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.

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 |

#### M is a multiple of 26. Which of the following cannot be true?

## M is odd.Hint: All multiples of 26 are also multiples of 2, so they must be even. | |

## M is a multiple of 3.Hint: 3 x 26 is a multiple of both 3 and 26. | |

## M is 26.Hint: 1 x 26 is a multiple of 26. | |

## M is 0.Hint: 0 x 26 is a multiple of 26. |

Question 2 |

#### The histogram below shows the frequency of a class's scores on a 4 question quiz.

#### What was the mean score on the quiz?

\( \large 2.75\) Hint: There were 20 students who took the quiz. Total points earned: \(2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55\), and 55/20 = 2.75. | |

\( \large 2\) Hint: How many students are there total? Did you count them all? | |

\( \large 3\) Hint: How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode. | |

\( \large 2.5\) Hint: How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4 -- you have to weight them properly. |

Question 3 |

#### Below is a portion of a number line.

#### Point A is one-quarter of the distance from 0.26 to 0.28. What number is represented by point A?

\( \large0.26\) Hint: Please reread the question. | |

\( \large0.2625\) Hint: This is one-quarter of the distance between 0.26 and 0.27, which is not what the question asked. | |

\( \large0.265\) | |

\( \large0.27\) Hint: Please read the question more carefully. This answer would be correct if Point A were halfway between the tick marks, but it's not. |

Question 4 |

#### Use the graph below to answer the question that follows:

#### The graph above represents the equation \( \large 3x+Ay=B\), where A and B are integers. What are the values of A and B?

\( \large A = -2, B= 6\) Hint: Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2. | |

\( \large A = 2, B = 6\) Hint: Try plugging (0,-3) into this equation. | |

\( \large A = -1.5, B=-3\) Hint: The problem said that A and B were integers and -1.5 is not an integer. Don't try to use slope-intercept form. | |

\( \large A = 2, B = -3\) Hint: Try plugging (2,0) into this equation. |

Question 5 |

#### A biology class requires a lab fee, which is a whole number of dollars, and the same amount for all students. On Monday the instructor collected $70 in fees, on Tuesday she collected $126, and on Wednesday she collected $266. What is the largest possible amount the fee could be?

## $2Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $7Hint: A possible fee, but not the largest possible fee. Check the other choices to see which are factors of all three numbers. | |

## $14Hint: This is the greatest common factor of 70, 126, and 266. | |

## $70Hint: Not a factor of 126 or 266, so couldn't be correct. |

Question 6 |

#### Kendra is trying to decide which fraction is greater, \( \dfrac{4}{7}\) or \( \dfrac{5}{8}\). Which of the following answers shows the best reasoning?

## \( \dfrac{4}{7}\) is \( \dfrac{3}{7}\)away from 1, and \( \dfrac{5}{8}\) is \( \dfrac{3}{8}\)away from 1. Since eighth‘s are smaller than seventh‘s, \( \dfrac{5}{8}\) is closer to 1, and is the greater of the two fractions. | |

## \( 7-4=3\) and \( 8-5=3\), so the fractions are equal.Hint: Not how to compare fractions. By this logic, 1/2 and 3/4 are equal, but 1/2 and 2/4 are not. | |

## \( 4\times 8=32\) and \( 7\times 5=35\). Since \( 32<35\) , \( \dfrac{5}{8}<\dfrac{4}{7}\)Hint: Starts out as something that works, but the conclusion is wrong. 4/7 = 32/56 and 5/8 = 35/56. The cross multiplication gives the numerators, and 35/56 is bigger. | |

## \( 4<5\) and \( 7<8\), so \( \dfrac{4}{7}<\dfrac{5}{8}\)Hint: Conclusion is correct, logic is wrong. With this reasoning, 1/2 would be less than 2/100,000. |

Question 7 |

#### Exactly one of the numbers below is a prime number. Which one is it?

\( \large511 \) Hint: Divisible by 7. | |

\( \large517\) Hint: Divisible by 11. | |

\( \large519\) Hint: Divisible by 3. | |

\( \large521\) |

Question 8 |

#### Which of the graphs below represent functions?

**I.**

**II.**

**III.**

**IV.**

## I and IV only.Hint: There are vertical lines that go through 2 points in IV . | |

## I and III only.Hint: Even though III is not continuous, it's still a function (assuming that vertical lines between the "steps" do not go through 2 points). | |

## II and III only.Hint: Learn about the vertical line test. | |

## I, II, and IV only.Hint: There are vertical lines that go through 2 points in II. |

Question 9 |

#### A cylindrical soup can has diameter 7 cm and height 11 cm. The can holds g grams of soup. How many grams of the same soup could a cylindrical can with diameter 14 cm and height 33 cm hold?

\( \large 6g\) Hint: You must scale in all three dimensions. | |

\( \large 12g\) Hint: Height is multiplied by 3, and diameter and radius are multiplied by 2. Since the radius is squared, final result is multiplied by \(2^2\times 3=12\). | |

\( \large 18g\) Hint: Don't square the height scale factor. | |

\( \large 36g\) Hint: Don't square the height scale factor. |

Question 10 |

#### Below are front, side, and top views of a three-dimensional solid.

#### Which of the following could be the solid shown above?

## A sphereHint: All views would be circles. | |

## A cylinder | |

## A coneHint: Two views would be triangles, not rectangles. | |

## A pyramidHint: How would one view be a circle? |

Question 11 |

#### Which of the numbers below is the decimal equivalent of \( \dfrac{3}{8}?\)

## 0.38Hint: If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct. | |

## 0.125Hint: This is 1/8, not 3/8. | |

## 0.375 | |

## 0.83Hint: 3/8 is less than a half, and 0.83 is more than a half, so they can't be equal. |

Question 12 |

#### Below is a pictorial representation of \(2\dfrac{1}{2}\div \dfrac{2}{3}\):

#### Which of the following is the best description of how to find the quotient from the picture?

## The quotient is \(3\dfrac{3}{4}\). There are 3 whole blocks each representing \(\dfrac{2}{3}\) and a partial block composed of 3 small rectangles. The 3 small rectangles represent \(\dfrac{3}{4}\) of \(\dfrac{2}{3}\). | |

## The quotient is \(3\dfrac{1}{2}\). There are 3 whole blocks each representing \(\dfrac{2}{3}\) and a partial block composed of 3 small rectangles. The 3 small rectangles represent \(\dfrac{3}{6}\) of a whole, or \(\dfrac{1}{2}\).Hint: We are counting how many 2/3's are in 2 1/2: the unit becomes 2/3, not 1. | |

## The quotient is \(\dfrac{4}{15}\). There are four whole blocks separated into a total of 15 small rectangles.Hint: This explanation doesn't make much sense. Probably you are doing "invert and multiply," but inverting the wrong thing. | |

## This picture cannot be used to find the quotient because it does not show how to separate \(2\dfrac{1}{2}\) into equal sized groups.Hint: Study the measurement/quotative model of division. It's often very useful with fractions. |

Question 13 |

\( \large \dfrac{17}{24}\) Hint: You might try adding segments so each quadrant is divided into 6 pieces with equal area -- there will be 24 regions, not all the same shape, but all the same area, with 17 of them shaded (for the top left quarter, you could also first change the diagonal line to a horizontal or vertical line that divides the square in two equal pieces and shade one) . | |

\( \large \dfrac{3}{4}\) Hint: Be sure you're taking into account the different sizes of the pieces. | |

\( \large \dfrac{2}{3}\) Hint: The bottom half of the picture is 2/3 shaded, and the top half is more than 2/3 shaded, so this answer is too small. | |

\( \large \dfrac{17}{6} \) Hint: This answer is bigger than 1, so doesn't make any sense. Be sure you are using the whole picture, not one quadrant, as the unit. |

Question 14 |

#### Use the graph below to answer the question that follows.

#### Which of the following is a correct equation for the graph of the line depicted above?

\( \large y=-\dfrac{1}{2}x+2\) Hint: The slope is -1/2 and the y-intercept is 2. You can also try just plugging in points. For example, this is the only choice that gives y=1 when x=2. | |

\( \large 4x=2y\) Hint: This line goes through (0,0); the graph above does not. | |

\( \large y=x+2\) Hint: The line pictured has negative slope. | |

\( \large y=-x+2\) Hint: Try plugging x=4 into this equation and see if that point is on the graph above. |

Question 15 |

#### The letters A, and B represent digits (possibly equal) in the ten digit number x=1,438,152,A3B. For which values of A and B is x divisible by 12, but not by 9?

\( \large A = 0, B = 4\) Hint: Digits add to 31, so not divisible by 3, so not divisible by 12. | |

\( \large A = 7, B = 2\) Hint: Digits add to 36, so divisible by 9. | |

\( \large A = 0, B = 6\) Hint: Digits add to 33, divisible by 3, not 9. Last digits are 36, so divisible by 4, and hence by 12. | |

\( \large A = 4, B = 8\) Hint: Digits add to 39, divisible by 3, not 9. Last digits are 38, so not divisible by 4, so not divisible by 12. |

Question 16 |

#### The "houses" below are made of toothpicks and gum drops.

#### Which of the following does not represent the number of gumdrops in a row of h houses?

\( \large 2+3h\) Hint: Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house. | |

\( \large 5+3(h-1)\) Hint: Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses. | |

\( \large h+(h+1)+(h+1)\) Hint: Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors. | |

\( \large 5+3h\) Hint: This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3. |

Question 17 |

#### P is a prime number that divides 240. Which of the following must be true?

## P divides 30Hint: 2, 3, and 5 are the prime factors of 240, and all divide 30. | |

## P divides 48Hint: P=5 doesn't work. | |

## P divides 75Hint: P=2 doesn't work. | |

## P divides 80Hint: P=3 doesn't work. |

Question 18 |

#### The first histogram shows the average life expectancies for women in different countries in Africa in 1998; the second histogram gives similar data for Europe:

#### How much bigger is the range of the data for Africa than the range of the data for Europe?

## 0 yearsHint: Range is the maximum life expectancy minus the minimum life expectancy. | |

## 12 yearsHint: Are you subtracting frequencies? Range is about values of the data, not frequency. | |

## 18 yearsHint: It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18. | |

## 42 yearsHint: Read the question more carefully. |

Question 19 |

#### In the triangle below, \(\overline{AC}\cong \overline{AD}\cong \overline{DE}\) and \(m\angle CAD=100{}^\circ \). What is \(m\angle DAE\)?

\( \large 20{}^\circ \) Hint: Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each. | |

\( \large 25{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 30{}^\circ \) Hint: If two sides of a triangle are congruent, then it's isosceles, and the base angles of an isosceles triangle are equal. | |

\( \large 40{}^\circ \) Hint: Make sure you're calculating the correct angle. |

Question 20 |

#### Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them). They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15.

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

\( \large 8x+16x=9x+15x\) Hint: What would x represent in this case? Make sure you can describe in words what x represents. | |

\( \large x+(x+2)=(x+1)+(x+1)\) Hint: What would x represent in this case? Make sure you can describe in words what x represents. | |

\( \large x+(x+8)=(x+1)+(x+7)\) 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. | |

\( \large x+8+16=x+9+15\) Hint: What would x represent in this case? Make sure you can describe in words what x represents. |

List |

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