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**Q1. x + 9 = 13, Find x = ?**

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**Answer: B**
Isolate the unknown on one side. Subtract 9 => from each side x = 13 – 9 => x = 4

**Q2. 3² + 4(5 – 2) = ?**

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**Answer: A**
Perform operations in parentheses first, then exponents, and then the remaining operations.

**Q3.** 1 \frac14 × 2 \frac12 = ?

- A. 2 \frac12
- B. 2 \frac14
- C. 2\frac34
- D. 3 \frac18

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**Answer: D**
Change the mixed numbers to improper fractions. Carry out the operation by multiplying thet wo numerators and the two denominators.

**Q4. The square root of 64 =**

**Q5. . What is the value of the following expression if x = 2 and y = 4? **

**2x³y²**

- A. 52
- B. 106
- C. 256
- D. 512

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**Answer: C**
Substitute 2 for x and 4 for y into the expression. Multiply out the exponents.

**Q6. Add:**

**3x² + 3xy + 4y + 2y²**

**3x² + xy + 9y + y²**

**−5x² − 2xy − 13y + y²**

**−3x² + 3xy + y − 4y**

- A. 2x + xy + 2y + y²
- B. − 2x − xy + y + y²
- C. −3x² − 2xy − 3y + y²
- D. −2x² + 5xy + y

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**Answer: D **

**Q7. Factor the following expression:** y² − 16y + 48

- A. (y − 1)(y +48)
- B. (y − 4)(y − 12)
- C. (y − 4)(y + 4)
- D. (y +1)(y − 16)

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**Answer: B**
Note the minus sign in the middle term and the plus sign in the third term. This should tell you that the factors will contain a minus sign in

each term. In this problem, the fact that the two terms will have a minus sign should lead you to the correct answer, as only one answer has a minus sign in each term. However, not all questions of this type will have that kind of clue. Note that the first term in each factor will be y. Now you need to find two numbers that multiply to 48 and add to 16. Those numbers are 4 and 12. This gives the factors (y − 4)(y − 12)

**Q8. Solve for x. **12x + 6 = 8x +10

- A. x = 1
- B. x = 2
- C. x = 4
- D. x = 6

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**Answer: A**
To solve such problems, move all the terms with an unknown to one side of the equal sign and the numbers to the other.

**Q9. Solve for the two unknowns.**

3y + 3x = 24

6y + 3x = 39

- A. y = 3; x = 5
- B. y = 4; x = 6
- C. y = 5; x = 3
- D. y = 6; x = 2

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**Answer: C**
Set each equation equal to zero. Next, arrange one of the equations so that when it is subtracted from or added to the other equation, one of the terms becomes zero and drops out of the equation. Next, solve for the remaining unknown.

Q10. **x¹² / x**^{4}

- A. x
^{−}^{4}
- B. x
^{8}
- C. x
^{18}
- D. x
^{−16}

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**Answer: B**
To divide numbers with exponents, subtract the exponents. In this problem, subtract the 4 from the 12, leaving x^{8} as the correct answer.

**Q11. Solve for y. **

**y² + 7y = −10**

- A. y = −5; y = −2
- B. y = 1; y = −10
- C. y = −2; y = 6
- D. y = 5; y = −1

View Correct Answer

**Answer: A**
Set the equation to equal zero:

**Q12. Multiply:** \frac{6y}{11} × \frac{2}{5x}

- A. 6y + 5x =22
- B. 22y / 5x
- C. 5y/ 22x
- D. 22y / 55x

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**Answer: D**
multiply fractions, multiply the numerators and denominators.

**Q13. Divide:** \frac{6x}{11} ÷ \frac{2}{5y}

- A. 3y + 11x =2
- B. 15xy / 11
- C. 12/ 22xy
- D. 11y / 25x

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**Answer: B**
To divide fractions, invert the second term and multiply.

**Q14.** \sqrt[3]27

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**Answer: A**
The cube root is the number that, when multiplied by itself three times, results in the answer. In this instance, 3 × 3 × 3 = 27, so the cube root of 27 = 3.

*To answer most questions of this type on the ASVAB, you just need to memorize some basic cubes. It would be wise to memorize all the*

*cubes from 2 to 10, just to prepare for ASVAB test item possibilities*

**Q15. Solve for g ** \fracgh =a

- A. ga / h
- B. g =a/h
- C. g = ah
- D. g = a ÷ h

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**Answer: C**
Isolate the variable of interest on one side of the equation. In this problem, you must multiply each side by h, leaving g on the left side of the

equation and h on the right side. Therefore, the answer is g = ah.

**Q16. Which of the following is an equilateral triangle?**

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**Answer: D**
An equilateral triangle has three equal sides and angles, so D is the correct answer.

**Q17. What is the perimeter of the following rectangle?**

- A. 12 m
- B. 18 m
- C. 24 m
- D. 12 m

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**Answer: C**
To find the perimeter of a quadrilateral, add the lengths of the four sides. In this instance, 9 meters + 9 meters + 3 meters + 3 meters + 24

meters, the correct answer

**Q18. What is the circumference of the following circle?**

- A. 6.56 m
- B. 12.56 m
- C. 25.12 m
- D. 35.12 m

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**Answer: C**
The formula for the circumference of a circle is Πd. The figure gives the radius, which is one-half the length of the diameter. To find the diameter, multiply the radius by 2. In this problem, the diameter is 8 meters. Multiplying 8 by Π gives the correct answer of 25.12 meters.

**Q19. In the following equilateral triangle, what is the measure of ∠1?**

- A. 30°
- B. 45°
- C. 60°
- D. 90°

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**Answer: C**
An equilateral triangle has three equal angles. A triangle has a total of 180°, so each angle must be 60°.

**20. If ∠1 is 34°, what is the measure of ∠2?**

- A. 56°
- B. 110°
- C. 146°
- D. 180°

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**Answer: C**
A straight line or straight angle is 180°. So if **∠**1 is 34°, **∠**2 is the difference between 180° and 34°, or 146°.

**Q21. In the following right triangle, what is the length of side AB?**

- A. 3 m
- B. 5 m
- C. 7 m
- D. 12 m

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**Answer: B**
**∠**C is a right angle, so you can employ the Pythagorean Theorem

**Q22. What is the area of the following triangle?**

- A. 8 ft²
- B. 12 ft²
- C. 15 ft²
- D. 16 ft²

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**Answer: D**
This is a right triangle, so 4 ft is the height of the triangle and 8 ft is the base. The formula for the area of a triangle is ½ bh.

**Q23. What is the diameter of the following circle?**

- A. 40 cm
- B. 80 cm
- C. 160 cm
- D. 640 cm

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**Answer: C**
The diameter is 2r. r = 80 cm, so the diameter is 160 cm.

**Q24. If lines A and B are parallel and are intersected by line C and ∠2 is 30°, what is the measure of ∠7?**

- A. 30°
- B. 50°
- C. 112°
- D. 130°

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**Answer: A**
**∠**2 and **∠**7 are alternate exterior angles and therefore are equal in measure. So both **∠**2 and **∠**7 are 30°.

**Q25. What is the volume of a cylinder with a height of 15 m and a radius of 5 m?**

- A. 235.50 m³
- B. 1,177.50 m³
- C. 1,280.25 m³
- D. 1,340.25 m³

View Correct Answer

**Answer: B**
The formula for finding the volume of a cylinder is V = ∏r ² h.