Practice Test 11 - Algebra 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. Given $s(x)=5x-2$, what is the value of $s(-4)$?
2. What is the coefficient of $x$ in the expression $x+5$?
3. Given $g(x) = 3x^2 + 2x - 1$, what is $g(-1)$?
4. An amount of medicine in the bloodstream is modeled by $M(t)=1000(0.80)^t$, where $t$ is in hours. What percent rate of change does this function represent per hour?
5. Given $f(x) = -3x - 2$, evaluate $f(3)$.
6. A function $A(s) = s^2$ represents the area of a square with side length $s$. In a geometry class, students are asked to find areas of squares that can be constructed using available materials. If the materials allow for side lengths from 0.5 inches to 12 inches, but the measurement tools only read to the nearest 0.1 inch, which domain best reflects this situation?
7. A cyclist rides at a constant speed of 18 km/hr for 45 min. Find the distance traveled in kilometers, and show unit tracking (convert minutes to hours).
8. A rectangle is measured with a ruler marked in millimeters. The length is 12.4 cm and the width is 7.8 cm (each measured to the nearest 0.1 cm). Measurements were made to this precision. Report the calculated area with appropriate precision.
9. Consider the equation $y = 2x - 3$. Which statement best describes the relationship between the equation and its graph?
10. A store offers a membership where customers pay $30 annually and then receive a 15% discount on all purchases. Without membership, customers pay full price. For what annual spending amount $x$ (in dollars) would the membership cost exactly break even with non-membership shopping?
11. Use the geometric series formula $S_n=\dfrac{a(1-r^n)}{1-r}$ to calculate the sum $3+3(1.1)+3(1.1)^2+\cdots+3(1.1)^9.$ (So $a=3$, $r=1.1$, $n=10$.)
12. A digital thermometer reads to the nearest 0.1°C. It shows 19.6°C. What is an appropriate level of precision for reporting this temperature?
13. Temperature conversion can be written as the literal equation $C = \frac{5}{9}(F - 32)$, where $C$ is degrees Celsius and $F$ is degrees Fahrenheit. Solve $C = \frac{5}{9}(F - 32)$ for $F$.
14. A lab models the temperature (in °C) of a cooling liquid as room temperature plus an exponential cooling term. Let $f(t)=22$ and $g(t)=15(0.8)^t$, where $t$ is in minutes. Find $(f+g)(t)$.​
15. Solve $x^2+10x+34=0$ using the quadratic formula. Express both solutions in $a\pm bi$ form, using $i^2=-1$.
16. A quantity grows by 5% per year, modeled by $(1.05)^t$. Rewrite $(1.05)^t$ to reveal the equivalent quarterly growth factor (4 quarters per year).
17. Find the product: $(x^2 + 2x - 3)(x + 4)$
18. A bacteria culture starts with 300 bacteria and triples every hour. What function models the population $P(t)$ after $t$ hours?
19. In physics, distance is modeled by $d = rt$, where $d$ is distance, $r$ is rate (speed), and $t$ is time. Solve $d = rt$ for $t$.
20. A ball is thrown upward from a platform 6 feet high with an initial upward velocity of 40 ft/s. Its height in feet after $t$ seconds is modeled by $h(t)=-16t^2+40t+6$. Which formula represents this height function?

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