Hints will display for most wrong answers; explanations for most right answers.   You can attempt a question multiple times; it will only be scored correct if you get it right the first time.  To see ten new questions, reload the page.

I used the official objectives and sample test to construct these questions, but cannot promise that they accurately reflect what’s on the real test.   Some of the sample questions were more convoluted than I could bear to write.   See terms of use.   See the MTEL Practice Test main page to view questions on a particular topic or to download paper practice tests.

## MTEL General Curriculum Mathematics Practice

 Question 1
 I. $$\large \dfrac{1}{2}+\dfrac{1}{3}$$ II. $$\large .400000$$ III. $$\large\dfrac{1}{5}+\dfrac{1}{5}$$ IV. $$\large 40\%$$ V. $$\large 0.25$$ VI. $$\large\dfrac{14}{35}$$

#### I, III, V, VI

Hint:
I and V are not at all how fractions and decimals work.

#### III, VI

Hint:
These are right, but there are more.

#### II, III, VI

Hint:
These are right, but there are more.

#### II, III, IV, VI

Question 1 Explanation:
Topic: Converting between fractions, decimals, and percents (Objective 0017)
 Question 2

#### The expression $$\large{{8}^{3}}\cdot {{2}^{-10}}$$ is equal to which of the following?

 A $$\large 2$$Hint: Write $$8^3$$ as a power of 2. B $$\large \dfrac{1}{2}$$Hint: $$8^3 \cdot {2}^{-10}={(2^3)}^3 \cdot {2}^{-10}$$ =$$2^9 \cdot {2}^{-10} =2^{-1}$$ C $$\large 16$$Hint: Write $$8^3$$ as a power of 2. D $$\large \dfrac{1}{16}$$Hint: Write $$8^3$$ as a power of 2.
Question 2 Explanation:
Topic: Laws of Exponents (Objective 0019).
 Question 3

#### Let d represent the distance a passenger travels in miles (with $$d>\dfrac{1}{7}$$). Which of the following expressions represents the total fare?

 A $$\large \2.60+\0.40d$$Hint: It's 40 cents for 1/7 of a mile, not per mile. B $$\large \2.60+\0.40\dfrac{d}{7}$$Hint: According to this equation, going 7 miles would cost $3; does that make sense? C $$\large \2.20+\2.80d$$Hint: You can think of the fare as$2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or$2.80 per mile). Alternatively, you pay $2.60 for the first 1/7 of a mile, and then$2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d. D $$\large \2.60+\2.80d$$Hint: Don't count the first 1/7 of a mile twice.
Question 3 Explanation:
Topic: Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020), and select the linear equation that best models a real-world situation (Objective 0022).
 Question 4

#### A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

 A $$\large 28 \dfrac{4}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine. B $$\large 28 \dfrac{1}{4}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? C $$\large 28 \dfrac{1}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? D $$\large 87.5$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
Question 4 Explanation:
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
 Question 5

#### The student‘s solution is correct.

Hint:
Try plugging into the original solution.

#### 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.

#### The student did not correctly use the distributive property.

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

#### The student did not correctly use the commutative property.

Hint:
Commutative property is $$a+b=b+a$$ or $$ab=ba$$.
Question 5 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 6

#### $$\large A-B+C\div D\times E$$?

 A $$\large A-B-\dfrac{C}{DE}$$Hint: In the order of operations, multiplication and division have the same priority, so do them left to right; same with addition and subtraction. B $$\large A-B+\dfrac{CE}{D}$$Hint: In practice, you're better off using parentheses than writing an expression like the one in the question. The PEMDAS acronym that many people memorize is misleading. Multiplication and division have equal priority and are done left to right. They have higher priority than addition and subtraction. Addition and subtraction also have equal priority and are done left to right. C $$\large \dfrac{AE-BE+CE}{D}$$Hint: Use order of operations, don't just compute left to right. D $$\large A-B+\dfrac{C}{DE}$$Hint: In the order of operations, multiplication and division have the same priority, so do them left to right
Question 6 Explanation:
Topic: Justify algebraic manipulations by application of the properties of order of operations (Objective 0020).
 Question 7

#### Which of the equations below could best be used to explain why the children's conjecture is correct?

 A $$\large 8x+16x=9x+15x$$Hint: What would x represent in this case? Make sure you can describe in words what x represents. B $$\large x+(x+2)=(x+1)+(x+1)$$Hint: What would x represent in this case? Make sure you can describe in words what x represents. C $$\large x+(x+8)=(x+1)+(x+7)$$Hint: x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x. D $$\large x+8+16=x+9+15$$Hint: What would x represent in this case? Make sure you can describe in words what x represents.
Question 7 Explanation:
Topic: Recognize and apply the concepts of variable, equality, and equation to express relationships algebraically (Objective 0020).
 Question 8

#### It is too high by a factor of 100

Question 8 Explanation:
Topics: Estimation, Scientific Notation in the real world (Objective 0016).
 Question 9

#### The result is always the number that you started with! Suppose you start by picking N. Which of the equations below best demonstrates that the result after Step 6 is also N?

 A $$\large N*2+20*5-100\div 10=N$$Hint: Use parentheses or else order of operations is off. B $$\large \left( \left( 2*N+20 \right)*5-100 \right)\div 10=N$$ C $$\large \left( N+N+20 \right)*5-100\div 10=N$$Hint: With this answer you would subtract 10, instead of subtracting 100 and then dividing by 10. D $$\large \left( \left( \left( N\div 10 \right)-100 \right)*5+20 \right)*2=N$$Hint: This answer is quite backwards.
Question 9 Explanation:
Topic: Recognize and apply the concepts of variable, function, equality, and equation to express relationships algebraically (Objective 0020).
 Question 10

#### The picture below represents a board with pegs on it, where the closest distance between two pegs is 1 cm.  What is the area of the pentagon shown?

 A $$\large 8\text{ c}{{\text{m}}^{2}}$$Hint: Don't just count the dots inside, that doesn't give the area. Try adding segments so that the slanted lines become the diagonals of rectangles. B $$\large 11\text{ c}{{\text{m}}^{2}}$$Hint: Try adding segments so that the slanted lines become the diagonals of rectangles. C $$\large 11.5\text{ c}{{\text{m}}^{2}}$$Hint: An easy way to do this problem is to use Pick's Theorem (of course, it's better if you understand why Pick's theorem works): area = # pegs inside + half # pegs on the border - 1. In this case 8+9/2-1=11.5. A more appropriate strategy for elementary classrooms is to add segments; here's one way. There are 20 1x1 squares enclosed, and the total area of the triangles that need to be subtracted is 8.5 D $$\large 12.5\text{ c}{{\text{m}}^{2}}$$Hint: Try adding segments so that the slanted lines become the diagonals of rectangles.
Question 10 Explanation:
Topics: Calculate measurements and derive and use formulas for calculating the areas of geometric shapes and figures (Objective 0023).
There are 10 questions to complete.

If you found a mistake or have comments on a particular question, please contact me (please copy and paste at least part of the question into the form, as the numbers change depending on how quizzes are displayed).   General comments can be left here.