Math Knowledge

Question 1

Find the diagonal of a square whose area is 9.

Ⓐ. 1.5
Ⓑ. 3
Ⓒ. 3√2
Ⓓ. 9√2

Answer 1

Ⓒ. 3√2 (Note: all sides on a square are the same)

Solution:
Area of a Square = ℓ²
9 = ℓ²
(√9) = ℓ
3 = ℓ

c² = (a² + b²) = (3² + 3²) = (9 + 9) = 18
c = √18 = √9(2) = 3√2

Question 2

If 4 + x ≥ 13, what is the value of (x≥)?

Ⓐ. 9
Ⓑ. 17
Ⓒ. 17x
Ⓓ. 4x

Answer 2

Ⓐ. 9

Solution:
4 + x ≥ 13
x ≥ 13 - 4
x ≥ 9

Question 3

(n + 6)(n + 6) = ?

Ⓐ. n² - 36n - 36
Ⓑ. n² - 12n - 36
Ⓒ. n² + 12n + 36
Ⓓ. n² + 12n - 36

Answer 3

Ⓒ. n² + 12n + 36

Solution:
n + 6)(n + 6) = n(n + 6) + 6(n + 6
(n + 6)(n + 6) = n² + 6n + 6n + 36
(n + 6)(n + 6) = n² + 12n + 36

Question 4

17 is 8% of what number?

Ⓐ. 212.50
Ⓑ. 136
Ⓒ. 1.36
Ⓓ. 21.25

Answer 4

Ⓐ. 212.50

Solution:
17 = 8%
17/x = 8/100
8x = 1700
x = 1700/8
x = 212.50

Question 5

Which of the following is an acute angle?

Ⓐ. 109°
Ⓑ. 289°
Ⓒ. 19°
Ⓓ. 199°

Answer 5

Ⓒ. 19°

Solution:
Acute angle

Question 6

A circle has a diameter of 18 inches. What is its approximate circumference?

Ⓐ. 254.47
Ⓑ. 56.55
Ⓒ. 28.27
Ⓓ. 81.00

Answer 6

Ⓑ. 56.55

Solution:
∅ = 18"
Circumference = ∅π
Circumference = 18π
Circumference = 56.55"

Question 7

The square root of 64 is?

Ⓐ. √8
Ⓑ. 88
Ⓒ. 8
Ⓓ. 2√8

Answer 7

Ⓒ. 8

Solution:
√64 = 8

Proof:
8 • 8 = 64
8² = 64

Question 8

(n + 6)(n + 8)=?

Ⓐ. n² - 48n + 48
Ⓑ. n² + 48n - 48
Ⓒ. n² + 14n + 48
Ⓓ. n² - 48n - 48

Answer 8

Ⓒ. n² + 14n + 48

Solution:
n + 6)(n + 8) = n(n + 8) + 6(n + 8
(n + 6)(n + 8) = n² + 8n + 6n + 48
(n + 6)(n + 8) = n² + 14n + 48

Question 9

Which of the following pairs are supplementary angles?

Ⓐ. 34°, 56°
Ⓑ. 34°, -34°
Ⓒ. 79°, 101°
Ⓓ. 124°, 146°

Answer 9

Ⓒ. 79°, 101°

Solution:
Supplementary angle = 180°
79° + 101° = 180°

Question 10

What is the area of a triangle with dimensions:
Base = 13
Height = 6

Ⓐ. 39
Ⓑ. 156
Ⓒ. 78
Ⓓ. 19.5

Answer 10

Ⓐ. 39

Solution:
Area of a triangle = (1/2)bh
AΔ = (1/2)(13•6)
AΔ = (1/2)(78)
AΔ = 39

Question 11

Find the slope of the line running through the points (4, 5) and (3, 3).

Ⓐ. 2
Ⓑ. 1/2
Ⓒ. -2
Ⓓ. 1/-2

Answer 11

Ⓐ. 2

Solution:
( 4, 5), ( 3, 3)
(x₁,y₁), (x₂,y₂)
M = (y₂ - y₁)/(x₂ - x₁)
M = (3 - 5)/(3 - 4)
M = (-2)/(-1)
M = 2/1
M = 2

Question 12

Solve for 4! (the factorial of ‘4’)

Ⓐ. 16
Ⓑ. 44
Ⓒ. 120
Ⓓ. 24

Answer 12

Ⓓ. 24

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Solution:
the factorial symbol is an exclamation point
4! = 24
4 • 3 • 2 • 1 = 24
12 • 2 • 1 = 24
24 • 1 = 24
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Question 13

A circle has a diameter of 2”. What is its approximate area?

Ⓐ. 3.24
Ⓑ. 1.57
Ⓒ. 9.87
Ⓓ. 3.14

Answer 13

Ⓓ. 3.14 (Note: π ≈ 3.14)

Solution:
r = d/2 = 2/2 = 1
Area of a Circle = πr²
AO = πr²
AO = (3.14)(1²)
AO = (3.14)(1)
AO = 3.14"