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MTEL General Curriculum Mathematics Practice

Question 1

A sales companies pays its representatives $2 for each item sold, plus 40% of the price of the item.   The rest of the money that the representatives collect goes to the company.  All transactions are in cash, and all items cost $4 or more.   If the price of an item in dollars is p, which expression represents the amount of money the company collects when the item is sold?

A
\( \large \dfrac{3}{5}p-2\)
Hint:
The company gets 3/5=60% of the price, minus the $2 per item.
B
\( \large \dfrac{3}{5}\left( p-2 \right)\)
Hint:
This is sensible, but not what the problem states.
C
\( \large \dfrac{2}{5}p+2\)
Hint:
The company pays the extra $2; it doesn't collect it.
D
\( \large \dfrac{2}{5}p-2\)
Hint:
This has the company getting 2/5 = 40% of the price of each item, but that's what the representative gets.
Question 1 Explanation: 
Topic: Use algebra to solve word problems involving fractions, ratios, proportions, and percents (Objective 0020).
Question 2

Use the problem below to answer the question that follows:

T shirts are on sale for 20% off. Tasha paid $8.73 for a shirt.  What is the regular price of the shirt? There is no tax on clothing purchases under $175.

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

A
\( \large 0.8p=\$8.73\)
Hint:
80% of the regular price = $8.73.
B
\( \large \$8.73+0.2*\$8.73=p\)
Hint:
The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c.
C
\( \large 1.2*\$8.73=p\)
Hint:
The 20% off was off of the ORIGINAL price, not off the $8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b.
D
\( \large p-0.2*\$8.73=p\)
Hint:
Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.
Question 2 Explanation: 
Topics: Use algebra to solve word problems involving percents and identify variables, and derive algebraic expressions that represent real-world situations (Objective 0020).
Question 3

The expression \( \large {{7}^{-4}}\cdot {{8}^{-6}}\) is equal to which of the following?

A
\( \large \dfrac{8}{{{\left( 56 \right)}^{4}}}\)
Hint:
The bases are whole numbers, and the exponents are negative. How can the numerator be 8?
B
\( \large \dfrac{64}{{{\left( 56 \right)}^{4}}}\)
Hint:
The bases are whole numbers, and the exponents are negative. How can the numerator be 64?
C
\( \large \dfrac{1}{8\cdot {{\left( 56 \right)}^{4}}}\)
Hint:
\(8^{-6}=8^{-4} \times 8^{-2}\)
D
\( \large \dfrac{1}{64\cdot {{\left( 56 \right)}^{4}}}\)
Question 3 Explanation: 
Topics: Laws of exponents (Objective 0019).
Question 4

Here is a student's work solving an equation:

\( x-4=-2x+6\)

\( x-4+4=-2x+6+4\)

\( x=-2x+10\)

\( x-2x=10\)

\( x=10\)

Which of the following statements is true?

A

The student‘s solution is correct.

Hint:
Try plugging into the original solution.
B

The student did not correctly use properties of equality.

Hint:
After \( x=-2x+10\), the student subtracted 2x on the left and added 2x on the right.
C

The student did not correctly use the distributive property.

Hint:
Distributive property is \(a(b+c)=ab+ac\).
D

The student did not correctly use the commutative property.

Hint:
Commutative property is \(a+b=b+a\) or \(ab=ba\).
Question 4 Explanation: 
Topic: Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties (Objective 0020).
Question 5

Which of the following points is closest to \( \dfrac{34}{135} \times \dfrac{53}{86}\)?

A

A

Hint:
\(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A.
B

B

Hint:
Estimate with simpler fractions.
C

C

Hint:
Estimate with simpler fractions.
D

D

Hint:
Estimate with simpler fractions.
Question 5 Explanation: 
Topic: Understand meaning and models of operations on fractions (Objective 0019).
There are 5 questions to complete.

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