Download Adv Alg Test S1 1 Prep - Tamalpais Union High School District

Redwood High School. Department of Mathematics
Hard Worker's Name:___________________________________
Advanced Algebra S1 Test #1 Prep Package . Please work in your notebook
Sketch a graph of f.
1) f(x) = 3x2 - 7x
Use the discriminant to determine the number of real
solutions.
13) t2 - 4t + 4 = 0
13)
14) (5 + 2x)2 = 0
Find the vertex of the parabola
15) y = 5x2 - 8
16) y = -2x2 - 24x - 66
14)
15)
16)
Find the y-intercepts and any x-intercepts.
17) y = x2 + 5x + 9
17)
Graph the function using its vertex, axis of symmetry, and
intercepts.
2) f(x) = x2 - 8x
2)
3) f(x) = x2 + 2x - 3
3)
4) f(x) = 2x2 - 8x + 9
4)
Factor the polynomial completely.
5) 2y3 + 14y2 - 10y2 - 70y
18) y = -3x2 - 8x + 2
5)
Solve the quadratic equation.
19) 8x2 = 24x
19)
20) x(x - 8) = 20
20)
21) x2 + 12x + 36 = 10
21)
Use the discriminant to determine the number of real
solutions.
22) t2 + 8t + 16 = 0
22)
6) 10z 2 + 11z - 6
6)
7) 10z 2 - 35z - 20
7)
23) (3 + 7x)2 = 0
8) 12x3 - 1200x
8)
Sketch a graph of f by hand.
24) f(x) = 3(x + 4)2 - 1
Solve the quadratic equation.
9) 5x2 = 65
9)
Factor the trinomial completely.
25) -x2 - 3x + 70
10) x(x - 1) = 20
11) x2 + 8x + 16 = 13
12) 3x2 + 8x + 1 = 0
18)
23)
25)
10)
26) 15x2 + 22x + 8
26)
27) 10y2 + 23y + 12
27)
28) -25x2 + 30x + 16
28)
11)
12)
1
Solve the system by addition.
35) 2x - 5y = 49
4x = 47 + 10y
Sketch a graph of f. indicate vertex, X and Y intercepts and
Axis of symmetry. Show your work
29) f(x) = -3x2 + 3x
36)
1
1
x+ y=4
7
8
35)
36)
3
3
x + y = 11
7
8
Solve the problem.
37) A vendor has learned
that, by pricing hot dogs
at $1.00, sales will reach
122 hot dogs per day.
Raising the price to $1.50
will cause the sales to fall
to 102 hot dogs per day.
The number of hot dogs,
N, is a linear function of
the price, x. Write a linear
function that models the
number of hot dogs sold
per day when the price is
x dollars each.
Solve the system by graphing.
30) 4x - 2y = 16
4x + 2y = 24
Factor by grouping.
38) 10x2 - 15x + 8x - 12
39) 20x2 - 8x + 15x - 6
31) 3x - 9y = 6
1
2
y= x3
3
31)
32) 6x - y = 18
x + 6y = 40
32)
Solve the system by substitution.
33) x + 8y = 59
2x + 8y = 54
33)
7x 5y
+
=4
3
4
34)
34)
37)
38)
39)
Factor the trinomial completely.
40) 2x2 - 12x + 16
40)
41) 4x3 + 8x2 - 60x
41)
42) 18x2 - 63x - 36
42)
43) -2x3 - 4x2 + 96x
43)
44) -2x2 - 10x + 48
44)
Solve the equation using the quadratic formula.
45) 5x2 = -12x - 5
45)
5x
- 2y = 21
6
46) x2 - 6x + 13 = 0
2
46)
Graph.
47) y = x2 + 3x - 9
47)
48) y = -x2 + 3x - 9
48)
49) y = 2x2 + 2x - 7
49)
50) y = -4x2 - 2x - 9
3
50)
Answer Key
Testname: ADV ALGEBRA TEST S1 1 V4.1
1)
2) vertex (4, -16)
intercepts (0, 0), (8, 0)
3) vertex (-1, -4)
intercepts (1, 0), (- 3, 0), (0, -3)
4
Answer Key
Testname: ADV ALGEBRA TEST S1 1 V4.1
4) vertex (2, 1)
intercept (0, 9)
5) 2y(y + 7)(y - 5)
6) (2z + 3)(5z - 2)
7) 5(2z + 1)(z - 4)
8) 12x(x + 10)(x - 10)
9) ± 13
10) -4, 5
11) -4 ± 13
-4 ± 13
12)
3
13) One real solution
14) One real solution
15) (0, -8)
16) (-6, 6)
17) y-intercept (0, 9), no x-intercepts
-4 + 22
-4 - 22
, 0 and
,0
18) y-intercept (0, 2), x-intercepts
3
3
19) 0, 3
20) -2, 10
21) -6 ± 10
22) One real solution
23) One real solution
24)
25) -(x - 7)(x + 10)
5
Answer Key
Testname: ADV ALGEBRA TEST S1 1 V4.1
26) (3x + 2)(5x + 4)
27) (2y + 3)(5y + 4)
28) -(5x + 2)(5x - 8)
29)
30) {(5, 2)}
31) Infinite number
32) One
33) {(-5, 8)}
34) {(6, -8)}
35)
36)
37) N(x) = -40x + 162
38) (5x + 4)(2x - 3)
39) (4x + 3)(5x - 2)
40) 2(x - 2)(x - 4)
41) 4x(x - 3)(x + 5)
42) 9(2x + 1)(x - 4)
43) -2x(x - 6)(x + 8)
44) -2(x - 3)(x + 8)
-6 ± 11
45)
5
46) {3 ± 2i}
47)
6
Answer Key
Testname: ADV ALGEBRA TEST S1 1 V4.1
48)
49)
50)
7