Grade 11 Diagnostic Pre-Test

Answer all 18 questions, then submit. There's no time limit and no penalty for guessing — do your best on each one. On the next screen you'll get course recommendations based on what you miss.

Q1.

If \(f(x)=3x^2-2x+1\), what is \(f(-1)\)?

\(6\) \(2\) \(-4\) \(0\)

Q2.

What is the domain of \(g(x)=\sqrt{x-7}\)?

\([7,\infty)\) \((-\infty,7]\) \((7,\infty)\) All real numbers

Q3.

What value is excluded from the domain of \(r(x)=\frac{5}{x+4}\)?

\(-4\) \(4\) \(0\) \(5\)

Q4.

The graph of \(y=f(x)\) is transformed to \(y=-f(x+2)+6\). Which description is correct?

left 2, reflected over the x-axis, up 6 right 2, reflected over the x-axis, up 6 left 2, reflected over the y-axis, down 6 right 2, no reflection, up 6

Q5.

If \(f(x)=x^2-1\) and \(g(x)=x+3\), which expression equals \(f(g(x))\)?

\((x+3)^2-1\) \(x^2+2\) \(x^2-1+3\) \((x^2-1)+3\)

Q6.

What is the inverse of \(h(x)=4x-3\)?

\(h^{-1}(x)=\frac{x+3}{4}\) \(h^{-1}(x)=\frac{x-3}{4}\) \(h^{-1}(x)=4x+3\) \(h^{-1}(x)=3x-4\)

Q7.

A quadratic is written as \(y=3(x-2)(x+5)\). Which information is most visible?

The x-intercepts are 2 and -5. The vertex is \((2,-5)\). The y-intercept is 3. The axis of symmetry is \(x=3\).

Q8.

What is the average rate of change of \(f(x)=x^3\) from \(x=1\) to \(x=3\)?

\(13\) \(9\) \(26\) \(12\)

Q9.

What is the vertex of \(y=2(x-6)^2-1\)?

\((6,-1)\) \((-6,-1)\) \((6,1)\) \((-1,6)\)

Q10.

What is \((x+3)(x+4)\)?

\(x^2+7x+12\) \(x^2+12\) \(x^2+4x+3\) \(2x+7\)

Q11.

Factor \(2x^2-x-15\) completely.

\((2x+5)(x-3)\) \((2x-5)(x+3)\) \((x+5)(2x-3)\) \(2(x^2-x-15)\)

Q12.

What is the end behavior of \(q(x)=-x^3+7x\)?

left up, right down left down, right up both ends up both ends down

Q13.

Simplify \(\frac{x^2-9}{x-3}\), with the original restriction included.

\(x+3,\ x\ne3\) \(x+3\), no restrictions \(x-3,\ x\ne-3\) \(x^2+3,\ x\ne3\)

Q14.

Simplify \(\sqrt{72}\).

\(6\sqrt{2}\) \(8\sqrt{3}\) \(36\sqrt{2}\) \(2\sqrt{6}\)

Q15.

Which value is not allowed in \(\frac{x+2}{x^2-16}\)?

\(x=4\) or \(x=-4\) \(x=2\) only \(x=-2\) only All real numbers are allowed

Q16.

Which expression solves \(50(1.04)^t=90\) for \(t\)?

\(\frac{\log(1.8)}{\log(1.04)}\) \(\frac{\log(90)}{\log(1.04)}\) \(\frac{\log(1.04)}{\log(1.8)}\) \(\frac{90}{50\cdot1.04}\)

Q17.

What is \(300^\circ\) in radians?

\(\frac{5\pi}{3}\) \(\frac{3\pi}{5}\) \(\frac{4\pi}{3}\) \(\frac{7\pi}{6}\)

Q18.

What is the period of \(y=4\sin(5x)-2\)?

\(\frac{2\pi}{5}\) \(5\pi\) \(\frac{\pi}{5}\) \(2\pi\)