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Transcript
1. Find the equation of the line that passes through these two points (-3, 2), (5,6) (Answer using
slope-intercept form)
1
7
ans: y  x 
2
2
2. Find the equation of a line that passes through (2, 5) and is parallel to y = -4x + 2(Answer
using slope-intercept form)
ans: y = -4x + 13
3. Find the equation of a line that passes through (4, -2) and is perpendicular to y = 2x –
3(Answer using slope-intercept form)
1
ans: y   x
2
4. Find the domain and range of following functions
a) f(x) = -2x + 5
Ans:
Domain : all real numbers
Range: all real numbers
b) f(x) = x2 + 3
Ans:
Domain all real numbers
Range: all numbers greater than 3
c) f(x) = |2x + 5|
ans:
Domain: all real numbers
Range: al real numbers greater than or equal to 0
5. Find the domain of following functions
a) f(x) = x2 – 5x + 7
ans: All real numbers
3
f ( x) 
4x  1
ans: all real numbers except -1/4
b) f(x) = |2x + 5|
ans: all real numbers
6. Perform indicated algebra operation, given f(x) = 2x – 1 and g(x) = -x + 4
(f+g)(x)
(f-g)(x)
(f∙g)(x)
ans: x + 3
ans: 3x – 5
ans: -2x2 + 9x – 4
2x  1
ans:
x4
(f/g)(x)
7.Using same functions from above, calculate,
(f+g)(2)
ans: 5
(f-g)(3)
ans: 4
(f∙g)(-1)
ans: -15
(f/g)(5)
ans: -9
8. Solve following equations
a) 2x = 3(x – 5) + 11 – 5x
b) 0.5x + 3 = 0.2(x – 3)
1
4 x  1  3 x  5
2
c) 3
ans: x = -1
ans: x= -1.2
ans: x = -28
8. Solve for variable b
ans: b 
a) x = 5yb
b) y 
ba
x
x
5y
ans: b  xy  a
9. Simplify following exponential expressions(exponents must be positive numbers)
(-3x-2y)(x3y2z)2
ans:-3 x4y5z2
y2
16 y 10
(-4x5y-1)-2
ans:
a 5b 3
a 7b
b2
2
ans: a
 12 x 1 y 4
30 x 6 y 2
  4 x 2 y 3 


3 4
 5x y 

ans:
2
ans:
2y2
5x 7
25 x10 y 2
16
10. Solve following systems of linear equations (try all different methods – substitution,
elimination, matrices, Cramer’s rule)
3x  4 y  5

2 x  y  1
 1 7
 ,

5
5


ans:
4 x  5 y  2

 8 x  10 y  2
ans: no solution
 2 x  3 y  7

4 x  6 y  14
ans: infinitely many solutions
3
11
2
 3 x  4 y  12

1 x  7 y  1
18
2
 3
ans: (-2, 3)
3x  y  2 z  12

2 x  3 y  z  5
 x  3 y  8 z  22

ans: (3, 1, 2)
x  y  7

3 y  2 z  9
4 x  z  5

ans: (2, 5, -3)
11. Find the determinant of following matrices
2 4
3 5
ans: -2
 2 1 1
1
2 1
3
4
3
ans: 2
12. A store sells regular coffee for $8 a pound and gourmet coffee for $14 a pound. To get rid of
40 pounds of the gourmet coffee, a shop keeper makes a blend to put on sale for $10 a pound.
How many pounds of regular coffee should he use?
Ans: 80lbs
13. Ben invested $28,000 in to two accounts. One account gives 7% return, the other 10%. If the
interest was $2,560, how much was in each account?
Ans: $8,000 in 7%, $20,000 in 10%
14. A car heads west from a city at 65 miles per hour. At the same time a bus heads west at 50
miles per hour. How long before the two are 37.5 miles apart?
Ans: 2.5 hours