MCT 4C
EXPONENTIAL FUNCTIONS & LOGARITHMS NAME_________________________
Practice test
K/U: /41
TAP: /19
COMM :
/5 WORK OF GOOD FORM MUST BE DEMONSTRATED
KNOWLEDGE:
1. SIMPLIFY THE FOLLOWING EXPRESSIONS AS A SINGLE POWER WITH POSITIVE EXPONENTS. {11
marks}
a)
(𝒎𝟓 𝒏𝟐 )(𝒎−𝟑 𝒏−𝟏 )
𝟑
𝟐
[ /4]
𝒎𝟒 𝒏−𝟐
c)(𝒂𝒃−𝟓 )
𝟐
𝒙𝟒
[ /2]
b)
[ /2]
d)(√𝒙)(√𝒙𝟓 )
[ /3]
𝟏
𝒙𝟑
2. COMPLETE THE FOLLOWING CHART: { 6 marks}
POWER FORM
𝟏𝟐𝟏
RADICAL FORM
𝟑
𝟐
𝟒
( √𝟐𝟓𝟔)
EXPONENT FORM
𝟖𝟑 = 𝟓𝟏𝟐
𝟑
LOGARITHM FORM
log5625 = 4
EVALUATE
3. SOLVE THE FOLLOWING EXPONENTIAL EQUATIONS. {YOU MUST USE LIKE BASES TO SOLVE—NO
LOGARITHMS. USE THE NUMBER OF MARKS TO INDICATE AMOUNT OF WORK REQUIRED.}{11 marks}
𝟏
a) 𝟗𝟔𝒙 =
[ /4]
b)𝟓(𝟒𝒙 ) = 𝟏𝟎
[ /3]
𝟐𝟕
c) 𝟔𝒙+𝟐 = 𝟕𝟕𝟕𝟔𝟐𝒙+𝟏
[ /4]
4. WRITE EACH EXPRESSION AS A SINGLE LOGARITHM ANDEVALUATE IT.
a) log2256 – log24
[ /3]
{9 marks}
b) log220 – log25 + log28
[ /3]
c) log318 + log35 – log310 [ /3]
5. EVALUATE EACH LOGARITHM TO THE NEAREST 3 DECIMAL PLACES.
a) log46
[ /2]
b) log350
{4 marks}
[ /2]
TAP: WORK OF GOOD FORM MUST BE SHOWN FOR POTENTIAL FULL MARKS.
1. Bacteria doubles every 5 hours. How long will it take for their number to grow from 400
to 51200?(Solve using like bases.)
[ /4]
2. Chicken Pox virus spores triple in number every 7 hours. If you are infected by a
stranger’s cough with 15 spores, how long until you are very sick with 900
spores?{Round to the nearest whole hour.}
[ /5]
3. You purchased a used Mazda 3 for $7500. It sold new for $21000. The car dealership
advised you that this car depreciated at a rate of 21% per year. How old was the car
that you bought? {Round to the nearest half year.}
[ /5]
4. Radon has a half-life of 63 years. How long will it take for 89 kg of radon to decay to 20
kg? {Round to the nearest whole year.}
[ /5]