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ISEE Middle Level Math : Algebraic Concepts

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6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #471 : Algebraic Concepts

What is the value of the expression $7-4+(5-3)^{2{}}-25\div5$ $\displaystyle 7-4+(5-3)^{2{}}-25\div5$ ?

Possible Answers:

$\displaystyle 8$

$\displaystyle -2$

$\displaystyle 4$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

Below are the steps for solving the expression:

$7-4+(5-3)^{2{}}-25\div5$ $\displaystyle 7-4+(5-3)^{2{}}-25\div5$

First, parentheses are solved for.

$7-4+(2)^{2{}}-25\div5$ $\displaystyle 7-4+(2)^{2{}}-25\div5$

Next, we take the square of 2, and can also solve for 25 divided by 5.

7-4+4-5 $\displaystyle 7-4+4-5$

The -4 and +4 cancel each other out, leaving

7-5 $\displaystyle 7-5$

This reduces to 2, the correct answer.

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Example Question #1 : Algebra

Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?

Possible Answers:

22 dollars

60 dollars

30 dollars

20 dollars

Correct answer:

22 dollars

Explanation:

Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.

Below are the prices that will be charged based on this make up:

2 pairs of people at 40 dollars per pair = 80 dollars

1 solo person at 30 dollars per person = 30 dollars

80 dollars plus 30 dollars is 110 dollars, the grand total.

When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.

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Example Question #266 : Equations

Solve for $\displaystyle x$ .

$\frac{3x}{7}=\frac{4}{3}$ $\displaystyle \frac{3x}{7}=\frac{4}{3}$

Possible Answers:

$\frac{9}{28}$ $\displaystyle \frac{9}{28}$

$\frac{27}{9}$ $\displaystyle \frac{27}{9}$

$\frac{28}{9}$ $\displaystyle \frac{28}{9}$

$\displaystyle 3$

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

Correct answer:

$\frac{28}{9}$ $\displaystyle \frac{28}{9}$

Explanation:

$\frac{3x}{7}=\frac{4}{3}$ $\displaystyle \frac{3x}{7}=\frac{4}{3}$

To solve, we will need to isolate $\displaystyle x$ . Begin by cross-multiplying:

$3x\times3=4\times7$ $\displaystyle 3x\times3=4\times7$

9x=28 $\displaystyle 9x=28$

Divide both sides by 9.

$x=\frac{28}{9}$ $\displaystyle x=\frac{28}{9}$

The fraction cannot be reduced, making it our final answer.

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Example Question #261 : Equations

On average, 1 in 50 apples that grow in an orchard will not be harvested. Of those, half will rot on the ground. If 500 apples are growing in an orchard, how many will rot on the ground?

Possible Answers:

$\displaystyle 1$

$\displaystyle 50$

$\displaystyle 5$

$\displaystyle 10$

$\displaystyle 15$

Correct answer:

$\displaystyle 5$

Explanation:

If there are 500 apples and 1 in 50 will remain unharvested, then we can find the number of unharvested apples by multiplying.

$500\times \frac{1}{50}=10$ $\displaystyle 500\times \frac{1}{50}=10$

10 apples will remain unharvested. Of those, half will rot on the ground. Multiply to find how many apples rot on the ground.

$10\times\frac{1}{2}=5$ $\displaystyle 10\times\frac{1}{2}=5$

5 apples will rot on the ground.

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Example Question #472 : Algebraic Concepts

Solve for $\displaystyle x$ :

$3x=4(2+4^{2})-5$ $\displaystyle 3x=4(2+4^{2})-5$

Possible Answers:

$\displaystyle 67$

$\frac{67}{3}$ $\displaystyle \frac{67}{3}$

$\displaystyle 22$

$\frac{22}{3}$ $\displaystyle \frac{22}{3}$

None of these

Correct answer:

$\frac{67}{3}$ $\displaystyle \frac{67}{3}$

Explanation:

Start by evaluating the right side of the equation using order of operations.

$3x=4(2+4^{2})-5$ $\displaystyle 3x=4(2+4^{2})-5$

$\displaystyle 3x=4(2+16)-5$

$\displaystyle 3x=4(18)-5$

3x=72-5 $\displaystyle 3x=72-5$

3x=67 $\displaystyle 3x=67$

Divdie both side by 3 to solve for the variable.

$x=\frac{67}{3}$ $\displaystyle x=\frac{67}{3}$

The fraction acnnot be simplified.

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Example Question #471 : Algebraic Concepts

Solve:

$6^{3}*2=$ $\displaystyle 6^{3}*2=$

Possible Answers:

423 $\displaystyle 423$

324 $\displaystyle 324$

234 $\displaystyle 234$

432 $\displaystyle 432$

Correct answer:

432 $\displaystyle 432$

Explanation:

First perform the cubing:

$6^{3}=216$ $\displaystyle 6^{3}=216$

Then multiply:

$\displaystyle 216*2=432$

Answer: 432 $\displaystyle 432$

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Example Question #472 : Algebraic Concepts

Solve:

$7^{2}*19=$ $\displaystyle 7^{2}*19=$

Possible Answers:

$\displaystyle 58$

139 $\displaystyle 139$

391 $\displaystyle 391$

931 $\displaystyle 931$

Correct answer:

931 $\displaystyle 931$

Explanation:

First complete the squaring:

$7^{2}=49$ $\displaystyle 7^{2}=49$

Then multiply:

$\displaystyle 49*19=931$

Answer: 931 $\displaystyle 931$

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Example Question #473 : Algebraic Concepts

Solve:

$2^{4}*20=$ $\displaystyle 2^{4}*20=$

Possible Answers:

230 $\displaystyle 230$

110 $\displaystyle 110$

320 $\displaystyle 320$

323 $\displaystyle 323$

Correct answer:

320 $\displaystyle 320$

Explanation:

First look at any numbers that have exponents:

$2^{4}=16$ $\displaystyle 2^{4}=16$

Then multiply:

$\displaystyle 16*20=320$

Answer: 320 $\displaystyle 320$

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Example Question #474 : Algebraic Concepts

Solve:

$3^{3}*30=$ $\displaystyle 3^{3}*30=$

Possible Answers:

800 $\displaystyle 800$

990 $\displaystyle 990$

900 $\displaystyle 900$

810 $\displaystyle 810$

Correct answer:

810 $\displaystyle 810$

Explanation:

First do the cubing:

$3^{3}=27$ $\displaystyle 3^{3}=27$

Then multiply:

$\displaystyle 27*30=810$

Answer: 810 $\displaystyle 810$

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Example Question #475 : Algebraic Concepts

$9^{2}*12=$ $\displaystyle 9^{2}*12=$

Possible Answers:

910 $\displaystyle 910$

978 $\displaystyle 978$

980 $\displaystyle 980$

972 $\displaystyle 972$

Correct answer:

972 $\displaystyle 972$

Explanation:

First perform the squaring:

$9^{2}=81$ $\displaystyle 9^{2}=81$

Then multiply:

$\displaystyle 81*12=972$

Answer: 972 $\displaystyle 972$

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ISEE Middle Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #471 : Algebraic Concepts

Example Question #1 : Algebra

Example Question #266 : Equations

Example Question #261 : Equations

Example Question #472 : Algebraic Concepts

Example Question #471 : Algebraic Concepts

Example Question #472 : Algebraic Concepts

Example Question #473 : Algebraic Concepts

Example Question #474 : Algebraic Concepts

Example Question #475 : Algebraic Concepts

All ISEE Middle Level Math Resources

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