ASVAB Math Knowledge Practice Test 4: Systems of Equations, Coordinates and Radicals
- Systems of Equations, Coordinates and Radicals
- 10 questions
- 15 minutes
These problems cover systems of two equations, the coordinate plane and square roots. Check a system answer by putting it back into both equations.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
If 2x + y = 11 and x − y = 1, what is the value of y?
Correct answer: C
Add the equations: 3x = 12, so x = 4, and then y = 4 − 1 = 3. The answer 4 is the value of x, not y.
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Question 2
Which ordered pair (x, y) is the solution of the system 4x − 3y = 5 and y = x − 1?
Correct answer: A
Substitute: 4x − 3(x − 1) = 5, so x + 3 = 5 and x = 2; then y = 1. The pair (1, 2) has the values reversed and does not satisfy 4x − 3y = 5.
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Question 3
What is the distance between the points (1, 2) and (7, 10)?
Correct answer: D
The horizontal change is 6 and the vertical change is 8, so the distance is the square root of 36 + 64 = 100, which is 10. The answer 14 adds the two changes instead of using the Pythagorean theorem.
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Question 4
In which quadrant of the coordinate plane is the point (−3, 5)?
Correct answer: B
A negative x and a positive y place the point up and to the left, in Quadrant II. Quadrant IV has positive x and negative y.
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Question 5
The point (5, −2) is reflected across the x-axis. What are the coordinates of its image?
Correct answer: C
Reflecting across the x-axis keeps x and changes the sign of y. The answer (−5, −2) is a reflection across the y-axis.
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Question 6
Which expression is equal to 72 in simplest form?
Correct answer: A
72 = 36 × 2, and the square root of 36 is 6, so the result is 6√2. The answer 36√2 forgets to take the root of 36.
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Question 7
What is 3 × 15 in simplest form?
Correct answer: D
Multiply under one root: √45 = √(9 × 5) = 3√5. The answer √18 adds 3 and 15 instead of multiplying them.
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Question 8
Which expression is equal to 63?
Correct answer: B
Multiply the top and bottom by √3: 6√3 ÷ 3 = 2√3. The answer 6√3 forgets to divide by the 3 that appears in the denominator.
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Question 9
What are all the solutions of |x − 3| = 5?
Correct answer: A
The expression inside can equal 5 or −5: x − 3 = 5 gives 8, and x − 3 = −5 gives −2. The pair −8 and 2 comes from mixing up the signs.
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Question 10
What are all the solutions of x2 − 5 = 31?
Correct answer: C
Add 5 to both sides: x2 = 36, so x = 6 or x = −6. Dividing 36 by 2 to get 18 is a common slip, since squaring is not doubling.
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