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SAT II Math II : Mathematical Relationships

Study concepts, example questions & explanations for SAT II Math II

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Mathematical Relationships

Add the following numbers: $\displaystyle 137+189+774$

Possible Answers:

1180 $\displaystyle 1180$

1190 $\displaystyle 1190$

1100 $\displaystyle 1100$

1200 $\displaystyle 1200$

1290 $\displaystyle 1290$

Correct answer:

1100 $\displaystyle 1100$

Explanation:

Add the ones digits.

$\displaystyle 7+9+4 = 20$

Add the tens digits with the two as the carryover.

$\displaystyle 3+8+7+(2) = 20$

Add the hundreds digits with the two as the carryover.

$\displaystyle 1+1+7+(2) = 11$

Combine this number with the ones digits of the previous calculations.

The answer is: 1100 $\displaystyle 1100$

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Example Question #2 : Mathematical Relationships

Add the numbers: $\displaystyle 256+781+64$

Possible Answers:

1111 $\displaystyle 1111$

1101 $\displaystyle 1101$

1901 $\displaystyle 1901$

901 $\displaystyle 901$

1011 $\displaystyle 1011$

Correct answer:

1101 $\displaystyle 1101$

Explanation:

Add the ones digits.

$\displaystyle 6+1+4 = 11$

Carry the one, and add the tens digits.

$\displaystyle 5+8+6+(1) = 20$

Carry the two, and add the hundreds digits.

$\displaystyle 2+7+0+(2) = 11$

Combine this number with the ones digit of the other numbers.

The answer is: 1101 $\displaystyle 1101$

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Example Question #3 : Mathematical Relationships

Add the numbers: $\displaystyle 34+497+89$

Possible Answers:

650 $\displaystyle 650$

520 $\displaystyle 520$

510 $\displaystyle 510$

620 $\displaystyle 620$

550 $\displaystyle 550$

Correct answer:

620 $\displaystyle 620$

Explanation:

Add the ones digits.

$\displaystyle 4+7+9 = 20$

Carry the two, and add the tens digits.

$\displaystyle 3+9+8+(2) = 22$

Carry the two, and add the hundreds places.

$\displaystyle 0+4+0+(2) = 6$

Combine all ones digits.

The answer is: 620 $\displaystyle 620$

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Example Question #4 : Mathematical Relationships

Add the numbers: $\displaystyle 64+67+88$

Possible Answers:

219 $\displaystyle 219$

109 $\displaystyle 109$

229 $\displaystyle 229$

209 $\displaystyle 209$

129 $\displaystyle 129$

Correct answer:

219 $\displaystyle 219$

Explanation:

Add the ones digits.

$\displaystyle 4+7+8=19$

Add the tens digits using the one as the carryover.

$\displaystyle 6+6+8 +(1)= 21$

Combine this number with the ones digit of the first number solved.

The answer is: 219 $\displaystyle 219$

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Example Question #5 : Mathematical Relationships

Add the numbers: $\displaystyle 84+86+36$

Possible Answers:

206 $\displaystyle 206$

294 $\displaystyle 294$

216 $\displaystyle 216$

196 $\displaystyle 196$

194 $\displaystyle 194$

Correct answer:

206 $\displaystyle 206$

Explanation:

Add the ones digits.

$\displaystyle 4+6+6 = 16$

Carry the one and add the tens digits.

$\displaystyle 8+8+3+(1) = 20$

Combine this number with the ones digit of the first number.

The answer is: 206 $\displaystyle 206$

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Example Question #6 : Mathematical Relationships

Add the following numbers: $\displaystyle 23+64+97$

Possible Answers:

164 $\displaystyle 164$

184 $\displaystyle 184$

174 $\displaystyle 174$

284 $\displaystyle 284$

274 $\displaystyle 274$

Correct answer:

184 $\displaystyle 184$

Explanation:

Add the ones digits.

$\displaystyle 3+4+7= 14$

Carry the one and add the tens digits.

$\displaystyle 2+6+9+(1) = 18$

Combine this number with the ones digit of the first number.

The answer is: 184 $\displaystyle 184$

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Example Question #7 : Mathematical Relationships

Add the numbers: $\displaystyle 35+36+88$

Possible Answers:

139 $\displaystyle 139$

249 $\displaystyle 249$

149 $\displaystyle 149$

259 $\displaystyle 259$

159 $\displaystyle 159$

Correct answer:

159 $\displaystyle 159$

Explanation:

Add the ones digits.

$\displaystyle 5+6+8 = 19$

Add the tens digits with the one as the carryover.

$\displaystyle 3+3+8+(1)=15$

The answer is: 159 $\displaystyle 159$

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Example Question #8 : Mathematical Relationships

Add the numbers: $\displaystyle 34+64+87$

Possible Answers:

165 $\displaystyle 165$

175 $\displaystyle 175$

205 $\displaystyle 205$

195 $\displaystyle 195$

185 $\displaystyle 185$

Correct answer:

185 $\displaystyle 185$

Explanation:

Add the ones digits.

$\displaystyle 4+4+7= 15$

Add the tens digit with the carryover.

$\displaystyle 3+6+8+(1) = 18$

The answer is: 185 $\displaystyle 185$

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Example Question #9 : Mathematical Relationships

Solve for $\displaystyle x$:

$5^{x} = 432$ $\displaystyle 5^{x} = 432$

Give the solution to the nearest hundredth.

Possible Answers:

$x \approx 3.77$ $\displaystyle x \approx 3.77$

$x\approx 3.37$ $\displaystyle x\approx 3.37$

$x \approx 2.86$ $\displaystyle x \approx 2.86$

$x \approx 1.94$ $\displaystyle x \approx 1.94$

$x \approx 2.44$ $\displaystyle x \approx 2.44$

Correct answer:

$x \approx 3.77$ $\displaystyle x \approx 3.77$

Explanation:

One way is to take the common logarithm of both sides and solve:

$5^{x} = 432$ $\displaystyle 5^{x} = 432$

$\log \left (5^{x} \right )= \log 432$ $\displaystyle \log \left (5^{x} \right )= \log 432$

$x \log 5= \log 432$ $\displaystyle x \log 5= \log 432$

$x = \frac{\log 432}{\log 5} \approx \frac{2.6355}{0.6990} \approx 3.77$ $\displaystyle x = \frac{\log 432}{\log 5} \approx \frac{2.6355}{0.6990} \approx 3.77$

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Example Question #2 : Exponents And Logarithms

Solve for $\displaystyle k$:

$\left (e+1 \right ) ^{k} = 100$ $\displaystyle \left (e+1 \right ) ^{k} = 100$

Give your answer to the nearest hundredth.

Possible Answers:

$k \approx 1.43$ $\displaystyle k \approx 1.43$

$k \approx 1.69$ $\displaystyle k \approx 1.69$

$k \approx 3.51$ $\displaystyle k \approx 3.51$'

$k \approx 3.61$ $\displaystyle k \approx 3.61$

$k \approx 1.89$ $\displaystyle k \approx 1.89$

Correct answer:

$k \approx 3.51$ $\displaystyle k \approx 3.51$'

Explanation:

Take the common logarithm of both sides and solve for $\displaystyle k$:

$\left (e+1 \right ) ^{k} = 100$ $\displaystyle \left (e+1 \right ) ^{k} = 100$

$\log \left (e+1 \right ) ^{k} = \log 100$ $\displaystyle \log \left (e+1 \right ) ^{k} = \log 100$

$k \log \left (e+1 \right ) = 2$ $\displaystyle k \log \left (e+1 \right ) = 2$

$k= \frac{2}{ \log \left (e+1 \right ) }$ $\displaystyle k= \frac{2}{ \log \left (e+1 \right ) }$

$k= \frac{2}{ \log \left (2.7183+1 \right ) } \approx \frac{2}{ \log 3.7183 } \approx \frac{2}{1.3133} \approx 3.51$ $\displaystyle k= \frac{2}{ \log \left (2.7183+1 \right ) } \approx \frac{2}{ \log 3.7183 } \approx \frac{2}{1.3133} \approx 3.51$

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SAT II Math II : Mathematical Relationships

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #1 : Mathematical Relationships

Example Question #2 : Mathematical Relationships

Example Question #3 : Mathematical Relationships

Example Question #4 : Mathematical Relationships

Example Question #5 : Mathematical Relationships

Example Question #6 : Mathematical Relationships

Example Question #7 : Mathematical Relationships

Example Question #8 : Mathematical Relationships

Example Question #9 : Mathematical Relationships

Example Question #2 : Exponents And Logarithms

All SAT II Math II Resources

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