CIS MCTC App Int Alg
Ch. 1 Review
Name ____________________________________
Directions: You must show your steps. Your work must be neat. Circle your final answer(s).
LT 1.A – I can identify and use operations to combine real numbers.
3
1. Given the expression √64(√25 − √16)
a) How many operations are there?
b) Which one of the following words best describes the expression? Explain your answer choice.
Sum, difference, product, quotient
c) Simplify the expression. Show your steps.
2. Simplify
6+√62 −4(4)(2)
2(4)
3. Fill in the blanks using the appropriate vocabulary term based on the expression
30 is a _____________, 30 +34 is both a ____________ and a _____________,
__________ and a __________,
ln (
1
ln⁡(
10
1
10
√30+34
)
4
is both a
√30+34
is both a _____________ and a ______________,
4
√30+34
) is a ____________ and a ____________, and the entire expression is a _______________.
4
LT 1.B – I understand the difference between implicit and explicit grouping.
4. Decide where the expression contains any implicit or explicit grouping and state or show everywhere this
grouping takes place in the expression. Also indicate if any implicit operations are used. You do not need
to simplify the expression.
1
11−2
5 + √11 − 2
3
5. Decide where the expression contains any implicit or explicit grouping and state or show everywhere this
grouping takes place in the expression. Also indicate if any implicit operations are used. You do not need
to simplify the expression.
(6.52 − 10)2 + 4{6 − 2}
LT 1.C – I can apply exponent rules correctly and justify my results.
6. Give an example that displays why any non-zero base raised to the 0th power equals 1.
7. Rewrite
(−3)−2 ×(−3)5
using the exponent properties and then simplify the expression. You should be able
(−3)−4
to do this without the use of a calculator.
LT 1.D – I can apply and justify my use of logarithms.
15
8. Simplify ln⁡( )(0.12−1 ). Round to the hundredths place (that’s two decimal places).
4
9. Simplify log⁡(6.3(1.1) − 4.4). Round to the ten-thousandths place (that’s four decimal places).
10. Rewrite 5 𝑥 = 300 in logarithmic form. Then simplify the logarithmic expression.
LT 1.E – I can solve problems and justify my results using simple and continuously compounded interest.
11. Use the simple interest formula 𝐴 = 𝑃(1 + 𝑟𝑡) to find the amount in an account if $7,000 is invested at an
annual interest rate of 3.7% for 20 years.
rt
12. Use the present value formula P  Ae to find the amount you need to set aside today to have $500,000 in
30 years at 7% interest.
13. Use the formula r 
ln  A P 
t
to find what interest rate I’d need if I wanted $1,000 to become $15,000 in 20
years.
1
14. Use the formula t  ln  A P  r to find how long it will take $10 to become $100,000 at an annual rate of
7.25%.