Download Unit: Rationals Final Review Math 9

Unit: Rationals Calculator Permitted ‐ SHOW YOUR WORK Final Review Math 9 Name:________________________ Date: ________ Part 1: Factors 1. Express the following numbers as a product of prime numbers (order primes) a) 24 = b) 96 = c) 144 = Lowest Terms 1. Using Prime Factors (show your work) reduce the following fractions to lowest terms 48
96
24
a) = b) = c) = 96
144
144
Part 2: GCF & LCM 1. Find the GCF & LCM of the following sets of numbers (use prime factors and show your work): a) GCF(12,18) = b) GCF(18,24)= c) GCF(12,18,24)= a) LCM(12,18) = b) LCM(18,24)= c) LCM(12,18,24)= GCF & LCM ‐ Word Problems 1. Mr. Gasser works in factory with his two sons. He is really happy with his job because he gets to spend some time with his beloved sons not only at home but also at work! He is allowed to take a break every 150 minutes while his two sons are allowed to take breaks in 210 minutes and 270 minutes. How many minutes will they have to wait after they start work to get together for a break? Unit: Rationals Review Math 2. Ms. Franklin is shopping at a supermarket. She is getting things for the sandwiches she is going to prepare for next Sunday's picnic. She sees that hamburger buns come in packs of 12, but the hamburgers themselves are in packages of 16, cheese slices are in packages of 24. What's the least number of packages of each type should be purchased in order to make complete cheese burgers with not leftovers? Part 3: Rational Number Operations 1. Simplify: 8
a) 5 6
2. Simplify: 5
5
a) – 12 8
7
 15  8
b) *
*
 20
8
 27
3 7
4 3
b) – + 33 21  14
c) *
÷
24 55 25
c) 5  1 1
+ – 6
2
3
5
d) 9  10
21
3 3 3
d) +
– 4 2
5
Unit: Exponents Final Review Calculator Permitted ‐ SHOW YOUR WORK Math 9 Name:________________________ Date: ________ Part 1: Exponents 1. Write as an exponent (without brackets): 2. Simplify using exponents (without brackets): a) (–4)( –4)(–4)( –4)(–4)( –4) a) (–2)(3)( 2)(3)( –3)(–2)( –5)(–5)( –3)(–2) 3. Express the following numbers as a product of prime numbers in order using exponents: a) 54 = b) 48 = c) 144 = 4. Evaluate: b) –(32 – 23)2 c) 20 – (–1)185659374 a) – 24(–3)3 5. Simplify ‐ using only positive exponents on the variables: 2
4 x 8 y 7
a) x 5 x 6  b) c) 3xy 3  8 9 16x y
d) 3x y
3
3
 e) 32x y
3
4
3
6x y  f) 4 x y 
 x y  4
3
3
3
3
8
6
6
4 4
6. Express the following as a power of 10: a) 10 b) 10 000 10 c) 10 1
1000
d) 1 10 10 Unit: Exponents Final Review Math 9 Part 2: Scientific Notation 1. Write the following in Scientific Notation (use 2 decimal places in all your answers): a) 3 765 000 000 b) 0.000 000 0722 4 c) 0. 008 998 2. Use Scientific Notation to calculate the following (use 2 decimal places in all your answers): 7.52  10 30
a) 4.70 x 10 ‐98 x 4.34 x 1053 b) c) 4.70 x 10 ‐18 x 4.01 x 10 ‐25 27 4.70  10
Part 3: Square Root & Number Systems 1. First estimate and then find the following square roots with a calculator to 5 decimal places: a) 8 b) 70 c) 508 d) 4189 Number Systems 1. Categorize the following Real numbers as to the “smallest” set they belong to, simplify the expression (if possible) to get to the real number that is expressed… N = ”Natural,” W = ”Whole,” Z = ”Integer,” Q = ”Rational,” Q = ”Irrational” 5
10
1. a)  b) c) 0 d)  100 2
2
Unit: Exponents Final Review 2. a) 4
5
b)  4 c) 8
2
d) Math 9  Part 4: Word problems (answer in scientific notation with 2 decimal places): 1. The earth’s circumference is approximately 40 075 km. If the average person is 0.5 m from shoulder‐to‐shoulder. How many people can stand shoulder‐to‐shoulder around the equator? 2. The earth’s land mass is approximately 149,000,000.5 square kilometres. If each person on earth (7 billion) were to have an equal share of the land, how much land would each person get? 3. The speed of light is about 300 000 km/s. A light year is the distance that light can travel in one year. The Andromeda Galaxy is 2.4×1019 km from earth – how many light years is it away Bonus: 24 x 4 y 3 36w 9 y 2 2
Simplify: 
6 4  
6 3  54w z   4 x z 