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CLT Practice Exam - 2025
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1. Which of the following is equivalent to [latex] 3(2 - 5) + 3 \times 7 [/latex]?
First, simplify the expression inside the parentheses: [latex] 3(2 - 5) = 3 \times (-3) = -9 [/latex]. Then add the multiplication: [latex] 3 \times 7 = 21 [/latex]. Now add the two results: [latex] -9 + 21 = 12 [/latex].
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2. Which of the following could be the next term in the arithmetic sequence below? [latex] 2, 5, 8, 11, ? [/latex]
The common difference between consecutive terms in the arithmetic sequence is [latex] 3 [/latex]. Therefore, the next term after 11 is [latex] 11 + 3 = 14 [/latex].
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3. Which of the following is equivalent to [latex] (-2)^3 + 5^2 [/latex]?
Simplify each part separately: [latex] (-2)^3 = -8 [/latex] and [latex] 5^2 = 25 [/latex]. Then add the results: [latex] -8 + 25 = 17 [/latex].
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4. Simplify the expression [latex]\frac{5x^3y^2}{15x^2y}[/latex]
Simplify by canceling common factors in the numerator and denominator: [latex] \frac{5x^3y^2}{15x^2y} = \frac{5}{15} times \frac{x^3}{x^2} \times \frac{y^2}{y} = \frac{1}{3} \times x \times y = \frac{xy}{3} [/latex].
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5. If ~ is defined such that a ~ b = [latex] 3a^2 - b [/latex], which of the following is equivalent to [latex] (-1) [/latex] ~ [latex] (-5) [/latex]?
Using the definition of the operation, substitute [latex] a = -1 [/latex] and [latex] b = -5 [/latex]. This gives [latex] (-1) (-5) = 3(-1)^2 - (-5) = 3(1) + 5 = 8 [/latex].
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6. How many integers between [latex] 100 [/latex] and [latex] 120 [/latex] (inclusive) meet both of the conditions?
1. The sum of the digits is greater than 5.
2. The integer is prime.
The prime numbers between [latex] 100 [/latex] and [latex] 120 [/latex] are [latex] 101, 103, 107, 109, 113 [/latex]. Only [latex] 107 [/latex] and [latex] 109 [/latex] have digit sums greater than 5. Therefore, there are 2 integers that meet both conditions.
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7. A student proposes the following rule: All isosceles triangles are also equilateral triangles. Which of the following is a counterexample?
An isosceles triangle has two equal angles, but an equilateral triangle has three equal angles. A triangle with angles 55°, 55°, and 70° is isosceles but not equilateral, so it is a counterexample.
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8. What is the slope of the line defined by the equation [latex] 3x - 5 = 0 [/latex]?
The equation [latex] 3x - 5 = 0 [/latex] simplifies to [latex] x = \frac{5}{3} [/latex], which represents a vertical line. Vertical lines have an undefined slope.
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9. If the equation [latex]x^2 + bx + 4 = 0[/latex] has only one solution, and [latex]b[/latex] is a positive integer, which of the following could be the value of [latex]b[/latex]?
For the quadratic equation to have one solution, the discriminant must be zero. Solving [latex]b^2 - 16 = 0[/latex] gives [latex]b = pm 4[/latex]. Therefore, [latex]b[/latex] could be 4.
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10. What is the x-coordinate of the solution of the system of equations below? [latex]x + y = 10[/latex]
and [latex]-x + 2y = 2[/latex]
From the first equation, solve for [latex]y[/latex]: [latex]y = 10 - x[/latex]. Substitute into the second equation: [latex]-x + 2(10 - x) = 2[/latex]. Simplifying gives [latex]x = 6[/latex].
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11. Which of the following is an equation of a line that is perpendicular to the line [latex]y = -3x + 7[/latex]?
The slope of the line [latex]y = -3x + 7[/latex] is -3. The slope of a line perpendicular to it is the negative reciprocal, [latex] frac{1}{3}[/latex]. Therefore, the line [latex]y = frac{1}{3}x - 7[/latex] is perpendicular.
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12. Which of the following expressions is equivalent to [latex]\frac{(x^7)(y^3)}{(x^5)(y^2)}[/latex]?
Simplify the expression by subtracting the exponents of [latex]x[/latex] and [latex]y[/latex]. This gives [latex]x^{7 - 5}y^{3 - 2} = x^2y[/latex].
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13. A poster is delivered in a right cylindrical container made of cardboard, with a plastic top and bottom. If the radius of the top and bottom is 10 cm and the height is 100 cm, what is the surface area of the cardboard portion of the container?
The surface area of the cylindrical side is given by the formula [latex]2pi rh[/latex], where [latex]r[/latex] is the radius and [latex]h[/latex] is the height. Substituting [latex]r = 10[/latex] and [latex]h = 100[/latex], the surface area is [latex]2000pi[/latex] square centimeters.
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14. Let [latex]c[/latex] be an integer. If [latex]c > 0[/latex], [latex]d > c[/latex], and [latex]d[/latex] is prime, then which of the following must be true of [latex](cd)^2[/latex]?
[latex](cd)^2[/latex] is positive and larger than both [latex]c[/latex] and [latex]d[/latex]. Therefore, [latex](cd)^2[/latex] must be greater than [latex]d^3c[/latex].
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15. An isosceles triangle has one interior angle that measures 20°. What are the measures of the other two angles?
In an isosceles triangle, two angles are equal. The sum of the angles in a triangle is 180°. If one angle is 20°, the sum of the other two angles is 160°, so each must be 80°.
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16. If m is an odd negative integer, which of the following describes [latex] -m^2 [/latex]?
Since [latex] m^2 [/latex] is the square of an odd number, it is positive, and multiplying by [latex] -1 [/latex] makes it negative. Therefore, [latex] -m^2 [/latex] is an odd negative integer.
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17. In triangle ABC, AB = 15 in, BC = 13 in, and AC = 10 in. Which angle in the triangle has the largest measure?
In any triangle, the largest angle is opposite the longest side. The longest side here is AB = 15 in, so the largest angle is [latex] C [/latex].
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18. What is the value of [latex] x [/latex] in the rectangle below? (Note: The figure is not necessarily drawn to scale.)
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19. In a pet store, different kinds of pets are sold. Of the pets that the store currently has, [latex]\frac{1}{3}[/latex] of the pets are rabbits and [latex]\frac{1}{3}[/latex] are cats. The rest are birds, ferrets, and guinea pigs. There are two birds for every guinea pig and an equal number of ferrets and guinea pigs. Based on this information, which of the following is NOT true?
First, calculate the proportion of the remaining pets. After removing the rabbits and cats, [latex]\frac{1}{3}[/latex] of the pets remain. Based on the given ratios, birds, ferrets, and guinea pigs can be distributed as follows: Ferrets and guinea pigs each make up [latex]\frac{1}{9}[/latex] of the total, and birds make up [latex]\frac{2}{9}[/latex] of the total.
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20. If [latex] |2 + x^3| > 5 [/latex]. Which of the following could be the value of [latex] x [/latex]?
Just sub in values and ensure to take absolute value function into account. Subbing in -2, produces 6 which is indeed greater than 5.
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21. Which transformation of point [latex] A(-2, 3) [/latex] results in the image [latex] A'(2, 3) [/latex]?
The transformation involves reflecting the point across the y-axis, changing the sign of the x-coordinate while keeping the y-coordinate the same.
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22. Annabelle's English class has 20% more students than her social studies class. If her social studies class has 20 students, how many students are in her English class?
To calculate 20% more than 20, multiply 20 by 1.2: [latex] 20 times 1.2 = 24 [/latex]. Therefore, there are 24 students in her English class.
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23. Three congruent equilateral triangles are arranged so that they form an isosceles trapezoid. If the perimeter of one of the triangles is 24 in, what is the perimeter of the trapezoid?
Each equilateral triangle has a perimeter of 24 in, so each side of the triangle is [latex] 24/3 = 8 [/latex] in. The trapezoid has a base made up of two triangle sides (8 + 8 = 16 in), plus two more triangle sides for the legs, and another side for the top. Thus, the perimeter is [latex] 16 + 8 + 8 + 8 = 40 [/latex] in.
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24. A circle has a diameter of 12 cm. What is the circumference of the circle? [latex] pi = 3.14159 [/latex]
The formula for the circumference of a circle is [latex] C = pi \times d [/latex], where [latex] d [/latex] is the diameter. Since the diameter is 12 cm, the circumference is [latex] 12pi [/latex] cm.
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25. A molecule of potassium sorbate contains one potassium atom, seven hydrogen atoms, six carbon atoms, and two oxygen atoms. If a sample of potassium sorbate contains 56 hydrogen atoms, how many TOTAL potassium and oxygen atoms does that sample have?
The ratio of hydrogen atoms to potassium and oxygen atoms in one molecule is 7:3. If there are 56 hydrogen atoms, this corresponds to 8 molecules of potassium sorbate. Therefore, the sample contains [latex] 8 times 3 = 24 [/latex] total potassium and oxygen atoms.
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26. Planet Z has an atmosphere with 25% nitrogen. Planet Y's atmosphere contains 30% oxygen and 50% nitrogen. Planet X's atmosphere consists of 40% carbon dioxide, 30% oxygen, and 30% nitrogen. An astrophysicist predicts that Planet Z, Planet Y, and Planet X will each increase their nitrogen levels by 50% over the next millennium. If her prediction is accurate, which of the following would be true of the three planets' atmospheres after the next millennium?
1. Planet Z to have an atmoshpere with 75% Nitrogen
2. Planet Y will still have proportionally the highest Nitrogen levels of all
3. Planet X will lose about 15% of its Oxygen.
This is an increase in percentage problem. Imagine we have 100milliliters of air in a balloon. Apply the new percentage change and you will see the answer is B.
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27. A set of four positive consecutive integers includes three prime numbers. What is the sum of this set?
The four consecutive integers are 2, 3, 4, and 5. Among them, 2, 3, and 5 are prime numbers. The sum of these integers is [latex] 2 + 3 + 4 + 5 = 14 [/latex].
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28. A student analyzes the velocities of four different cars. Each car starts with an initial velocity of zero, [latex] V_0 [/latex], and has a constant acceleration of [latex] a [/latex]. The velocity [latex] v [/latex] at time [latex] t [/latex] is given by the equation: [latex] v = v_0 + at [/latex]. The student notes that Car A's velocity and Car B's velocity are the same for some [latex] t > 0 [/latex]. Car C's acceleration was three times the acceleration of Car A and of Car B at time [latex] t [/latex]. Car D's velocity was 1/6 that of Car C at time [latex] t [/latex]. Which of the following can be concluded?
Car C's velocity at time [latex] t [/latex] is three times that of Car A and Car B. Since Car D's velocity is 1/6 that of Car C, the velocity ratio is 2:1:6 for Car A, Car D, and Car C.
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29. If m is an odd negative integer, which of the following describes [latex] -m^3 [/latex]?
Since m is an odd negative integer, [latex] -m^3 [/latex] is an odd positive integer.
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30. In triangle ABC, AB = 17 in, BC = 12 in, and AC = 8 in. Which angle in the triangle has the largest measure?
In any triangle, the largest angle is opposite the longest side. The longest side here is AB = 17 in, so the largest angle is C.
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31. In a pet store, [latex]\frac{1}{4} [/latex] of the pets are rabbits and [latex] \frac{1}{3} [/latex] are cats. The rest are birds, ferrets, and guinea pigs. Which of the following is NOT true?
From the given fractions, we calculate the proportions for ferrets, guinea pigs, and birds. Ferrets make up [latex] \frac{1}{8} [/latex], not [latex] \frac{1}{9} [/latex].
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32. If [latex] |2 + x^4| > 9 [/latex], which of the following could be the value of [latex] x [/latex]?
By solving the inequality [latex] |2 + x^4| > 9 [/latex], we find that the possible value of [latex] x [/latex] is 3.
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33. A set of five consecutive integers includes three prime numbers. What is the sum of this set?
The set of integers [latex] 5, 6, 7, 8, 9 [/latex]contains the primes 5 and 7. The sum of the set is 35.
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34. Car A’s velocity is equal to Car B’s at [latex]t > 0[/latex], Car C’s acceleration is 4 times Car A’s, and Car D’s velocity is [latex]1/8 [/latex]that of Car C’s. What can be concluded?
Given the ratios of velocities, the correct conclusion is that the ratio of Car A to Car D to Car C is[latex] 4:1:8.[/latex]
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35. If @ is defined such that [latex]a@b = 4a^2 - b [/latex], what is equivalent to [latex](-2)@(-6)? [/latex]
Using the definition of @, [latex] (-2)@(-6) = 4(-2)^2 - (-6) = 16 + 6 = 22. [/latex]
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