UWI Preliminary Mathematics II - Sample Test 1
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Sample Test 1 MATH 0102 February 16, 2015 Scheduled test time: 8:00 am - 10:00 am, February 23, 2015 Location: Roy Marshall Teaching Complex LT2 19 1. Solve the system by the method of substitution x 2 + y =0 x 2 - 4x - y =0 Similar question: x 2 + y 2 = 169 x 2 - 8y = 104 2. Break-Even Analysis A small software company invests $ 25,000 to produce a software package that will sell for $ 69.95. Each unit can be produced for $ 45.25 (a) How many units must be sold to break even? (b) How many items must be sold to make a profit of $ 12,000? 3. Solve the system by the method of elimination x+3 4 + y-1 3 =1 2x - y = 12 4. Sketch the graph of the system of inequalities x 2 + y 2 ≤ 36 4x - 3y ≤ 0 5. Sketch the region determined by the constraints. The find the minimum and maximum values of the objective function (if possible) and where they occur, subject to the indicated constrains. Objective function: z =3x +4y 1
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University of The West Indies offers preliminary courses for those leaving secondary school.This is a sample test from the prelim mathematics program.
Transcript of UWI Preliminary Mathematics II - Sample Test 1
Sample Test 1 MATH 0102
February 16, 2015
Scheduled test time: 8:00 am - 10:00 am, February 23, 2015
Location: Roy Marshall Teaching Complex LT2 19
1. Solve the system by the method of substitution{x2 + y = 0x2 − 4x− y = 0
Similar question: {x2 + y2 = 169x2 − 8y = 104
2. Break-Even Analysis A small software company invests $ 25,000 to produce a software package that
will sell for $ 69.95. Each unit can be produced for $ 45.25
(a) How many units must be sold to break even?
(b) How many items must be sold to make a profit of $ 12,000?
3. Solve the system by the method of elimination{x+34 + y−1
3 = 12x− y = 12
4. Sketch the graph of the system of inequalities{x2 + y2 ≤ 364x− 3y ≤ 0
5. Sketch the region determined by the constraints. The find the minimum and maximum values of
the objective function (if possible) and where they occur, subject to the indicated constrains.
Objective function:
z = 3x + 4y
1
Constrains: x + 3y ≤ 123x + 2y ≤ 15x ≥ 0y ≥ 0
6. Use matrices to solve the system of equations (if possible). Use Gaussian elimination with
back-substitution 3x + 2y − z + w = 0x− y + 4z + 2w = 25−2x + y + 2z − w = 2x + y + z + w = 6
7. In this exercise, find x and y 16 4 5 4−3 13 15 60 2 4 0
=
16 4 2x + 1 4−13 13 15 3x
0 2 3y − 5 0
8. Solve for X in the equation 3X + A = B, given
A =
(1 −20 3
), B =
(−3 42 1
)
9. Evaluate the expression
(6 5 −11 −2 0
){ 0 3−1 −34 1
+
−2 3−3 50 −3
}
Scheduled test time: 8:00 am - 10:00 am, February 23, 2015
Location: Roy Marshall Teaching Complex LT2 19
GOOD LUCK ! :)
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