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ISEE Lower Level Math : Algebraic Concepts

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All ISEE Lower Level Math Resources

10 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Equations

Determine the value of .

$-2x^{2} +36 = -14$

Possible Answers:

Correct answer:

Explanation:

To solve, we need to isolate .

$-2x^{2} +36 = -14$

Subtract $\small 36$ from both sides.

-2x^2+36-36=-14-36

-2x^2=-50

Divide both sides by $\small -2$ .

$\frac{-2x^2}{-2}=\frac{-50}{-2}$

x^2=25

Now, take the square root of both sides.

$\sqrt{x^2}=\sqrt{25}$

x=5

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Example Question #12 : Equations

Simplify the expression.

$-7x^{^{2}}-2x +6x -3 +3x^{2}$

Possible Answers:

$-4x^{2}-4x-3$

$10x^{2} +4x -2$

$4x^{2}-4x-3$

$-4x^{2}+4x-3$

$-4x^{2}+4x+3$

Correct answer:

$-4x^{2}+4x-3$

Explanation:

To simplify, you will need to combine like terms.

First, combine the two terms that have an $x^{2}$ .

$-7x^{2}+3x^{2}=-4x^{2}$

Then combine the two terms that have an .

-2x+6x=4x

Last, put them all together.

$-4x^{2} +4x -3$

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Example Question #13 : Equations

What value of makes this statement true?

y - 12 = 39

Possible Answers:

y=47

y=27

y=37

y=51

y=41

Correct answer:

y=51

Explanation:

Add 12 to each side:

y - 12 = 39

y - 12 + 12 = 39 + 12

y = 51

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Example Question #14 : Equations

What value of makes this statement true?

y + 12 = 39

Possible Answers:

y = 37

y = 21

y = 11

y = 27

y = 17

Correct answer:

y = 27

Explanation:

Subtract 12 from both sides:

y + 12 = 39

y + 12 -12 = 39 -12

y = 27

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Example Question #15 : Equations

Solve for x.

5x-3=12

Possible Answers:

Correct answer:

Explanation:

5x-3=12

Add 3 to both sides.

5x = 12+3

5x=15

Divide both sides by 5.

$\frac{5x}{5}=\frac{15}{5}$

Reduce.

x=5

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Example Question #16 : Equations

At the grocery store, Sarah bought 3 bags of flour that cost $2 each and a frozen pizza. Her total was $11. Which equation should be used to find the cost of the frozen pizza (p)?

Possible Answers:

3+2+p=11

2(3)-p=11

3(2)+p=11

3+2p=11

Correct answer:

3(2)+p=11

Explanation:

Try to think of the story problem as a math equation.

3 bags of flour cost $2 each: 3 x 2 or 3(2)

One frozen pizza = p

Total = 11

The 3 bags and the frozen pizza are added together to make the total, so the correct answer is: 3(2)+p=11

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Example Question #17 : Equations

The total combined weight of a dog, cat, and mouse is 12 pounds. If the dog weighs three times as much as the mouse, and the mouse half as much as the cat, how much does the mouse weigh?

Possible Answers:

3 pounds

5 pounds

2 pounds

4 pounds

Correct answer:

2 pounds

Explanation:

1 mouse + 1 cat + 1 dog = 12 pounds

Since we're told how much the cat and dog weigh compared to the mouse, we can recognize:

1 mouse + 2 mice + 3 mice = 12 pounds

Add the mice together:

6 mice = 12 pounds

1 mouse = 12 $\div$ 6 = 2 pounds

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Example Question #18 : Equations

Simplify:

8y+15-4y-4

Possible Answers:

11-4y

12y+19

15y

4y+11

Correct answer:

4y+11

Explanation:

Combine like terms:

8y-4y=4y

15-4=11

Put them together for the answer:

4y+11

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Example Question #19 : Equations

4+r=6

7+s=10

What is the sum of r+s ?

Possible Answers:

Correct answer:

Explanation:

First, solve for and :

4+r=6

r=6-4=2

7+s=10

s=10-7=3

Since r=2 and s=3 ,

r+s=2+3=5 .

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Example Question #20 : Equations

Solve the equation for :

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

Possible Answers:

x=9

x=7

x=42

x=14

x=21

Correct answer:

x=21

Explanation:

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

4x=3(7+x)

4x=21+3x

4x-3x=21

x=21

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All ISEE Lower Level Math Resources

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ISEE Lower Level Math : Algebraic Concepts

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #11 : Equations

Example Question #12 : Equations

Example Question #13 : Equations

Example Question #14 : Equations

Example Question #15 : Equations

Example Question #16 : Equations

Example Question #17 : Equations

Example Question #18 : Equations

Example Question #19 : Equations

Example Question #20 : Equations

All ISEE Lower Level Math Resources

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