is 2. B is correct.

Question 19

If the average of 7 consecutive even numbers is 24, then the largest number is

A. 26
B. 28
C. 30
D. 34

Answer 19

C. 30

The average of 7 consecutive even numbers is 24. In a set of evenly spaced numbers, the median is the same as the average. That means that 24 must be the middle number of the set of numbers. So the set must be {18, 20, 22, 24, 26, 28, 30}. The largest number is 30, choice C.

Question 20

A box that has dimensions of 2 inches by 3 inches by 4 inches has a total surface area of

A. 24 square inches
B. 26 square inches
C. 48 square inches
D. 52 square inches

Answer 20

D. 52 square inches

The surface area of a rectangular solid is 2lw + 2lh + 2wh. In this case that would be (2 x 2 x 3) + (2 x 2 x 4) + (2 x 3 x 4) = 12 + 16 + 24 = 52 square inches, choice D.

Question 21

If 100/x = 10n, then which of the following is equal to nx?

A. 10
B. 10x
C. 100
D. 10xn

Answer 21

A. 10

If 100/x = 10n, then cross multiply to get 100 = 10nx. Divide both sides by 10 to solve for nx.

nx = 100/10 = 10. A is correct.

Question 22

A circle is divided into three central angles measuring (4x + 15) degrees, (2x - 5) degrees, and (6x - 10) degrees. What is the value of x?

A. 15
B. 30
C. 55
D. 70

Answer 22

B. 30

A circle contains 360 degrees, so:

(4x + 15) + (2x - 5) + (6x - 10) = 360
4x + 2x + 6x + 15 - 5 - 10 = 360
12x = 360
x = 30

Question 23

If 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1, then 5! =

A. 15
B. 75
C. 120
D. 125

Answer 23

C. 120

5! = 5 x 4 x 3 x 2 x 1 = 120

Question 24

Melissa took 5n photographs on a certain trip. If she gives n photographs to each of her 3 friends, how many photographs will she have left?

A. 2n
B. 3n
C. 4n - 3
D. 4n + 3

Answer 24

A. 2n

If Melissa has 5n photographs, and she gives n photographs to each of three friends, she would have given away 3n photographs. 5n - 3n = 2n. A is correct.