# 2014 June(72C) Math Question 1 Choice C

To calculate the mean of n numbers, take the sum of the n numbers and divide it by n. $$\frac{370+310+380+340+310}{5}=342$$

# 2014 June(72C) Math Question 2

- Cost Choice H

A discount is a percentage that is subtracted from a number.

For example, a 10% discount of $30 is$3 (10% converted to a decimal is .10 and .10 x 30 is 3).

$12 x 25% =$3

# 2014 June(72C) Math Question 3 Choice A

$$450 = c\cdot 10^3 \\$$ $$\Rightarrow x=0.45$$

# 2014 June(72C) Math Question 4

- Cost Choice H

% increase = Increase ÷ Original Number × 100

$12 × 106% =$12.72

# 2014 June(72C) Math Question 5 Choice E

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

The constant for the sequence in question is -3. Therefore the sequence is:

1, -3, 9, -27, 81, -243, 729, ...

# 2014 June(72C) Math Question 6 Choice K

A square root of a number a is a number y such that y^2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is a. $$\sqrt{a} = 36 \\ ⇒a = 36^2 = 1296$$

# 2014 June(72C) Math Question 7 Choice C

$10 +$0.65 × 15 = \$19.75

# 2014 June(72C) Math Question 8 Choice K

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

In descending order, the set of numbers is:

13, 15, 16, 19, 19, 22, 25, 25, 26, 27, 28, 29

Median = (22 + 25) / 2 = 23.5

# 2014 June(72C) Math Question 9 Choice C

A relationship of direct proportionality that, when plotted on a graph, traces a straight line. In linear relationships, any given change in an independent variable will always produce a corresponding change in the dependent variable.

Thus, d = at + k

14 = 0⋅a + k

20 = 1⋅a + k

k = 14

a = 6

d = 6t + 14

# 2014 June(72C) Math Question 10 Choice K

x = 5/24 - 5/8 = 5/24 - 15/24 = - 10/24 = - 5/12

# 2014 June(72C) Math Question 11 Choice A

The absolute value of a number is its distance from zero on a number line . For instance, and have the same absolute value (). So, the absolute value of a positive number is just the number itself, and the absolute value of a negative number is its opposite.

|-0.4|= 0.4

|-0.042| = 0.042

|-0.0048| = 0.0048

|0.04| = 0.04

|0.047| = 0.047

# 2014 June(72C) Math Question 12 Choice G The sum of measures of three angles of any triangle is invariably equal to 180°.

Vertical Angles are angles opposite each other when two lines cross. They are always equal.

∠A = 180° - 35° - 45° = 100°

# 2014 June(72C) Math Question 13 Choice B

Let the number of large figurines be L;

Let the number of small figurines be S;

L + S = 70

12⋅L = 8⋅S

L = 28, S= 42

# 2014 June(72C) Math Question 14 Choice K

√(2x) = 1+11 = 12

⇒ 2x = 144

⇒ x = 72

# 2014 June(72C) Math Question 15 Choice C

A circle has a total of 360 degrees all the way around the center.

So if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around.

$$\frac{4}{4+1+1+3}\times 360°= 160°$$

# 2014 June(72C) Math Question 16 Choice K

To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.

The perimeter of a rectangle is equal to the sum of all the sides. However, since a rectangle's opposite sides are congruent, we only need to know the length and width.

L × W = 32

L = 2W

⇒ W = 4, L = 8

⇒ Perimeter = (4 + 8) × 2 = 24

# 2014 June(72C) Math Question 17 Choice C

Given the final speed, vf (which is 220 fps), and the initial speed, vi (which is 88 fps), and you know the time needed (3 seconds), you can find the acceleration, a. Because vf – vi = a⋅t

vf – vi = a⋅t

⇒ 220 - 88 = 3a

⇒ a = 44

# 2014 June(72C) Math Question 18 Choice J

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 108

670,000,000 + 700,000,000 = 1,370,000,000 = 1.37 ✕ 109

# 2014 June(72C) Math Question 19 Choice D The angle measure of a straight line is 180 degrees.

# 2014 June(72C) Math Question 20 Choice H

Rule name Rule Example
Product rules a na m = a n+m 23 ⋅ 24 = 23+4 = 128
a nb n = (a b) n 32 ⋅ 42 = (3⋅4)2 = 144
Quotient rules a n / a m = a nm 25 / 23 = 25-3 = 4
a n / b n = (a / b) n 43 / 23 = (4/2)3 = 8
Power rules (bn)m = bn⋅m (23)2 = 23⋅2 = 64
bnm = b(nm) 232 = 2(32)= 512
m√(bn) = b n/m 2√(26) = 26/2 = 8
b1/n = nb 81/3 = 38 = 2
Negative exponents b-n = 1 / bn 2-3 = 1/23 = 0.125
Zero rules b0 = 1 50 = 1
0n = 0 , for n>0 05 = 0
One rules b1 = b 51 = 5
1n = 1 15 = 1
Minus one rule (-1)n = -1 , n odd v
(-1)n = 1 , n even
(-1)5 = -1
Derivative rule (xn) = nx n-1 (x3) = 3⋅x3-1
Integral rule xndx = xn+1/(n+1)+C x2dx = x2+1/(2+1)+C

$$\Rightarrow \frac{(3x)^2}{x^5}=\frac{9x^2}{x^5}=\frac{9}{x^{5-2}}=\frac{9}{x^{3}}$$

# 2014 June(72C) Math Question 21 Choice A

⇒ 4x - 2x = …

# 2014 June(72C) Math Question 22 Choice F

When parallel lines get crossed …

# 2014 June(72C) Math Question 23 Choice A

# 2014 June(72C) Math Question 55 Choice E

The square root must be …

# 2014 June(72C) Math Question 56 Choice F

It can be observed that …

# 2014 June(72C) Math Question 57 Choice E

The absolute value of a …

# 2014 June(72C) Math Question 58 Choice J

The smallest angle must be …

# 2014 June(72C) Math Question 59 Choice D

To reduce a fraction to …

# 2014 June(72C) Math Question 60 Choice J As we can see from …