Download Invitational Mathematics Competition Algebra 1 Individual Test

Invitational Mathematics
Competition
Algebra 1
Individual Test
December 12, 2016
1
Directions: The use of a calculator is not allowed during this exam. Fill in the circle on the bubble sheet corresponding to
the letter of the correct answer. For all questions, NOTA represents none of the above answers is correct.
Solve the equation.
7x + 2 5
6x
+ =1)
2
2
7
A) x =
21
61
B) x = -
21
61
C) x = -
49
37
D) x = -
49
61
E) NOTA
2) The formula for the perimeter of a rectangle is P = 2L + 2W. Solve the formula for L. Use this formula to find the length of
the rectangle if the perimeter, P, is 30 feet and the width, W, is 6 feet.
A) L = 9 feet
B) L = 15 feet
C) L = 24 feet
D) L = 12 feet
E) NOTA
Solve the equation.
1
3
x-2
3) x + 2 =
2
4
A) x = 16, 0
B) x = 16, 12
C) x = 10
D) no solution
E) NOTA
4) A poster in the shape of a triangle has one side that is five inches more the length of the shortest side, and another side that
is three inches less than twice the shortest side. Find the dimensions of the poster if its perimeter is 46 inches.
A) 11 inches, 16 inches, 20 inches
B) 12 inches, 16 inches, 19 inches
C) 11 inches, 17 inches, 19 inches
D) 11 inches, 16 inches, 19 inches
E) NOTA
Solve for x.
5) 8x - 7 - 9(x - 9) < 0
A) x < 88
B) x > 74
C) x > -88
D) x < -74
E) NOTA
Solve for x and graph the results.
6) -4x < -20 and x + 4 > 2
A)
B)
C)
D)
no solution
E) NOTA
2
Solve and graph the solutions.
7) x
4
A)
B)
C)
D)
E) NOTA
Solve.
1
8) Find the slope of the line perpendicular to the line passing though (-3, 1) and ( , 4).
4
A)
13
12
B) -
13
12
C)
12
13
D)
20
13
E) NOTA
Write the equation of the line in the graph.
9)
A) y = 5x + 9
B) y = 9x +
1
5
C) y = 9x
D) y =
1
x+9
5
E) NOTA
Evaluate the function.
4
, find r(a - 5).
10) If r(x) =
x-9
A) -
4
20
a+
9
9
B)
-1
a-9
C)
4
a - 14
D)
4
2
a-9 7
E) NOTA
3
Graph the linear function by plotting the x- and y-intercepts.
1
11) y - x = 4
2
A)
B)
C)
D)
E) NOTA
4
Provide an appropriate response.
12) Find the range of the function for the domain.
f(x) = x + 4 Domain = { -2, -1, 0, 1, 2 }
A) Range = {2, 3, 0, 5, 6}
B) Range = {-6, -5, -4, -3, -2}
C) Range = {2, 3, 4, 5, 6}
D) Range = {2, 3, 4, 5, 6, 7}
E) NOTA
Solve.
13) The cost of having a car towed is given by the linear function C(x) = 3x + 65, where C(x) is in dollars and x is the number of
miles the car is towed. Find the cost of having a car towed 8 miles.
A) $89
B) $79
C) $68
D) $24
E) NOTA
14) Robin is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an
estimate of $210 for materials and equipment rental plus $45 per hour for labor. Company B gave and estimate of $290 for
materials and equipment rental plus $35 per hour for labor. Create a cost equation for each company where y is the total
cost of the landscaping and x is the number of hours of labor. Determine how many hours of labor will be required for the
two companies to cost the same.
A) 12 hours
B) 7 hours
C) 8 hours
D) 11 hours
E) NOTA
Multiply.
15) (p + 9q)(p - 9q)
A) p2 - 18pq - 81q2
B) p2 - 81q2
C) p2 - 18q2
D) p2 + 18pq - 81q2
E) NOTA
For the polynomial, state the degree and whether or not the polynomial is a monomial, a binomial, or a trinomial.
5
4
xy
16) xy3 +
6
5
A) Binomial, degree 6
B) Binomial, degree 4
C) Binomial, degree 3
D) Binomial, degree 2
E) NOTA
Multiply.
17) (w - 11)2
A) w2 - 22w + 121
B) w2 + 121
C) w + 121
D) 121w2 - 22w + 121
E) NOTA
5
Graph the system of inequalities.
18) 2x + 3y 6
x-y 3
x 1
A)
B)
C)
D)
E) NOTA
6
Divide.
19) (x2 + 11x + 9) ÷ (x + 9)
9
A) x + 2 +
x+9
B) x + 2 -
9
x+9
C)
x+2
x+9
D) x + 3
E) NOTA
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
20) x3 + 4x2 - 9x - 36
A) (x2 - 9)(x + 4)
B) Prime
C) (x + 3)(x - 3)(x + 4)
D) (x - 3)2 (x + 4)
E) NOTA
Simplify.
21)
1
k+ 6
5
k2 - 36
A)
5
k- 6
B)
k- 6
5
C) k - 6
D)
k+ 6
5
E) NOTA
Solve the equation and check your solution. If there is no solution, say so.
5-a 3 7
+ =
22)
a
4 a
A) a = 8
B) a =
29
20
C) No solution
D) a = -8
E) NOTA
C) 2x2 y 7x
D) 4x2 y 7x
E) NOTA
C) x = -4
D) x = 2, 8
E) NOTA
Divide and simplify. Assume that all variables represent positive numbers.
56x5 y6
23)
2y4
A) 2x4 y2 7xy
B) 28xy x
Solve the radical equation. Check all proposed solutions.
24) 2x + 11 = x + 7
4
A) x = 8
B) x = -4,
3
Divide.
25)
2
6+i
A)
12
2
+
i
35 35
B)
12
2
+
i
37 37
C)
12
2
i
37 37
Solve the equation. Express any complex numbers using i notation.
26) (2x - 5)2 = 81
A) x = 4, -14
B) x = 2, -7
C) x = 14, -4
12
2
i
35 35
E) NOTA
D) x = 7, -2
E) NOTA
D)
7
Write a quadratic equation having the given solutions.
27) 8, 5
A) x2 - 40x + 13 = 0
B) x2 + 40x + 13 = 0
C) x2 - 13x + 40 = 0
D) x2 + 13x + 40 = 0
E) NOTA
Find the missing side(s).
28) b = 3, c =
A) 11
8; find a
B)
5
C) 5
D)
11
E) NOTA
Solve and graph.
29) x2 - 9x + 20 > 0
A) x > 5
B) x < 4
C) 4 < x < 5
D) x < 4 or x > 5
E) NOTA
8
Find the vertex, the y-intercept, and the x-intercepts (if any exist), and graph the function.
30) f(x) = -x2 - 2x + 3
A)
B)
C)
Vertex (- 1, - 4);
x-int = (-3,0) and (1, 0);
y-int = (0, 3)
Vertex (- 1, 4);
x-int = (-3,0) and (1, 0);
y-int = (0, 3)
Vertex (1, 4);
x-int = (-1,0) and (3, 0);
y-int = (0, 3)
9
D)
Vertex (- 1, 4);
x-int = (-1,0) and (3, 0);
y-int = (0, 3)
E) NOTA
10
Answer Key
Testname: ALGEBRA 1_14TH_COMPETITION_FGCU_2016 - FIRST EDIT
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
D
A
A
D
B
C
C
B
D
C
D
C
A
C
B
B
A
D
B
C
B
D
C
A
C
D
C
B
D
B
11