# 2011 April(67F) Math Question 1

Choice D

$$6\times10=60$$ $$60\div(6-1)=12$$

# 2011 April(67F) Math Question 2

- Cost

Choice G

$$58.95\times0.8=47.16$$

# 2011 April(67F) Math Question 3

Choice C

$$30:44=70:x$$ $$44\times70=30x$$ $$x=102.66$$

# 2011 April(67F) Math Question 4

Choice F

$$(5+2-(-3)(2+(-3))$$ $$=(5+2+3)(2-3)$$ $$=(10)(-1)$$ $$=-10$$

# 2011 April(67F) Math Question 5

Choice A

To maximize the value of x, you must minimize the value of

$$y^{2}$$ $$y^{2}=0,\ x^{2}=256$$ $$x=\pm\sqrt{256}=\pm16$$

The positive 16 is the answer.

# 2011 April(67F) Math Question 6

Choice J

If Antoine rode the roller coaster, he must be more than 4 feet tall.

# 2011 April(67F) Math Question 7

Choice C

$$N(4)=\frac{1200\times4^{2}+10}{4^{2}+1}$$ $$=\frac{1200\times16+10}{16+1}$$ $$=\frac{19200}{17}$$ $$\approx 1130$$

# 2011 April(67F) Math Question 8

Choice J

$$3x^{5}\cdot7x^{9}=(3\cdot7)(x^{5}\cdot x^{9})$$ $$=21x^{14}$$

# 2011 April(67F) Math Question 9

Choice B

$$\frac{3}{5+4+3}=\frac{3}{12}=\frac{1}{4}$$

# 2011 April(67F) Math Question 10

Choice G

$$35=5\times7$$ $$56=2^{3}\times7$$ $$16=2^{4}$$ $$\Rightarrow2^{4}\times5\times7=16\times5\times7=560$$

# 2011 April(67F) Math Question 11

Choice B

Because triangles ABC and DEC are congruent,

$$\angle CAB=\angle CDE$$ $$\angle CDE= 180° – 45° – 70° = 65°$$

# 2011 April(67F) Math Question 12

Choice F

$$=\frac{\frac{57}{7}}{\frac{15}{14}}$$ $$=\frac{57}{7}\times\frac{14}{15}$$ $$=\frac{114}{15}$$ $$=\frac{38}{5}$$

# 2011 April(67F) Math Question 13

Choice D

$$x + y = 15 ---(1)$$ $$x – y = 9---(2)$$ $$(1)+(2)$$ $$2x=24$$ $$x=12$$ $$y=3$$ $$xy=12(3)=36$$

# 2011 April(67F) Math Question 14

Choice J

1. Draw A as a point on a circle.

2. Draw B 6 units counterclockwise from A.

3. Draw C 2 units clockwise from point A, between A and B in the clockwise direction.

4. Draw D 9 units clockwise from A, between C and B in the clockwise direction.

Now your points are in the correct order, A, C, B, D in the clockwise direction.

# 2011 April(67F) Math Question 15

Choice D

$$\frac{(83 + 88 + 92 + 99)}{4}=90.5$$

# 2011 April(67F) Math Question 16

Choice K

$$Slope-intercept (y = mx + b) form$$ $$6x – 2 = y \Rightarrow y = 6x – 2$$

# 2011 April(67F) Math Question 17

Choice B

$$\Rightarrow (x – 7)(x + 4) = 0$$ $$x=7,-4$$ $$7+(-4)=3$$

# 2011 April(67F) Math Question 18

Choice G

$$=\mid-20+18\mid=\mid-2\mid=2$$

# 2011 April(67F) Math Question 19

Choice C

$$\frac{3}{8}=0.375$$ $$\frac{5}{16}=0.3125$$ $$\frac{11}{32}=0.34375$$

# 2011 April(67F) Math Question 20

Choice K

$$Slope=\frac{(y2 – y1)}{(x2 – x1)}$$ $$=\frac{10-8}{-2-3}$$ $$=\frac{2}{-5}$$

Choice E

# 2011 April(67F) Math Question 28

Choice G

B is 10 blocks east …

# 2011 April(67F) Math Question 29

Choice E

$$b=6c \Rightarrow c=\frac{1}{6}b$$ $$a=2c=2(\frac{1}{6}b)=\frac{1}{3}b$$

Choice J

# 2011 April(67F) Math Question 32

Choice J

$$6\times6\times5=180$$

# 2011 April(67F) Math Question 33

Choice E

The triangle is a 3-4-5 …

# 2011 April(67F) Math Question 34

Choice H

Shade any square whose reflection …

# 2011 April(67F) Math Question 35

Choice C

$$4x(x)=80$$ $$\Rightarrow 4x^{2}=80$$ $$\Rightarrow x=\sqrt{20}$$ …

# 2011 April(67F) Math Question 36

Choice K

The volume of this rectangular …

# 2011 April(67F) Math Question 37

Choice B

$$t = 10f – 20$$ …

# 2011 April(67F) Math Question 38

Choice G

$$Tangent=\frac{opposite}{adjacent}$$ $$\tan25°=\frac{x}{100}$$ $$x=100\tan25°=100\times0.47=47$$

# 2011 April(67F) Math Question 39

Choice E

3-4-5 triangle (6-8-10)

# 2011 April(67F) Math Question 40

Choice J

$$4^{3}=64$$ $$4\times3=12$$ $$12^{3}=1728$$

The volume …

# 2011 April(67F) Math Question 41

Choice E

$$(x-h)^{2}+(y-k)^{2}=r^{2}$$

Based on this equation, …

# 2011 April(67F) Math Question 42

Choice J

The perimeter of a rectangle …

# 2011 April(67F) Math Question 43

Choice A

There are 2 possible vertical …

# 2011 April(67F) Math Question 44

Choice F

The current area of the …

# 2011 April(67F) Math Question 45

Choice E

Compared to y = cos …

# 2011 April(67F) Math Question 46

Choice K

$$0\lt p\lt q$$

(F)\ 0\lt …

# 2011 April(67F) Math Question 47

Choice D

$$a=b\times0.25$$ $$\frac{b\times1.35}{b\times0.25}=\frac{1.35}{0.25}=5.4$$

# 2011 April(67F) Math Question 48

Choice H

$$\sin^{2}\theta+\cos^{2}\theta-4$$ $$=1-4$$ $$=-3$$

# 2011 April(67F) Math Question 49

Choice E

Therefore, the line of reflection …

# 2011 April(67F) Math Question 50

Choice H

$$\frac{x}{144°}=\frac{60}{360°}$$ $$x=144\times\frac{60}{360}=24$$

# 2011 April(67F) Math Question 51

Choice B

The plane section of such …

# 2011 April(67F) Math Question 52

Choice F

$$\log x=y \Rightarrow a^{y}=x$$ $$b^{4}=81$$ …

Choice D

f(x + a) + b …

# 2011 April(67F) Math Question 54

Choice F

Based on parallel line properties， …

# 2011 April(67F) Math Question 55

Choice D

To maximize the value of P(x,y), you must maximize the value of 4x + 3y.

At point B, P(x,y) = 4 • 0 + 3 • 4 = 12.

At point C, P(x,y) =4 • 4 + 3 • 0 = 16.

The value of P(x,y) is higher at point C then at point B and points B and C are connected by a straight line delineating an edge of the shaded region, no other points along this line or anywhere else in the shaded region can have a higher value than point C.

# 2011 April(67F) Math Question 56

Choice F

(F) Look at the graph of P(x,y) above question 55 and compare it to the graph in 56 that labels the quadrants. P(x,y) contains points in quadrants I and II only.

# 2011 April(67F) Math Question 57

Choice A

Tangent is defined as opposite/adjacent. …

# 2011 April(67F) Math Question 58

Choice K

If f(x)=0 when x=3, (x …

# 2011 April(67F) Math Question 59

Choice C

$$\frac{5}{1000000}=5\cdot 10^{-6}$$

# 2011 April(67F) Math Question 60

- FOIL

Choice F

$$(a^{2}-b^{2})=(a+b)(a-b)$$ (a – b)\gt (a …