Choice J
$$\angle BCA=\angle ECF=31°$$ $$\angle BAC=\angle BCA=31°$$ $$\angle ABC=180°-31°-31°=118°$$
Choice D
$$(7+\frac{1}{5})\div(1+\frac{1}{10})$$ $$=\frac{36}{5}\times\frac{10}{11}$$ $$=\frac{72}{11}$$ $$=6\frac{6}{11}$$
Choice C
$$3^{2}+x^{2}=5^{2}$$ $$\Rightarrow x=4$$ $$3^{2}+5^{2}=y^{2}$$ $$\Rightarrow …
Choice F
$$\sqrt{(7-2)^{2}+(3-3)^{2}}$$ $$=\sqrt{5^{2}+0^{2}}$$ $$=5$$
Choice E
$$13+7+5+2=27$$
Choice G
$$Day\ 1=750-0=750$$ $$Day\ 2=875-750=125$$ $$Day\ …
Choice A
$$\overline{BC}=\sqrt{15^{2}-9^{2}}=12$$ $$\sin A=\frac{12}{15}=\frac{4}{5}$$
Choice F
$$(a-1)(a-1)$$ $$=a^{2}-a-a+1$$ $$=a^{2}-2a+1$$
Choice B
$$r=18\div2=9$$ $$2\pi\times9=18\pi$$
Choice K
$$x^{2}+2=3$$ $$x^{2}=1$$ $$x=1,-1$$
Choice D
$$54\times24=1200$$ $$120\div225=5.3333...$$
Choice K
$$(60+34)2=194\times2=188$$
Choice B
$$1\ yard = 3\ feet$$ …
Choice H
$$\frac{1}{2}\times\frac{2}{6}=\frac{1}{6}$$
Choice C
$$r\times r\times r^{2}=128 $$ $$\Rightarrow …
Choice G
$$x^{2}-4\neq0 $$ $$\Rightarrow x^{2}\neq4 $$ …
Choice A
Choice H
$$\sqrt{(9-5)^{2}+(12-6)^{2}}$$ $$=\sqrt{4^{2}+6^{2}}$$ $$=\sqrt{16+36}$$ $$=\sqrt{52}\approx 7.2$$ …
Choice D
$$n=5,180°(n-2)$$ $$\Rightarrow 180°(5-2)=540°$$ $$540°-120°-120°-80°-80°=140°$$
Choice K
$$\sin ?=\frac{3.7}{5.4}$$ $$?=\frac{3.7}{5.4}\sin^{-1}$$
Choice D
$$30°:60°:90°$$ $$=1:\sqrt{3}:2$$ $$=20:20\sqrt{3}:40$$ $$h=20\sqrt{3}\approx34.64...$$
Choice H
$$\frac{35}{25}$$ $$=\frac{42}{30}$$ $$=\frac{7}{5}$$ $$=\frac{\overline{AB}}{40}$$ $$\Rightarrow …
Choice B
$$4:\sqrt{52}=x:\sqrt{13}$$ $$\Rightarrow x=2$$ $$2^{2}+y^{2}=(\sqrt{13})^{2}$$ $$=4+y^{2}=13$$ …
Choice J
$$\frac{50\times3+40\times2}{5}$$ $$=\frac{230}{5}$$ $$=46$$
Choice B
Choice G
$$(x+3)^{2}-x^{2}$$ $$=x^{2}+3x+3x+9-x^{2}$$ $$=6x+9$$
Choice B
$$60°:60°:60°$$ $$=1:1:1$$ $$\overline{AB}=\frac{9}{2}\times\frac{1}{2}=\frac{9}{4}$$
Choice K
$$a=\frac{1}{\sqrt{b}}$$ $$(\frac{1}{\sqrt{b}})^{2}\times b=\frac{1}{b}\times b=1$$
Choice A
$$3x+2y=5$$ $$2y=-3x+5$$ $$y=\frac{-3}{2}x+\frac{5}{2}$$ $$m'=\frac{-3}{2}$$ $$m\times …
Choice F
$$\frac{7-x}{2}=n$$ $$7-x=2n$$ $$x=7-2n$$ $$n=1,x=5$$ $$n=2,x=3$$ …
Choice A
$$Revenue$$ $$=xp$$ $$=(52-p)p$$ $$=52p-p^{2}$$ $$=-1(p^{2}-52p)$$ …
Choice J
$$6\div4=\frac{3}{2}$$ $$9\div6=\frac{3}{2}$$ $$9\times\frac{3}{2}=\frac{27}{2}=13.5$$
Choice A
$$V=V_{0}(1-r)^{t}$$ $$\frac{V}{V_{0}}=(1-r)^{t}$$ $$\sqrt[t]{\frac{V}{V_{0}}}=1-r$$ $$r=1-\sqrt[t]{\frac{V}{V_{0}}}$$
Choice H
$$V=V_{0}(1-r)^{t}$$ $$V=20000(1-0.1)^{3}$$ $$=20000(0.9)^{3}$$ $$=20000(0.729)$$ $$=14580$$
Choice E
$$V=V_{0}(1-r)^{t}$$ $$\frac{1}{2}=1(1-0.075)^{t}=(1-0.075)^{t}$$ $$\log\frac{1}{2}=\log(1-0.075)^{t}$$ $$t=\frac{\log\frac{1}{2}}{\log(1-0.075)}$$
Choice F
$$\overline{BC}=x$$ $$a^{2}=7^{2}+16^{2}-2\times7\times 16\times 0.81$$ $$a^{2}=49+256-181.44=123.56$$ …
Choice D
$$A.\ 1:3=40:120$$ $$B.\ 2:5=48:120$$ $$C.\ …
Choice K
Absolute value describes the distance …
Choice C
$$3\times15=45$$ $$60-45=15$$ $$5-3=2$$ $$15\div2=7...1$$ $$15-8=7$$
Choice J
$$\sin \theta=x$$ $$x^{2}-x=-\frac{1}{4}$$ $$x^{2}-x+\frac{1}{4}=0$$ $$4(x^{2}-x+\frac{1}{4})=0$$ …
Choice B
$$y=\frac{4}{3}x-2---(1)$$ $$(1)\times6\Rightarrow 6y=8x-12$$ $$8x-6y=12$$ $$\frac{12}{8}=\frac{3}{2}$$ …
Choice H
$$\pi r^{2}=\pi 6^{2}=36\pi$$ $$\frac{32\pi}{36\pi}=\frac{320}{360}$$ $$360-320=40$$ …