ISEE Lower Level Math : ISEE Lower Level (grades 5-6) Mathematics Achievement

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

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Example Questions

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Solve the following equation.

\dpi{100} 3(2-5)=\(\displaystyle \dpi{100} 3(2-5)=\) ?

Possible Answers:

\dpi{100} 9\(\displaystyle \dpi{100} 9\)

\dpi{100} 6\(\displaystyle \dpi{100} 6\)

\dpi{100} -9\(\displaystyle \dpi{100} -9\)

\dpi{100} -6\(\displaystyle \dpi{100} -6\)

Correct answer:

\dpi{100} -9\(\displaystyle \dpi{100} -9\)

Explanation:

\dpi{100} 2-5=-3\(\displaystyle \dpi{100} 2-5=-3\).

\dpi{100} 3\times -3=9\(\displaystyle \dpi{100} 3\times -3=9\)

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Solve

\(\displaystyle 4(6+3) - 9 =\)

Possible Answers:

\(\displaystyle 45\)

\(\displaystyle 26\)

\(\displaystyle 27\)

\(\displaystyle 28\)

\(\displaystyle 19\)

Correct answer:

\(\displaystyle 27\)

Explanation:

Use the distributive property to solve:

\(\displaystyle 4(6) + 4(3)= 36 - 9 = 27\)

Example Question #1 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Expand the expression.

\(\displaystyle (x+2)(3x-5)\)

Possible Answers:

\(\displaystyle 3x^{2}+x-3\)

\(\displaystyle 3x^{2}+x-10\)

\(\displaystyle 3x^{2}-x-10\)

\(\displaystyle 3x^{2}+11x+10\)

\(\displaystyle 3x^{2}-11x-10\)

Correct answer:

\(\displaystyle 3x^{2}+x-10\)

Explanation:

Use FOIL (first, outer, inner, last) to expand.

First: \(\displaystyle (x)(3x)= 3x^{2}\)

Outside: \(\displaystyle (x)(-5) = -5x\)

Inside: \(\displaystyle (2)(3x)=6x\)

Last: \(\displaystyle (2)(-5) =-10\)

Sum the four terms into one expression.

\(\displaystyle 3x^{2}-5x+6x-10\)

Simplify by combining like terms.

\(\displaystyle 3x^2+x-10\)

Example Question #2 : How To Find The Distributive Property

Simplify the expression:

\(\displaystyle 14x + 28 - 7x + 19\)

Possible Answers:

\(\displaystyle 7x - 47\)

\(\displaystyle 7x + 47\)

\(\displaystyle 54x\)

\(\displaystyle 7x + 9\)

\(\displaystyle 7x - 9\)

Correct answer:

\(\displaystyle 7x + 47\)

Explanation:

\(\displaystyle 14x + 28 - 7x + 19\)

\(\displaystyle =14x- 7x + 28 + 19\)

\(\displaystyle =\left (14- 7 \right )x + 28 + 19\)

\(\displaystyle =7x + 47\)

Example Question #3 : How To Find The Distributive Property

Simplify the expression:

\(\displaystyle 17x + 38 - 7x - 13\)

Possible Answers:

\(\displaystyle 10x - 51\)

\(\displaystyle 10x - 25\)

\(\displaystyle 10x + 51\)

\(\displaystyle 10x + 25\)

\(\displaystyle 250x\)

Correct answer:

\(\displaystyle 10x + 25\)

Explanation:

\(\displaystyle 17x + 38 - 7x - 13\)

\(\displaystyle =17x - 7x + 38 - 13\)

\(\displaystyle =\left (17 - 7 \right )x + 38 - 13\)

\(\displaystyle =10x + 25\)

Example Question #2 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Use the distributive property to expand:

\(\displaystyle (-x-2)(2x+3)\)

 

Possible Answers:

\(\displaystyle 2x^{2}-7x-6\)

\(\displaystyle -2x^{2}-x-6\)

\(\displaystyle -2x^{2}-7x-6\)

\(\displaystyle -2x^{2}+7x-6\)

Correct answer:

\(\displaystyle -2x^{2}-7x-6\)

Explanation:

Remember: FOIL (first, outer, inner, last) to expand.

F: \(\displaystyle (-x)(2x)= -2x^{2}\)

O: \(\displaystyle (-x)(3) = -3x\)

I: \(\displaystyle (-2)(2x)=-4x\)

L: \(\displaystyle (-2)(3) =-6\)

 

Now you have four terms:\(\displaystyle -2x^{2}-3x-4x-6\)

Simplify: \(\displaystyle -2x^{2}-7x-6\)

Example Question #1 : Distributive Property

Evaluate.

\(\displaystyle 25 - 2(3 \times 2)\)

Possible Answers:

\(\displaystyle 19\)

\(\displaystyle 22\)

None of the other answers.

\(\displaystyle 13\)

\(\displaystyle 23\)

Correct answer:

\(\displaystyle 13\)

Explanation:

When there is any number next to a set of parentheses the operation is multiplication of that number and anything inside of the parentheses.

Therefore, \(\displaystyle 2(3 \times 2)\) would be the same as  \(\displaystyle 2(6)\: \: [Since \: 3 \times 2 = 6]\). The \(\displaystyle 2\) would be multiplied by the \(\displaystyle 6\) since \(\displaystyle 2(6)\) is the same as \(\displaystyle 2 \times 6\).

The problem becomes \(\displaystyle 25 - 2 \times 6\) and based on the order of operations the multiplication operation would be solved first. \(\displaystyle [2 \times 6 = 12]\)

It solves to \(\displaystyle 25 - 12 = 13\).

Example Question #3 : Distributive Property

Choose the expression that correctly uses the distributive property to solve:

\(\displaystyle 5\times (12-8)\)

Possible Answers:

\(\displaystyle (5\times 12)-(5\times 8)\)

\(\displaystyle 5\times 12-8\)

\(\displaystyle (5\times 12)+(5\times 8)\)

\(\displaystyle (5+12)\times (5+8)\)

\(\displaystyle (5\times 12)-8\)

Correct answer:

\(\displaystyle (5\times 12)-(5\times 8)\)

Explanation:

To properly use the distributive property, multiple the first number by every number in parentheses:

\(\displaystyle (5\times 12)-(5\times 8)\)

Example Question #3 : How To Find The Distributive Property

Multiply:

\(\displaystyle -x(4x+7)\)

Possible Answers:

\(\displaystyle -4x^2-7x\)

\(\displaystyle -4x^2+7x\)

\(\displaystyle 4x^2-7x\)

\(\displaystyle 4x^2+7x\)

Correct answer:

\(\displaystyle -4x^2-7x\)

Explanation:

\(\displaystyle -x(4x+7)=(-x)(4x)+(-x)(7)=(-4x^2)+(-7x)=-4x^2-7x\)

Example Question #1 : How To Find The Distributive Property

Multiply:

\(\displaystyle (3+x)(2-4x)\)

Possible Answers:

\(\displaystyle 6+10x-4x^2\)

\(\displaystyle 6-10x-4x^2\)

\(\displaystyle 6-14x+4x^2\)

\(\displaystyle 6+14x+4x^2\)

Correct answer:

\(\displaystyle 6-10x-4x^2\)

Explanation:

Solve using the FOIL method:

First: \(\displaystyle (3)(2)=6\)

Outside: \(\displaystyle (3)(-4x)=-12x\)

Inside: \(\displaystyle (x)(2)=2x\)

Last: \(\displaystyle (x)(-4x)=-4x^2\)

Add together and combine like terms:

\(\displaystyle 6-12x+2x-4x^2=6-10x-4x^2\)

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