Physics, Foundation Programme – Problem Solving Exercises 2
Algebraic Experessions
1. Write the exponential expression in the simplest form so that all exponents are positive:
a) a: ,
b) a: ,
c) a:
d) a:
e) a:
f) a:
g) a:
h) a:
i) a:
j) a:
k) a:
2. Evaluate each expression. Express the result in scientific notation. Round using the
multiplication/division/addition/subraction rules for significant digits.
a) A:
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b) a:
c) a:
d) a:
e) a:
f) a:
g) a:
h) a:
3. For each polynomial determine its a) standard form, b) degree, c) coefficients, d) leading coefficient, e)
number of terms
a) a: a) ; b) 3; c) 1, 0, 0, -1; d) 1; e) 2
b) a: a) ;b) 4; c) -12,0,-3,0,-11; d) -12; e) 3
c) a: a) ; b) 3; c) -5,3,7,-1; d) -5; e) 4
4. Perform indicated operations and simplify if possible by combining like terms. Write the result in standard
form.
a) A:
b) a:
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c) * a:
d) * a:
5. Use the FOIL method to find the indicated product and simplify if possible. Write the result in standard
form.
a) A:
b) a:
c) a:
d) a:
e) a:
6. Use special product formulas to perform indicated operation.
a) A:
b) a:
c) a:
d) a: x
2
+10 x+25− y
2
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7. Evaluate the given polynomial for the indicated value of the variable:
a) , for a: 29
b) , for x=5 a: -46
c) , for x=-1 a: -1
8. The number of committees consisting of exactly 3 people that can be formed from a group of n people is
given by the polynomial
.
Find the number of committees consisting of exactly 3 people that can be formed from a group of 6 people.
Ans.: 20
9. Factor out the greatest common factor (GCF) for each polynomial:
a) a: -3x(5x+4)
b) a:
c) (use grouping) a:
10. Factor each difference of squares:
a) a:
b) a: ( y
2
−9)( y
2
+9)=( y−3)( y+3)( y
2
+9)
c) a: (x+7)(x+3)
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11. Factor each perfect square trinomial:
a) a:
b) a:
c) a:
12. Factor each sum or difference of cubes:
a) a:
b) a:
13. Factor each trinomial by the trial and error method:
a) a:
b) a:
c) a: (x+5)(x+7)
d) a: (x-3)(x-6)
14. Simplify each rational expression:
a) a:
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b)
a
2
−ab
ab−b
2
a:
a
b
,b≠0,b≠a
c) a: 3z-2, z≠
2
3
d) a:
p−2
q−1
,q≠1, p≠−2
15. Perform the indicated operation(s). State the result in the simplest form:
a) a: , r≠0
b) a: 2, t≠0
c) a: 2x
x−1
(x−5)(x+3)
, x≠5,x≠−3
d) a: , y≠−4
e) a: , x≠±3,x≠−4
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f) a: , v≠0
g) a: , m≠±1
h) a: , x≠0,a≠−x, x≠1
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