Top 10 Pre-Algebra Practice Questions
Top 10 Pre-Algebra Practice Questions: work through realistic questions in the same format and difficulty as the real test, then check every answer against a full step-by-step solution so you can see where you lost marks and what to review next.
Start your prep journey right now with these sample Pre-Algebra questions.
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8- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool?_______
9- The area of a circle is (64 π). Which of the following is the circumference of the circle?
A. 8(pi)
B. 12(pi)
C. 16(pi)
D. 64(pi)
10- What is the value of (3^6 ) ?______
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Answers:
1- D
Plug in the value of (x) and (y).
(x=3) and (y=-2)
((5(x-2y)+(2-x)^2)=(5(3-2(-2))+(2-3)^2)=(5(3+4)+(-1)^2) = 35+1=36)
2- D
The equation of a line in slope intercept form is: (y=mx+b)
Solve for (y).
(4x-2y=12 {Rightarrow} -2y=12-4x {Rightarrow} y=(12-4x){div}(-2) {Rightarrow} y=2x-6)
The slope of this line is 2.
The product of the slopes of two perpendicular lines is -1.
Therefore, the slope of a line that is perpendicular to this line is:
(m_{1} {times} m_{2} = -1 {Rightarrow} 2 {times} m_{2} = -1 {Rightarrow} m_{2} = frac{-1}{2})
3- D
Use FOIL method.
((2x+2y)(2x-y) = 4x^2-2xy+4xy-2y^2=4x^2+2xy-2y^2)
4- D
To solve absolute values equations, write two equations.
(x-10) could be positive 3, or negative 3. Therefore,
(x-10=3 Rightarrow x=13)
(x-10=-3 Rightarrow x=7)
Find the product of solutions: (7 times 13 = 91)
5- C
Use PEMDAS (order of operation):
([6 {times} (- 24) + 8], (- 4) + [4 × 5] {div} 2 )
( [- 144 + 8], (- 4) + [20] {div} 2 =
[- 144 + 8], (- 4) + 10 )
([- 136], (- 4) + 10 = [- 136] + 4 + 10 =, 122)
6- D
Solving Systems of Equations by Elimination
Multiply the first equation by (-2), then add it to the second equation.
({-2(2x+5y= 11) 4x-2y=-14} {Rightarrow} {-4x-10y= -22 4x-2y=-14} {Rightarrow} {-12y= -36} {Rightarrow} {y= 3})
Plug in the value of y into one of the equations and solve for x.
(2x+5(3)= 11 {Rightarrow} 2x+15= 11 {Rightarrow} 2x= -4 {Rightarrow} x= -2)
7- B
Write the numbers in order:
2, 19, 27, 28, 35, 44, 67
Median is the number in the middle. So, the median is 28
8- 8
Use formula of rectangle prism volume.
(V = (length) (width) (height) {Rightarrow} 2000 = (25) (10) (height) {Rightarrow} height = 2000 {div} 250 = 8)
9- C
The area of the circle is (16 π). Use the formula of areas of circles.
(Area = πr^2 ⇒ 64 π> πr^2⇒ 64 > r^2⇒ r < 8)
The radius of the circle is 8. Let’s put 8 for the radius. Now, use the circumference formula:
(Circumference =2πr=2π (8)=16π)
10- 729
((3^6 ) = 3 × 3 × 3 × 3 × 3 × 3 = 729)
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