Praxis Algebra I (5162)

1. Question 1 · Principles of Algebra

   : Simplifying like terms Simplify 7x+3x−5.
   • A.10x−5
   • B.4x−5
   • C.10x+5
   • D.4x+5
   Show answer and explanation

   Answer: A. 10x−5

   Combine like terms: 7x+3x=10x. The constant −5 remains. Result: 10x−5.

2. Question 2 · Principles of Algebra

   : Factoring by grouping Factor x³+2x²−9x−18.
   • A.(x−3)(x²+6)
   • B.(x−2)(x²−9)
   • C.(x+3)(x²−6)
   • D.(x+2)(x²−9)
   Show answer and explanation

   Answer: D. (x+2)(x²−9)

   Group: (x³+2x²)+(−9x−18)=x²(x+2)−9(x+2)=(x+2)(x²−9). Then x²−9=(x−3)(x+3) if needed.

3. Question 3 · Functions

   : Growth vs decay

   Which statement is true about f(x)=0.5^x ?
   • A.It represents exponential growth
   • B.It has a positive slope
   • C.It represents exponential decay
   • D.It is linear
   Show answer and explanation

   Answer: C. It represents exponential decay

   Since the base is between 0 and 1, the function decreases, representing exponential decay.

4. Question 4 · Number and Quantity

   : Dimensional analysis

   If a car travels 60 miles in 1.5 hours, what is its average speed?
   • A.30 mph
   • B.40 mph
   • C.45 mph
   • D.90 mph
   Show answer and explanation

   Answer: B. 40 mph

   Average speed = distance ÷ time = 60÷1.5=40 miles per hour.

5. Question 5 · Number and Quantity

   Reply “Yes Continue” to proceed with Practice Test 1, Section 4: Probability and Statistics (Questions 77–100).

   : Mean Find the mean of the data set: 4, 6, 8, 10.
   • A.6
   • B.7
   • C.8
   • D.9
   Show answer and explanation

   Answer: B. 7

   Explanation (corrected): The mean is the sum divided by the number of values: 28/4=7.

6. Question 6 · Probability and Statistics

   : Drawing conclusions

   What is statistical reasoning primarily used for?
   • A.Memorizing formulas
   • B.Drawing conclusions from data
   • C.Solving equations
   • D.Creating graphs
   Show answer and explanation

   Answer: B. Drawing conclusions from data

   Statistical reasoning involves interpreting data to make informed conclusions.

7. Question 7 · Principles of Algebra

   : Vertex interpretation

   The vertex of y=(x−2())²+1 is:
   • A.(2,1)
   • B.(−2,1)
   • C.(1,2)
   • D.(−1,2)
   Show answer and explanation

   Answer: A. (2,1)

   Vertex form y=(x−h())²+k has vertex (h,k).

8. Question 8 · Functions

   : Comparing quadratic graphs

   Which function opens downward?
   • A.y=2x²−3
   • B.y=−x²+4x
   • C.y=(x−1())²
   • D.y=x²−7x+1
   Show answer and explanation

   Answer: B. y=−x²+4x

   A negative leading coefficient indicates a downward-opening parabola.

9. Question 9 · Functions

   : Ordering real numbers Which list shows the numbers in increasing order? −0.8, √2, −1/2
   • A.−0.8, −1/2, √2
   • B.−1/2, −0.8, √2
   • C.√2, −1/2, −0.8
   • D.−0.8, √2, −1/2
   Show answer and explanation

   Answer: A. −0.8, −1/2, √2

   Approximate values: −0.8=−0.8, −1/2=−0.5, √2≈1.414. Ordered least to greatest: −0.8, −0.5, 1.414.

10. Question 10 · Number and Quantity

    : Reasonableness

    Which result is most reasonable for 6.1×0.5 ?
    • A.0.305
    • B.3.05
    • C.6.5
    • D.12.2
    Show answer and explanation

    Answer: B. 3.05

    Multiplying by 0.5 halves the number. Half of 6.1 is about 3.05.

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