Choice G
$$15=3\times5$$ $$6=2\times3$$ $$4=2\times2$$ $$2\times2\times3\times5=60$$
Choice E
$$\frac{1}{3}(\frac{5}{6}+\frac{1}{12}+\frac{1}{3})$$ $$=\frac{1}{3}(\frac{10}{12}+\frac{1}{12}+\frac{4}{12})$$ $$=\frac{1}{3}(\frac{15}{12})$$ $$=\frac{5}{12}$$
Choice G
$$50~100\Rightarrow 89,96$$ $$101~150\Rightarrow 103,104,106,113$$ $$151~200\Rightarrow 160,160,161$$
Choice K
$$160+1006+104+113+160+103+161+89+96=1092$$ $$\Rightarrow\frac{1092+x+y}{9+2}=\frac{1092+x+y}{11}$$
Choice B
$$\frac{3}{5}=\frac{8+r}{8+5+11+r}=\frac{8+r}{24+r}$$ $$3(24+r)=5(8+r)$$ $$72+3r=40+5r$$ $$32=2r$$ $$r=16$$
2012 December(71A) Math Question 22
Algebraic & Function Expressions
- Simplify Algebraic Expressions
Choice G
$$(5x^{3}-4x^{2}+7x-3)-(3x^{3}+4x^{2}-3x+1)$$ $$=2x^{3}-8x^{2}+10x-4$$
Choice E
$$\Rightarrow (E)$$
Choice J
$$f(-4)$$ $$=5(-4)^{2}-2(-4)+10$$ $$=5(16)+8+10$$ $$=80+8+10$$ $$=98$$
2012 December(71A) Math Question 25
Algebraic & Function Expressions
- Simplify Algebraic Expressions
Choice D
$$\frac{6}{12}=0.5$$ $$\Rightarrow (D)$$
Choice H
$$\tan\theta=\frac{3}{8}$$ $$\theta=\arctan\frac{3}{8}$$
Choice E
$$2+3d+2=22$$ $$\Rightarrow 4+3d=22$$
Choice G
$$3x+5y=6$$ $$5y=-3x+6$$ $$y=-\frac{3}{5}+6$$ $$m=-\frac{3}{5}$$
Choice C
$$3x-12-2x+6=-5x-15+6$$ $$x-6=-5x-9$$ $$6x=-3$$ $$x=-\frac{1}{2}$$
Choice H
$$If\ x=\frac{1}{2}$$ $$(\frac{1}{2})^{3}=\frac{1}{8}$$ $$0\lt\frac{1}{8}\lt1$$ $$\Rightarrow …
Choice E
$$\frac{(2a)^{6}+3a^{4}-5a^{4}}{2a}$$ $$=\frac{8a^{6}-2a^{4}}{2a}$$ $$=4a^{5}-a^{3}$$
Choice J
$$1.28\times10^{4}-3.5\times10^{3}$$ $$=12.8\times10^{3}-3.5\times10^{3}$$ $$=9.3\times10^{3}$$
Choice A
$$\overline{AB}^{2}=3^{2}+4^{2}=5^{2}$$ $$\overline{AB}=5$$ $$\sin A=\frac{3}{5}$$
Choice H
$$\frac{1}{12^{2}}:\frac{1}{6^{2}}$$ $$=\frac{1}{144}:\frac{1}{36}=1:4$$ $$l=10\times4=40$$
Choice C
$$3-(-2)=5$$ $$16-4=12$$ $$\sqrt{5^{2}+12^{2}}=\sqrt{25+144}=\sqrt{169}=13$$ $$\pi r^{2}=\pi …
Choice B
$$2w+7=\mid-2\mid$$ $$\mid-2\mid=2$$ $$2w+7=2\Rightarrow w=-2.5$$
Choice K
$$\Rightarrow (K)$$
Choice B
$$\frac{12+(-4)}{2}=4$$ $$\frac{18+2}{2}=10$$ $$\Rightarrow (4,10)$$
Choice G
$$\frac{\sin 58°}{50}=\frac{\sin 68°}{\overline{AB}}$$
Choice D
$$\frac{0+8}{2}=4$$ $$\frac{6+0}{2}=3$$
Choice J
$$\frac{4x}{6x^{2}}=\frac{2}{3x}$$
A rational number is …
Choice K
$$g(-2)=2(-2)-1=-5$$ $$f(-5)=3(-5)+2=-13$$
Choice B
$$36=6\times6$$ $$6\times4=24$$
Choice F
$$Distance=V \times Time$$ $$1 segment:2 …
Choice C
$$180°-43°-32°=105°=\angle B$$ $$\overline{AC}\gt\overline{BC}\gt\overline{AB}$$
Choice F
$$y=\mid x-1\mid-2$$ $$(1,-2)\Rightarrow -2=0-2$$
Choice E
$$h\gt 0,k\gt 0$$ $$16=4^{2}$$ $$4=2^{2}$$ …
Choice K
$$2\times4+2\times4$$ $$=8+8$$ $$=16$$
Choice A
$$2x-3y=6---(1)$$ $$(1)\times3$$ $$\Rightarrow 6x-9y=18$$ $$-9=k$$ …
Choice F
$$2^{0}=1$$ $$x^{2}+1=0$$ $$x^{2}=-1$$ $$x=\pm I$$ …
Choice D
$$\pi r^{2}$$ $$=\pi 10^{2}$$ $$=100\pi$$
Choice G
$$\widehat{AB}$$ $$=2\pi r\times\frac{1}{2}$$ $$=2\pi(20)\times\frac{1}{2}$$ $$=20\pi$$
Choice D
$$c\Rightarrow(10,\sqrt{3})$$
Choice J
$$90°\div2=45°$$
Choice E
$$\frac{10L}{L}=10$$ $$(L-4)10=10L-40$$
Choice K
$$T_{64}=1+2+3+...+64$$ $$=\frac{(1+64)64}{2}$$ $$=65\times32$$ $$=2080$$
Choice A
$$x^{2}+kx+17=0$$ $$\Rightarrow (x-17)(x-1)=0$$ $$\Rightarrow x^{2}-x-17x+17=0$$ …
Choice F
$$\overline{XY}=12$$ $$\tan\theta=\frac{4}{9}=\frac{\overline{XY}}{\overline{XZ}}=\frac{12}{\overline{XZ}}$$ $$4\times\overline{XZ}=9\times12$$ $$\overline{XZ}=27$$ $$Area=\overline{XZ}\times\overline{XY}\times\frac{1}{2}$$ …