OSTP Grade 11 CCRA Precalculus Practice

Practice playeasy

The function $h$ is defined by $h(t) = 125(1.18)^t$ . The function $h$ models the number of members in a club, where $t$ is the number of years after the club was founded. According to the model, what is the estimated number of members when the club was founded?

When the club was founded, $t = 0$ . So $h(0) = 125(1.18)^0 = 125$ members.

Practice playeasy

A substance has a half-life of $4$ years. What fraction remains after $12$ years?

$12 \div 4 = 3$ half-lives. Remaining: $\left(\dfrac{1}{2}\right)^{3} = \dfrac{1}{8}$ .

Practice playeasy

Taxi cost, in dollars, after $x$ miles:
$\begin{array}{c|c} x & f(x) \\ \hline 1 & 6 \\ 2 & 10 \\ 3 & 14 \\ 4 & 18 \end{array}$
The cost is $f(x)=mx+2\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The cost increases by $\text{\char36}4$ per mile, so $m = 4\textsf{.}$

Practice playmedium

The table shows values of a linear function $n\textsf{.}$
$\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline n(x) & 11 & 15 & 19 & 23 \end{array}$
Which of the following is $n(x)\textsf{?}$

From $x = 2$ to $x = 4\textsf{,}$ $n(x)$ increases by $4\textsf{,}$ so the constant rate is $\dfrac{4}{2} = 2\textsf{.}$ Using the point $(2, 11)$ gives $2(2) + b = 11\textsf{,}$ so $b = 7\textsf{.}$ Therefore $n(x) = 2x + 7\textsf{.}$

Practice playmedium

A line has slope $\dfrac{3}{2}$ and passes through the point $(4, 1)$ . Which equation represents this line in slope-intercept form?

Slope-intercept form is $y = mx + b$ . Substituting $(4, 1)$ with $m = \dfrac{3}{2}$ gives $1 = \dfrac{3}{2}(4) + b = 6 + b$ , so $b = -5$ . The equation is $y = \dfrac{3}{2}x - 5\textsf{.}$

Practice playmedium

A circle in the coordinate plane has a diameter with endpoints $(0, 0)$ and $(6, 8)\textsf{.}$ What is the radius of the circle?

The diameter length is $\sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{36 + 64} = \sqrt{100} = 10\textsf{.}$ The radius is half the diameter, so $r = \dfrac{10}{2} = 5\textsf{.}$

Practice playeasy

The equation $(x - 2)^2 + (y + 1)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $3$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(2, -1)$ and radius $4$ . Shifting down $3$ moves the center to $(2, -4)$ , so Circle B is $(x - 2)^2 + (y + 4)^2 = 16$ .

Practice playeasy

Convert $\dfrac{2\pi}{3}$ to degrees.

$\dfrac{2\pi}{3} \times \dfrac{180°}{\pi} = 120°$ .

OSTP Grade 11 CCRA Precalculus. Practice it free.

Precalculus skills

functions and their graphs

trigonometric functions

analytic geometry

modeling with functions

sequences and series

Topics mapped to this domain

Exponential functions in context (SAT)

Exponential and log formulas

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

Slope-point line equations (ACT/SAT/PSAT 8/9/10)

Circle diameter endpoints to radius (SAT)

Circle equation translations (ACT/SAT/PSAT 8/9/10)

Degree-radian conversion

Equation of a circle

Factored polynomial x-intercepts (SAT)

Finding inverse functions (ACT)

Function transformation descriptions

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Turn precalculus into game time.

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