Elementary Operations – Intermediate Algebra
Evaluating Expressions
Evaluate the following expression using the given values.
c  2ab 2 ;
a = – 1, b = – 2, c = 1
2)
3x
 y2
y
x = 6 and y = – 9
3)
b2  4ac
1)
3
a = 2, b = 8 and c = – 1
2
x
4)    4 y
z
x = –15, y = – 5, and z = 3
Adding and Subtracting Like Terms
Simplify the following expressions by combining any like terms.
5) 3b  6  7b  9
6) (8ac  9b)  (5ac  4a)  (b)
7) 5(a  4b)  (a  4b)  3b
8) 3 2 x  4 5 y   6  x  y 
9) 8  3 y  x   3 2   x   y 
Order of Operations
10) Evaluate
( 6)3
11) Evaluate
78  9
12) Simplify
9(7)  3(5)
13) Simplify
52  3 5  8
9 (9  3)  10  2
Scientific Notation
Multiply and write answer in scientific notation
14) (4.8  103 ) (4.1  10 5 )
15) (6.1  10  5 ) (4  10  4 )
Divide and write the result in scientific notation
16)
9.1  103
2.6  10  3
17) (2.0  107 )  (5.0  108 )
8.5  10  4
18)
1.7  1013
Discounts and Mark ups
19) A used automobile dealership recently reduced the price of a used compact car by 6%. If the
price of the car before discount was $18,300, find the discount and the new price.
20) A birthday celebration meal is $47.20 including tax, but not the tip. Find the total cost if a 10%
tip is added to the cost of the meal.
21) The original price of a pair of shoes was $84 but you paid $63. Find the rate of discount.
24) A junior one-day admission to an amusement park is $24. This price is increased by 80% for
adults. Find the mark–up and the adult price.
25) Find last year’s salary if, after a 4% raise, this year’s salary is $41,080.
ANSWERS
1) 9
2) 79
3) 72
4) 5
5) – 4b – 15
6) 13ac – 4a + 8b
7) 4a – 21b
8) – 54y
9) 21y – 2x
10) – 216
11) 79
12) – 48
13)
16
49
14)
15)
16)
17) 4
18)
19)
20)
21)
22)
23)
Discount $1,098
$51.92
25%
Mark up $19.20
$39,500
New Price $17,202
Adult price $43.20