Free Printable Honors Pre-Calculus QBA #2

1.

Evaluate $\left(2\right)^{-2}$

a)

-4

b)

4

c)

$-\frac{1}{4}$

d)

$\frac{1}{4}$

2.

Evaluate $121^{\frac{1}{2}}$

a)

11

b)

60.5

c)

$\frac{1}{11}$

d)

14,641

3.

Evaluate $\sqrt[]{2}\cdot\sqrt[]{8}$

a)

$\sqrt[]{10}$

b)

3.99

c)

4

d)

$\sqrt[]{6}$

4.

Simplify $\left(3x^2y^5\right)^3$

a)

$9x^5y^8$

b)

$27x^6y^{15}$

c)

$1x^{\frac{2}{3}}y^{\frac{5}{3}}$

d)

$3x^6y^{15}$

5.

Simplify $\frac{8n^{10}}{2n^5}$

a)

$4n^5$

b)

$6n^2$

c)

4n

d)

$\frac{4}{n^5}$

6.

Express $\sqrt[]{a^6b^3}$ using rational exponents. Assume all values of the variables are positive.

a)

$a^6b^3$

b)

$a^3b^{\frac{3}{2}}$

c)

$a^2b$

d)

$a^{12}b^6$

7.

Express $r^{\frac{1}{4}}s^{\frac{1}{2}}t^{\frac{2}{3}}$ using a single radical. Assume all values of the variables are positive.

a)

$\sqrt[4]{rs^2t^2}$

b)

$\sqrt[3]{r^4s^3t^2}$

c)

$\sqrt[12]{r^3s^6t^8}$

d)

$\sqrt[]{r^2st^3}$

8.

Describe the transformation on the parent graph for $y=3^x+4$ .

a)

translation left 4

b)

translation right 4

c)

translation down 4

d)

translation up 4

9.

Describe the transformation on the parent graph for $y=3^{\left(x-4\right)}$ .

a)

translation left 4

b)

translation right 4

c)

translation down 4

d)

translation up 4

10.

Describe the transformation on the parent graph for $y=-3^x$ .

a)

translation left 3

b)

translation down 3

c)

reflection over the x-axis

d)

reflection over the y-axis

11.

After 5 years, an account is worth $3500.00. Find the amount of money that was invested if the interest rate is 3.5% compounded continuously. Use $A=Pe^{\left(rt\right)}$

a)

$2,938.10

b)

$608.21

c)

$2,946.91

d)

$19.80

12.

Sarah invests $5400 in an account that compounds interest weekly at a rate of 4.1%. How much will she have in her account after 10 years? Use $A=P\left(1+\frac{r}{n}\right)^{\left(nt\right)}$

a)

$8,136.82

b)

$8,135.50

c)

$11,534.24

d)

$320,640.31

13.

The population of a certain city is decreasing by 1.5% per year. If there were 510,000 people in 2020, what will the population be by 2050? Use $N=N_0e^{\left(kt\right)}$

a)

799,839

b)

5,666

c)

325,190

d)

340,159

14.

Write $\log_b3=x$ in exponential form.

a)

$b^x=3$

b)

$3^x=b$

c)

$x^b=3$

d)

$x^3=b$

15.

Write $2^{-3}=\frac{1}{8}$ in logarithmic form.

a)

$\log_{-3}\ \frac{1}{8}=2$

b)

$\log_{-3}\ 2=\frac{1}{8}$

c)

$\log_2\ \frac{1}{8}=-3$

d)

$\log_2\ \left(-3\right)=\frac{1}{8}$

16.

Evaluate $\log_216=x$ .

a)

x = 4

b)

x = 8

c)

$x=\frac{1}{8}$

d)

x = -4

17.

Evaluate $\log_5\ \frac{1}{25}=x$ .

a)

x = 2

b)

x = 5

c)

$x=\frac{1}{5}$

d)

x = -2

18.

Evaluate $\log_55^7$ .

a)

1

b)

3

c)

5

d)

7

19.

Find the value of $\log_627.5$ using the change of base formula.

a)

0.661

b)

1.439

c)

1.850

d)

2.232

20.

Simplify $2\log_3x+\log_3y$ into a single logarithm and simplify if possible.

a)

$\log_3\left(\frac{y}{2}\right)$

b)

$\log_3\left(\frac{y}{x^2}\right)$

c)

$\log_3\left(x^2y\right)$

d)

$\log_3\left(xy^2\right)$

21.

Expand $\log_5\left(\frac{a^3b}{c^2}\right)$ using the properties of logarithms.

a)

$3\log_5a+\log_5b-2\log_5c$

b)

$3\log_5a-\left(\log_5b+2\log_5c\right)$

c)

$3\log_5a-\left(\log_5b-2\log_5c\right)$

d)

$\log_5\left(3a\right)+\log_5b-\log_5\left(2c\right)$

22.

Solve for x: $\log_4x+\log_4\left(x-2\right)=\log_415$

a)

x = -3

b)

x = 5

c)

x = -3 and 5

d)

x = -5 and 3

23.

Solve for x: $\log_23-\log_2\left(x+1\right)=3$

a)

$x=\frac{1}{12}$

b)

$x=\frac{1}{2}$

c)

No solution

d)

$x=-\frac{5}{8}$

24.

Solve for x: $\log_x36=2$

a)

x = 6

b)

x = 1296

c)

x = 5.17

d)

x = 1

25.

Solve for x: $5^x=200$

a)

x = 2.457

b)

x = 3.292

c)

x = 0.304

d)

x = 40

Honors Pre-Calculus QBA #2

Total questions: 25

Worksheet time: 2hrs 5mins

Similar Resources on Wayground