Choice H
$$\frac{7000}{100}\times$0.75+$20$$ $$=70\times$0.75+$20$$ $$=$52.5+$20$$ $$=$72.5$$
Choice E
$$f(x)=4x^{2}-11x$$ $$f(-5)=4\times(-5)^{2}-11\times(-5)$$ $$=4\times25-(-55)$$ $$=100+55=155$$
Choice G
Taho works 40 hours+10 hours.
$$ 40\ hours\Rightarrow $11\times 40=$440 $$ $$ 10\ hours\Rightarrow $11(1\frac{1}{2})\times 10=$16.5\times 10=$165 $$ $$ $440+$165=$605 $$
Choice E
$$8\ juniors+4\ seniors\Rightarrow 7\ juniors+4\ seniors$$ $$P(Seniors)=\frac{4}{7+4}=\frac{4}{11}$$
Choice B
$$P=\frac{Regular\ coffee\ without\ milk}{Total}$$ $$=\frac{10}{36}=\frac{5}{18}$$
Choice J
$$3x-5\lt2x+1$$ $$\Rightarrow 3x-5-2x+5\lt2x+1-2x+5$$ $$\Rightarrow x\lt6$$
2019 December(C03) Math Question 13
Algebraic & Function Expressions
- Simplify Algebraic Expressions
Choice G
$$1.36\times 10^{4}\times\frac{4}{100}$$ $$=1.36\times4\times10^{2}$$ $$=136\times4$$ $$=544$$
Choice B
$$\frac{(-6,9)+(2,5)}{2}$$ $$=\frac{(-6+2,9+5)}{2}$$ $$=\frac{(-4,14)}{2}$$ $$=(-2,7)$$
Choice K
$$\require{cancel} $$ $$\frac{x^{2}+2x}{x+2}=2$$ $$\Rightarrow x^{2}+2x=2(x+2)$$ $$\Rightarrow x\cancel{(x+2)}=2\cancel{(x+2)}$$ $$\Rightarrow x=2$$
Choice G
$$x:\ attend\ regular\ showing$$ $$y:\ attend\ matinees$$ $$x+y=5000$$ $$\Rightarrow y=5000-x$$ $$9.5x+(5000-x)7=44000$$ $$\Rightarrow 9.5x+35000-7x=44000$$ $$\Rightarrow 2.5x=9000$$ $$\Rightarrow x=3600$$ $$\Rightarrow y=5000-3600=1400$$
Choice A
$$\frac{2750}{5000}=0.55$$ $$\frac{1225}{5000}=0.245$$ $$\frac{625}{5000}=0.125$$ $$\frac{400}{5000}=0.08$$
Choice G
$$9\times6=54$$ $$3\times7=21$$ $$54+21=75$$
Choice C
$$\angle BEC=180°-\angle AEB=180°-145°=35°$$ $$\angle CED=90°-\angle …
Choice G
$$(5\sin(x)-14)-(5\sin(x)-7)=-7$$
Choice C
$$(9^{\frac{1}{2}}+16^{\frac{1}{2}})^{2}$$ $$=(\sqrt{9}+\sqrt{16})^{2}$$ $$=(3+4)^{2}$$ $$=7^{2}$$ $$=49$$
Choice F
$$12^{2}+x^{2}=13^{2}$$ $$\Rightarrow 144+x^{2}=169$$ $$\Rightarrow x^{2}=169-144=25$$ …
Choice C
$$\frac{2\times4}{2}=4$$ $$\frac{4\times6}{2}=12$$ $$4+12=16$$ $$6\times6=36$$ $$\Rightarrow\frac{16}{36}=\frac{4}{9}$$
Choice H
$$(4.25\times 10^{2x+4})(6\times 10^{7})=255$$ $$\Rightarrow 4.25\times6\times …
Choice D
$$If\ m=2,$$ $$(A)\ 2\leq\frac{1}{2}$$ $$(B)\ …
Choice J
$$V=\pi r^{2}h$$ $$\Rightarrow V=3.14\times 5^{2}\times3=235.5$$ …
Choice D
$$30^{2}+40^{2}=50^{2}$$
Choice F
Choice B
$$y=30(x+17)^{2}-42$$ $$\Rightarrow (-17,-42)$$
Choice H
$$\Box ABCD=15\times15=225$$ $$225\div10=22.5$$
Choice B
$$77\times10=770$$ $$\frac{770-x}{9}=78$$ $$770-x=78\times9=702$$ $$770-702=x=68$$
Choice J
$$A=A_{0}(2^{w5})$$ $$100=10(2^{w5})$$ $$10=(2^{w5})$$ $$\log 2^{10}=\log …
Choice E
$$\require{cancel} $$ $$\frac{x^{2}-x-6}{x^{2}-9}$$ $$=\frac{\cancel{(x-3)}(x+2)}{\cancel{(x-3)}(x+3)}$$ $$=\frac{x+2}{x+3}$$
Choice H
$$\frac{9\times12+4}{2}=\frac{112}{2}=56$$ $$12\times4=48$$ $$56=48+8$$
Choice A
$$\frac{1}{2}+\frac{1}{3}\cdot\frac{1}{4}\div\frac{1}{5}=\frac{x}{y}$$ $$\Rightarrow\frac{1}{2}+\frac{1}{3}\cdot\frac{1}{4}\cdot5=\frac{x}{y}$$ $$\Rightarrow\frac{1}{2}+\frac{5}{12}=\frac{x}{y}$$ $$\Rightarrow\frac{6}{12}+\frac{5}{12}=\frac{11}{12}$$ $$\Rightarrow11+12=23$$
Choice H
$$0.\overline{3178}=0.3178317831783178...$$ $$358\div4=89...2$$
Choice C
$$60\times0.1=6$$ 60\times0.3=18$$ 60\times0.6=36$$ $$\frac{6\times3+18\times2+36\times1}{6}$$ $$=\frac{18+36+36}{6}$$ …
Choice G
200/2400=8.33%
Choice A
$$600\times50+200\times5+400\times10$$
Choice J
$$10000(1+0.02)^{t}$$
Choice D
$$Anela:$$ $$375\div75=5$$ $$\Rightarrow 5hrs\ 30\ …
2019 December(C03) Math Question 46
Algebraic & Function Expressions
- Simplify Algebraic Expressions
Choice J
$$\frac{3x+5}{2x}-\frac{7x-3}{2x}$$ $$=\frac{-4x+8}{2x}$$ $$=\frac{-2x+4}{x}$$
Choice B
$$90\ ft\times30\ ft\ wide$$ $$1\ …
Choice H
$$x+y$$ $$x:1,2,3,4,5$$ $$y:1,2,3$$ $$Total=5\times3=15$$ $$Even+Odd=Even\ …
Choice A
$$a_{n}=a_{1}+(n-1)d$$ $$a_{3}=\frac{5}{2}=a_{1}+2d---(1)$$ $$a_{6}=\frac{1}{4}=a_{1}+5d---(2)$$ $$(2)-(1)$$ $$\Rightarrow …
Choice F
$$\require{cancel} $$ $$1-\frac{1}{9}=\frac{8}{9}$$ $$\frac{\frac{1}{9}}{\frac{8}{9}}=\frac{1}{\cancel{9}}\times\frac{\cancel{9}}{8}=\frac{1}{8}$$
Choice B
$$\frac{120\times0.05+80\times0.15}{200}$$ $$=\frac{6+12}{200}$$ $$=\frac{18}{200}$$ $$=\frac{9}{100}$$
Choice F
$$\tan\theta=\frac{7}{50}$$ $$\theta=\tan^{-1}\frac{7}{50}$$
Choice A
$$\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$$ $$\frac{(x-2)^{2}}{a^{2}}-\frac{(y-2)^{2}}{b^{2}}=1$$ $$(A)\frac{(x-2)^{2}}{1}-\frac{3(y-2)^{2}}{4}=1$$ $$(0,0)\Rightarrow \frac{(0-2)^{2}}{1}-\frac{3(0-2)^{2}}{4}=1$$ …
Choice K
$$c^{2}=a^{2}+b^{2}-2ab\cos C$$ $$c^{2}=\sqrt{250^{2}+700^{2}-2\times250\times700\times\cos 155°}$$
Choice A
$$a\gt b\gt c, b\gt0$$ $$(1)a=3,b=2,c=1$$ …
Choice J
$$c_6^2=\frac{6!}{2!(6-2)!}=\frac{6\times5}{1\times2}=15$$ $$P(All)-P(Sit\ next\ to\ each\ …
Choice C
$$2^{88}=................6$$ $$2^{90}=2^{88}\times4 =................6\times4=................4$$
Choice F
$$\frac{1}{2}\times\overline{RT}\times h$$ $$=\frac{1}{2}(c-a)(e-d)$$
Choice A
$$x(2+3i)=1$$ $$\star(a+bi)(a-bi)=a^{2}+b^{2}$$ $$x=\frac{1}{2+3i}\times\frac{2-3i}{2-3i}$$ $$=\frac{2-3i}{4+9}$$ $$=\frac{2-3i}{13}$$ …
Choice J
$$39=13\times h\Rightarrow h=3$$ $$(15\times12)\times3-\frac{1}{2}(5\times12)\times3$$ $$=540-90$$ …