DAT Quantitative Reasoning Math Practice Test Questions

B. 35

C. 45

D. 55

E. 65

6- If \(f(x)=2x^3+5x^2+2x\) and \(g(x)=-2\), what is the value of \(f(g(x))\)?

☐A. 36

☐B. 32

☐C. 24

☐D. 4

☐E. 0

7- In the following equation when z is divided by 3, what is the effect on \(x\)?
\(x = \frac{8y + \frac{r}{r + 1}}{\frac{6}{z}}\)

A. x is divided by 2

B. x is divided by 3

C. x does not change

D. x is multiplied by 3

E. x is multiplied by 2

8- A boat sails 40 miles south and then 30 miles east. How far is the boat from its start point?

A. 45 miles

B. 50 miles

C. 60 miles

D. 70 miles

E. 80 miles

9- \(x\) is \(y\%\) of what number?

A. \(\frac{100x}{y}\)

B. \(\frac{100y}{x}\)

C. \(\frac{x}{100y}\)

D. \(\frac{y}{100x}\)

E. \(\frac{xy}{100}\)

10- If the cotangent of an angle \(β\) is 1, then the tangent of angle \(β\) is

A. \(-1\)

B. 0

C. 1

D. 2

E. 3

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2- E
\(0.6x=(0.3)×20→x=10→(x+5)^2=(15)^2=225\)

3- E
The slop of line A is:\(m= \frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{4-3}=1\)
Parallel lines have the same slope and only choice \(E (y=x)\) has slope of 1.

4- C
When points are reflected over \(y\)-axis, the value of \(y\) in the coordinates doesn’t change and the sign of \(x\) changes. Therefore, the coordinates of point \(B\) is \((-10,3)\).

5- B
The area of trapezoid is:
\((\frac{8+12}{2})×x=100→10x=100→x=10\)
\(y=√(3^2+4^2 )=5\)
\(Perimeter \space is: 12+10+8+5=35\)

6- E
\(g(x)=-2, then f(g(x))= f(-2)=2 (-2)^3+5(-2)^2+2(-2)= -16+20-4=0\)

7- B
\(x = \frac{8y + \frac{r}{r + 1}}{\frac{6}{\frac{z}{3}}}\)
\(x = \frac{8y + \frac{r}{r + 1}}{\frac{3×6}{z}}\)
\(\frac{1}{3}×\frac{8y +\frac{r}{r + 1}}{\frac{6}{z}}=\frac{x}{3}\)

8- B
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(402 + 302 = c2 ⇒ 1600 + 900 = c2 ⇒ 2500 = c2 ⇒ c = 50\)

9- A
Let the number be \(A\). Then:
\(x=y\% ×A\)
Solve for \(A\).
\(x = \frac{y}{100}×A\)
Multiply both sides by \(100/y\):
\(x×\frac{100}{y}=\frac{y}{100}×\frac{100}{y}×A\)
\(A=\frac{100x}{y}\)

10- C
\(tangent β=\frac{1}{cotangent β}=1\)

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