Top 10 TExES Core Subjects EC-6 Math Practice Questions
Start your TExES Math test prep journey right now with these sample TExES Core Subjects EC-6 Math questions.
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n of these numbers? \(2, 27, 28, 19, 67, 44, 35\)
A. \(19\)
B. \(28\)
C. \(44\)
D. \(35\)
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. \(8 π\)
B. \(12 π\)
C. \(16 π\)
D. \(64 π\)
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 \(y=-2\)
\((5(x-2y)+(2-x))^2=(5(3-2(-2))+(2-3))^2=(5(3+4)+(-1))^2 = (34)^2=36\)
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 the 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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