3A
CHAPTER 3 TEST
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Name:
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1. Find the solution set of x + 4y ≤ 5 if each variable represents a whole number.
2. The perimeter of an isosceles triangle is 14 cm. Find all integral possibilities for the
lengths of its sides in centimeters. (Remember that the sum of the lengths of any two
sides of a triangle is greater than the length of the third side). Write an equation in
two variables, then find the solution.
3. Determine k so that the line 3x + ky = 7 has slope 2.
4−7. Find an equation in standard form with integers as coefficients of the lines satisfying
the given conditions:
4. containing (−1, 4) with slope
2
.
3
5. containing (−3, 4) and (−7, −2).
6. containing (5, −3) and parallel to the line 4x + 3y = 6.
7. containing (5, −2) and perpendicular to the line 3x − y = 9.
8−9. Solve.
9.
8. 2x + 3y = 12
−3x − 4y = −15
6 5
+ = −2
x
y
5 6
+ = −9
x
y
10−11. Solve by writing two equations in two variables.
10. Traveling against the current, the Scouts paddled 20 km in 4 hours. The return trip
with the current took 1.5 hours less. Find the Scouts’ paddling rate in still water and
the rate of the current.
11. The sum of the digits of a two-digit number is 8. When the digits of the number
are reversed, the result is 10 more than twice the original number. Find the original
number.
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12. Given F : x → 1 − 2x + x ; D = {−2, −1, 0, 1, 2}. Find the range.
2
13−14. If f(x) = 2 − 3x and g (x) = x − x , find each of the following.
13. g (f(2) )
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14. f(g (a) )
3A
CHAPTER 3 TEST
15−16. Find a formula of the form f(x) = mx + b for the linear function f.
15. m = f(−3) = 1
16. f(−6) = 2; f(4) = −5
17. Assume the relationship described is linear. Show the linear function and solve the
problem.
A load of 3.5 kg stretches a coil spring to a length of 80 cm, and a load of 5.5 kg
stretches it to a length of 96 cm. Find the length of the spring when a load of 6.5 kg
is attached to the spring.
18. Is {(−1, 3), (2, −1), (−2, 3), (3, 3)} a function? Explain.
19. Graph
2x − 3y > 6
3x + 2y > 4
20. Graph y = x + 1.
D = {−3, −2, −1, 0, 1, 2, 3}
21. Graph {(x, y): y > x − 4 and y < 2}
Extra Credit.
Find an equation of the line containing the altitude of triangle ABC through C if A is
(−5, 2), B is (4, 4), and C is (8, −1).
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Name: