2016 December(74H) Math Question 1

Choice C

The number of members who are not officers is 32-5=27.

Luis is one of the 27 members who are not officers. Therefore the probability that he will be chosen is$$\frac{1}{27}$$.

2016 December(74H) Math Question 2

Choice K

Since the two triangles are congruent. The following must be true: $$\angle A\cong\angle D\\$$ $$\angle B\cong\angle E \\$$ $$\angle C\cong\angle F\\$$ $$\overline{AB}\cong\overline{DE}\\$$ $$\overline{BC}\cong\overline{EF}\\$$ $$\overline{AC}\cong\overline{DF}$$

2016 December(74H) Math Question 3

Choice C

$$\angle BCD+\angle BCA = 180°$$ $$\Rightarrow\angle BCA=180°-100°=80°$$ $$\angle CAB+\angle ABC+\angle BCA=180°$$ $$\Rightarrow 65°+X°+80°=180°$$ $$\Rightarrow X°=35°$$

2016 December(74H) Math Question 4

Choice J

The area where 8 falls into is an overlap of rap and rock.

2016 December(74H) Math Question 5

Choice E

\begin{align} 2|2-9|-3(4+2) & = 2|-7|-3(6) \\ & = 2\cdot7-3\cdot6 \\ & = 14-18 \\ & = -4 \end{align}

2016 December(74H) Math Question 6

Choice G

\left\{ \begin{aligned} -2x+y &=2 \\ x+y&=5 \end{aligned} \right. \ \ \Rightarrow\ \ \left\{ \begin{aligned} x &=1 \\ y&=4 \end{aligned} \right. \ \ \Rightarrow\ \ Point \ of\ intersection\ is\ (1,4)

2016 December(74H) Math Question 7

Choice E

$$\frac{x}{4\frac{1}{2}}=\frac{10}{\frac{1}{2}}$$ $$\Rightarrow x=90$$

2016 December(74H) Math Question 8

Choice H

$$Cost=1.05+0.15\times(15-1)=3.15$$

2016 December(74H) Math Question 9

Choice C

$$Assessed\ value=56,000 \times \frac{3}{4}=42,000\\$$ $$\Rightarrow Yearly\ tax=3 \times\frac{42,000}{100}=1,260$$

2016 December(74H) Math Question 10

Choice K

The probability is $$\frac{4+8}{20}=\frac{3}{5}$$

2016 December(74H) Math Question 11

- Cost

Choice C

Let the number of month be m. $$75+65\cdot m=495\\ \Rightarrow m = 6.46\approx7$$

2016 December(74H) Math Question 12

Choice F

$$Slope\ of\ \overleftrightarrow{HM} = \frac{y_2-y_1}{x_2-x_1} =\frac{-4-2}{2-(-2)} =\frac{-6}{4}=-\frac{3}{2}$$

2016 December(74H) Math Question 13

Choice B

The questions asks what the ( ? ) should be in: $$45x^2+26x-8=(5x+4)(\quad?\quad)$$ To solve for the ( ? ), we need to perform the following: $$\begin{pmatrix}5&4\\\color{red}{\frac{45}{5}}&\color{red}{\frac{-8}{4}}\\ \end{pmatrix} \Rightarrow \begin{pmatrix}5&4\\\color{red}{9}&\color{red}{-2}\\ \end{pmatrix}\\$$ $$\Rightarrow (\quad?\quad) = (9x-2)$$

2016 December(74H) Math Question 14

Choice H

We know that $$sin^2x\ + cos^2x=1\\$$ $$\Rightarrow cos^2x=1-sin^2x=1-\frac{4}{13}=\frac{9}{13}$$

2016 December(74H) Math Question 15

Choice E

Let each side of small squares be k:

Area of rectangle region = $$6k\cdot8k=1\Rightarrow k^2=\frac{1}{6\cdot8}$$

Therefore, area of shaded region = $$7k\cdot5k = 7\cdot5\cdot k^2=\frac{7\cdot5}{8\cdot6}$$

2016 December(74H) Math Question 16

Choice J

It is given that $$\overline{AB} \cong \overline{AC}$$, thus $$\angle B =\angle C$$.

Because $$\angle A+\angle B +\angle C = 180^\circ;\ \angle A=48^\circ$$, we have: $$\angle C = \frac{180^\circ-48^\circ}{2}=66^\circ$$

2016 December(74H) Math Question 17

Choice B

It is given that $$a_5=39$$. All you need to do is plug in 6 for n: \begin{align} a_6 & =a_5+(6-1)^2\\ &=39+25\\ &=64 \end{align}

2016 December(74H) Math Question 18

Choice G

Because the line is parallel to the line represented by y = -2x - 4, the line has the same slope -2. Thus we can write the line as: $$y = -2x + b$$ Because the line passes through (0,7): $$7=-2\cdot0 +b\\$$ $$\Rightarrow b=7\\$$ Therefore, the line is: $$y = -2x + 7$$

2016 December(74H) Math Question 19

Choice D

The bedroom floor can be seen as being consisting of one rectangle and a square with lengths as below: Thus the area is $$5\times5+6\times9=79$$. The number of tiles needed is $$\frac{79\ ft^2}{1 \ ft^2}=79$$

2016 December(74H) Math Question 20

Choice F

We are told that the survey accurately predict how the 1,200 resident would respond: $$\require{cancel}\frac {x}{1200}=\frac {12}{60}\\$$ $$\Rightarrow x=\frac {12\times\cancel{1200}20}{\cancel{60}}=240$$

2016 December(74H) Math Question 21

Choice A

We are told that the …

Choice G

2016 December(74H) Math Question 58

Choice F

To make f(x) as small …

2016 December(74H) Math Question 59

Choice A

You don’t have to compute …

2016 December(74H) Math Question 60

Choice K

The coordinates of the center …