Indices, Log and Simultaneous Equations

Indices, Log and Simultaneous Equations

Assessment

Assessment

•

Created by

Sabih Siddiqui

•

Mathematics

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9th - 12th Grade

•

4 plays

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Medium

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5 questions

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1.

Multiple Choice

3 mins

1 pt

Solve the simultaenous equations


 3x2−xy+2y2=163x^2-xy+2y^2=16 
 2y−x=42y-x=4  

 x=−2, y=1x=-2,\ y=1 

  x=43, y=83x=\frac{4}{3},\ y=\frac{8}{3}  

 x=43, y=83x=\frac{4}{3},\ y=\frac{8}{3} 


 x=43, y=1x=\frac{4}{3},\ y=1  

 x=83, y=43x=\frac{8}{3},\ y=\frac{4}{3} 

 x=1, y=−2x=1,\ y=-2  

2.

Multiple Choice

5 mins

1 pt

Solve the simultaneous equations
 25x×4y=182^{5x}\times4^y=\frac{1}{8} 

 7x×492y=17^x\times49^{2y}=1  

 x=−23, y=16x=-\frac{2}{3},\ y=\frac{1}{6}  

 x=16, y=−23x=\frac{1}{6},\ y=-\frac{2}{3}  

 x=−2, y=1x=-2,\ y=1  

 x=−3, y=6x=-3,\ y=6  

3.

Multiple Choice

5 mins

1 pt

Solve the following simultaneous equations, giving your answer in the for

 a+b3a+b\sqrt{3}  where  aa  and bb  are integers.

 2x+y=92x+y=9 

 3x+2y=5\sqrt{3}x+2y=5  

 x=4+3,  y=1−23x=4+\sqrt{3},\ \ y=1-2\sqrt{3}  

 x=3,  y=−23x=\sqrt{3},\ \ y=-2\sqrt{3}  

 x=1−23,  y=4+3x=1-2\sqrt{3},\ \ y=4+\sqrt{3}  

 x=4−3,  y=1+23x=4-\sqrt{3},\ \ y=1+2\sqrt{3}  

4.

Multiple Choice

5 mins

1 pt

Solve the simultaneous equations

 log⁡2(x+4)=2log⁡2y\log_2\left(x+4\right)=2\log_2y 
 log⁡2(7y−x)=4\log_2\left(7y-x\right)=4  

 x=5 or 12,  y=3  or 4x=5\ or\ 12,\ \ y=3\ \ or\ 4  

 x=3 or 4,  y=5  or 12x=3\ or\ 4,\ \ y=5\ \ or\ 12  

 x=5 or −12,  y=−3  or 4x=5\ or\ -12,\ \ y=-3\ \ or\ 4  

 x=−5 or 12,  y=3  or −4x=-5\ or\ 12,\ \ y=3\ \ or\ -4  

5.

Multiple Choice

5 mins

1 pt

Solve the simultaneous equations

 8(p+1)4q=211\frac{8^{\left(p+1\right)}}{4^q}=2^{11} 
 3(2p+5)27(13)=93q\frac{3^{\left(2p+5\right)}}{27^{\left(\frac{1}{3}\right)}}=9^{3q}  

 p=2, q=4p=2,\ q=4  

 p=4, q=2p=4,\ q=2  

 p=−4, q=−2p=-4,\ q=-2  

 p=−2, q=−4p=-2,\ q=-4  

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