Advanced ATI TEAS 7 Math Questions 2024
**1.** Solve for \(x\) in the quadratic equation \(x^2 - 5x + 6 = 0\).
**Ans:** \(x = 2\) or \(x = 3\)
**2.** What is the solution to the system of equations:
\[2x + 3y = 12\]
\[4x - y = 1\]?
**Ans:** \(x = 2\), \(y = 4\)
**3.** Calculate the area of a sector with a central angle of \(60^\circ\) in a circle with a radius of 8.
**Ans:** 33.51 (using \(\frac{\theta}{360} \times \pi r^2\))
**4.** Solve for \(x\) in the equation \(\frac{3x + 5}{2} = 7\).
**Ans:** \(x = 3\)
**5.** What is the value of \( \log_{10}1000 \)?
**Ans:** 3
**6.** Determine the median of the following data set: {12, 7, 3, 18, 11, 6, 14, 10}.
**Ans:** 10.5
**7.** Find the value of \( \left(\frac{2}{5} \right)^{-2} \).
**Ans:** 6.25
**8.** Calculate the standard deviation for the data set {5, 7, 3, 7, 9}.
**Ans:** 1.41
, **9.** What is the volume of a cone with a base radius of 4 and a height of 9?
**Ans:** 150.8 (using \(\frac{1}{3}\pi r^2 h\))
**10.** Solve for \(x\) in the inequality \(3x - 7 \leq 8\).
**Ans:** \(x \leq 5\)
**11.** Find the length of the hypotenuse of a right triangle with legs of length 6 and 8.
**Ans:** 10 (using Pythagorean theorem)
**12.** What is the probability of rolling a sum of 7 on two dice?
**Ans:** \(\frac{6}{36}\) or \(\frac{1}{6}\)
**13.** Simplify the expression \(\frac{4x^2 - 9}{2x - 3}\).
**Ans:** \(2x + 3\)
**14.** Calculate the compound interest earned on $5000 at an annual interest rate of 4%
compounded quarterly for 2 years.
**Ans:** $408.16 (using \(A = P \left(1 + \frac{r}{n} \right)^{nt}\))
**15.** What is the value of \(\frac{d}{dx}(3x^3 - 4x^2 + 6x - 7)\)?
**Ans:** \(9x^2 - 8x + 6\)
**16.** Solve for \(x\) in the logarithmic equation \(\log_2 (x) = 5\).
**Ans:** \(x = 32\)
**17.** What is the area of a trapezoid with bases 10 and 15 and height 7?
**Ans:** 87.5
**1.** Solve for \(x\) in the quadratic equation \(x^2 - 5x + 6 = 0\).
**Ans:** \(x = 2\) or \(x = 3\)
**2.** What is the solution to the system of equations:
\[2x + 3y = 12\]
\[4x - y = 1\]?
**Ans:** \(x = 2\), \(y = 4\)
**3.** Calculate the area of a sector with a central angle of \(60^\circ\) in a circle with a radius of 8.
**Ans:** 33.51 (using \(\frac{\theta}{360} \times \pi r^2\))
**4.** Solve for \(x\) in the equation \(\frac{3x + 5}{2} = 7\).
**Ans:** \(x = 3\)
**5.** What is the value of \( \log_{10}1000 \)?
**Ans:** 3
**6.** Determine the median of the following data set: {12, 7, 3, 18, 11, 6, 14, 10}.
**Ans:** 10.5
**7.** Find the value of \( \left(\frac{2}{5} \right)^{-2} \).
**Ans:** 6.25
**8.** Calculate the standard deviation for the data set {5, 7, 3, 7, 9}.
**Ans:** 1.41
, **9.** What is the volume of a cone with a base radius of 4 and a height of 9?
**Ans:** 150.8 (using \(\frac{1}{3}\pi r^2 h\))
**10.** Solve for \(x\) in the inequality \(3x - 7 \leq 8\).
**Ans:** \(x \leq 5\)
**11.** Find the length of the hypotenuse of a right triangle with legs of length 6 and 8.
**Ans:** 10 (using Pythagorean theorem)
**12.** What is the probability of rolling a sum of 7 on two dice?
**Ans:** \(\frac{6}{36}\) or \(\frac{1}{6}\)
**13.** Simplify the expression \(\frac{4x^2 - 9}{2x - 3}\).
**Ans:** \(2x + 3\)
**14.** Calculate the compound interest earned on $5000 at an annual interest rate of 4%
compounded quarterly for 2 years.
**Ans:** $408.16 (using \(A = P \left(1 + \frac{r}{n} \right)^{nt}\))
**15.** What is the value of \(\frac{d}{dx}(3x^3 - 4x^2 + 6x - 7)\)?
**Ans:** \(9x^2 - 8x + 6\)
**16.** Solve for \(x\) in the logarithmic equation \(\log_2 (x) = 5\).
**Ans:** \(x = 32\)
**17.** What is the area of a trapezoid with bases 10 and 15 and height 7?
**Ans:** 87.5
