WorksheetsAlgebra 2 honers math review
Total questions: 100
Worksheet time: 50mins
Simplify the expression: (8 - 7i) - (7i) + 2
8 - 14i + 2
8 - 7i + 2
10 - 7i
10 - 14i
Simplify the expression: (-5 - 5i) + (-1 - 5i)
-6 - 10i
-6 - 5i
-4 - 10i
-4 - 5i
Solve the equation: log_6 4 + log_6 (x + 5) = 1
x = -1
x = -4
x = -3
x = -5
Solve the equation: log_9 5x^2 - log_9 5 = 4
x = 3
x = 5
x = 2
x = 4
Simplify the expression: (-2 + i)^2
4 - 4i + i^2
4 - 4i - 1
4 - 4i + 1
4 + 4i - 1
Solve the equation: log_4 4x^2 - log_4 4 = 4
x = 2
x = 4
x = 1
x = 3
Which of the following inequalities is represented by the graph?
y ≤ x^2 - 2x + 4
y ≥ x^2 - 2x + 4
y < x^2 - 2x + 4
y > x^2 - 2x + 4
Which of the following inequalities is represented by the graph?
y ≤ x^2 + 8x + 15
y ≥ x^2 + 8x + 15
y < x^2 + 8x + 15
y > x^2 + 8x + 15
Which of the following inequalities is represented by the graph?
y ≤ x^2 + 2x
y ≥ x^2 + 2x
y < x^2 + 2x
y > x^2 + 2x
Which of the following inequalities is represented by the graph?
y ≤ x^2 + 6x + 12
y ≥ x^2 + 6x + 12
y < x^2 + 6x + 12
y > x^2 + 6x + 12
Which of the following is the correct graph for the function f(x) = 4/x - 2?
Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -2
Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -1
Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 0
Graph with vertical asymptote at x = 1 and horizontal asymptote at y = -2
Which of the following is the correct graph for the function f(x) = 4/x - 1?
Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -2
Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -1
Graph with vertical asymptote at x = -1 and horizontal asymptote at y = 0
Graph with vertical asymptote at x = 1 and horizontal asymptote at y = -1
Which of the following is the correct graph for the function f(x) = 3/(x + 2)?
Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 0
Graph with vertical asymptote at x = 0 and horizontal asymptote at y = 2
Graph with vertical asymptote at x = 2 and horizontal asymptote at y = 0
Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 3
Divide r^4 - r^3 - 4r^2 - 3r - 1 by r + 1
r^3 - 2r^2 - 2r - 1
r^3 - r^2 - 3r - 1
r^3 - r^2 - 2r - 1
r^3 - 2r^2 - 3r - 1
Divide x^3 + 11x^2 + 23x - 42 by x + 6
x^2 + 5x + 7
x^2 + 5x - 7
x^2 + 6x + 7
x^2 + 6x - 7
Divide 8p^3 - 39p^2 + 29p - 4 by p - 4
8p^2 - 7p + 1
8p^2 - 7p - 1
8p^2 - 8p + 1
8p^2 - 8p - 1
Divide x^3 - 2x^2 - 26x - 8 by x + 4
x^2 - 6x - 2
x^2 - 6x + 2
x^2 - 7x - 2
x^2 - 7x + 2
Divide x^2 + 8x^2 - 10x + 1 by x - 1
x + 9x - 1
x + 9x + 1
x + 8x - 1
x + 8x + 1
Divide x^3 + 4x^2 - 5x - 18 by x + 2
x^2 + 2x - 9
x^2 + 2x + 9
x^2 + 3x - 9
x^2 + 3x + 9
Divide 10p^4 - 108p^3 + 83p^2 - 40p + 100 by p - 10
10p^3 - 8p^2 + 3p - 10
10p^3 - 8p^2 + 3p + 10
10p^3 - 9p^2 + 3p - 10
10p^3 - 9p^2 + 3p + 10
Which of the following equations represents the graph of a circle centered at the origin with a radius of 6?
x^2 + y^2 + 8x - 4y + 19 = 0
x^2 + y^2 - 8x + 4y + 19 = 0
x^2 + y^2 - 36 = 0
x^2 + y^2 - 2x - 2y - 2 = 0
Factor the expression 54u^3 - 2 completely.
2(27u^3 - 1)
2(27u - 1)(u^2 + u + 1)
2(27u - 1)(u^2 - u + 1)
54(u - 1)(u^2 + u + 1)
Factor the expression 2 - 432x^3 completely.
2(1 - 216x^3)
2(1 - 6x)(1 + 6x + 36x^2)
2(1 - 6x)(1 - 6x + 36x^2)
2(1 - 6x)(1 + 6x - 36x^2)
Factor the expression 54a^3 + 16 completely.
2(27a^3 + 8)
2(27a + 2)(a^2 - 2a + 4)
2(27a + 2)(a^2 - 2a + 8)
2(27a + 2)(a^2 - 2a + 16)
Factor the expression -2u^3 + 250 completely.
-2(u^3 - 125)
-2(u - 5)(u^2 + 5u + 25)
-2(u - 5)(u^2 - 5u + 25)
-2(u - 5)(u^2 + 5u - 25)
Factor the expression 108x^3 + 4 completely.
4(27x^3 + 1)
4(27x + 1)(x^2 - x + 1)
4(27x + 1)(x^2 + x + 1)
4(27x + 1)(x^2 - x + 4)
Factor the expression 54x^3 - 128 completely.
2(27x^3 - 64)
2(27x - 4)(x^2 + 4x + 16)
2(27x - 4)(x^2 - 4x + 16)
2(27x - 4)(x^2 + 4x - 16)
Factor the expression 216m^3 + 1 completely.
1(216m^3 + 1)
1(6m + 1)(36m^2 - 6m + 1)
1(6m + 1)(36m^2 + 6m + 1)
1(6m + 1)(36m^2 - 6m + 6)
Factor the expression 8 - 125x^3 completely.
(2 - 5x)(4 + 10x + 25x^2)
(2 - 5x)(4 - 10x + 25x^2)
(2 - 5x)(4 + 10x - 25x^2)
(2 - 5x)(4 - 10x - 25x^2)
Condense the expression ( 30 log_9 x + 6 log_9 y ) to a single logarithm.
log_9 (x^{30} y^6)
log_9 (x^{6} y^{30})
log_9 (x^{36} y)
log_9 (x y^{36})
Condense the expression ( 18 log_7 x + 3 log_7 y ) to a single logarithm.
log_7 (x^{18} y^3)
log_7 (x^{3} y^{18})
log_7 (x^{21} y)
log_7 (x y^{21})
Condense the expression ( 15 log_6 x + 5 log_6 y ) to a single logarithm.
log_6 (x^{15} y^5)
log_6 (x^{5} y^{15})
log_6 (x^{20} y)
log_6 (x y^{20})
Condense the expression ( 3 ln 7 + ln 10 / 3 ) to a single logarithm.
ln (7^3 * 10^(1/3))
ln (7^3 * 10^3)
ln (7 * 10^(1/3))
ln (7^3 * 10)
Expand the logarithm log_8 (10 * 3^2)^6.
6 log_8 (10) + 12 log_8 (3)
6 log_8 (10) + 6 log_8 (3^2)
6 log_8 (10) + 2 log_8 (3^6)
6 log_8 (10) + 6 log_8 (3)
Expand the logarithm log_4 (7 * 8^4)^6.
6 log_4 (7) + 24 log_4 (8)
6 log_4 (7) + 6 log_4 (8^4)
6 log_4 (7) + 4 log_4 (8^6)
6 log_4 (7) + 6 log_4 (8)
Expand the logarithm log_7 (6 * 5 * 11^2).
log_7 (6) + log_7 (5) + 2 log_7 (11)
log_7 (6) + log_7 (5) + log_7 (11^2)
log_7 (6) + 2 log_7 (5) + log_7 (11)
log_7 (6) + log_7 (5^2) + log_7 (11)
Expand the logarithm log_7 (11^5 / 2^4).
5 log_7 (11) - 4 log_7 (2)
5 log_7 (11) + 4 log_7 (2)
4 log_7 (11) - 5 log_7 (2)
4 log_7 (11) + 5 log_7 (2)
Expand the logarithm log_6 ( (8 * 3 * 7)^(1/3) ).
(1/3) (log_6 (8) + log_6 (3) + log_6 (7))
(1/3) (log_6 (8) + log_6 (3) - log_6 (7))
(1/3) (log_6 (8) - log_6 (3) + log_6 (7))
(1/3) (log_6 (8) - log_6 (3) - log_6 (7))
Evaluate log_8 (u^6 / v^6).
6 log_8 (u/v)
log_8 (u/v)
0
1
Evaluate log_7 (z^5 / x^(3/2)).
5 log_7 (z) - (3/2) log_7 (x)
log_7 (z) - (3/2) log_7 (x)
5 log_7 (z) + (3/2) log_7 (x)
log_7 (z) + (3/2) log_7 (x)
Evaluate log_2 ((5/6)^2).
2 log_2 (5/6)
log_2 (5/6)
-2 log_2 (5/6)
-log_2 (5/6)
Evaluate log_5 (sqrt(11) * 3 * 10).
log_5 (33 * sqrt(11))
log_5 (330)
log_5 (33)
log_5 (sqrt(330))
Evaluate log_7 (343).
3
2
1
0
Evaluate log_3 (243).
5
4
3
2
Evaluate log_3 (27).
3
2
1
0
Evaluate log_5 (125).
3
2
1
0
Evaluate log_5 (1/25).
-2
-1
0
1
Evaluate log_3 (9).
2
1
0
-1
Evaluate log_6 (216).
3
2
1
0
Evaluate log_4 (64).
3
2
1
0
Evaluate log_2 (1).
0
1
2
-1
Evaluate log_4 (16).
2
1
0
-1
Solve the quadratic equation: 2n^2 - 4n = 23.
(a)
Solve the quadratic equation: 2x^2 + 5 = -12x.
(a)
Solve the quadratic equation: 8n^2 - 4n = 5.
(a)
Solve the quadratic equation: 5x^2 = 4 - x.
(a)
Solve the quadratic equation: 10n^2 - 2n = 7.
(a)
Solve the quadratic equation: 5a^2 - 13 = -8a.
(a)
Solve the quadratic equation: x^2 = 12x + 20.
(a)
Solve the quadratic equation: 8r^2 - 13 = -7r.
(a)
Solve the quadratic equation: 3x^2 + 2x = 9.
(a)
Solve the quadratic equation: 11p^2 = -3p + 11.
(a)
Convert -75° to radians.
-5π/12
-5π/6
-π/4
-π/3
Convert 4π/3 radians to degrees.
120°
180°
240°
270°
Convert -220° to radians.
-11π/9
-11π/6
-5π/6
-7π/6
Convert -π/3 radians to degrees.
-45°
-60°
-90°
-120°
Convert 135° to radians.
3π/4
5π/6
2π/3
7π/6
Convert 210° to radians.
5π/6
7π/6
11π/6
4π/3
Convert 700° to radians.
35π/9
35π/18
25π/9
25π/18
Convert 11π/36 radians to degrees.
55°
60°
70°
90°
Convert 7π/6 radians to degrees.
180°
210°
240°
270°
Convert 60° to radians.
π/6
π/3
π/4
π/2
Find (g ∘ h)(x) if g(x) = x² - 2x and h(x) = -x - 4.
(x + 4)² - 2(x + 4)
(x - 4)² - 2(x - 4)
(-x - 4)² - 2(-x - 4)
(x + 4)² + 2(x + 4)
Find (f ∘ g)(x) if f(x) = -2x + 2 and g(x) = -2x³ - 4x.
-2(-2x³ - 4x) + 2
-2(-2x³ - 4x) - 2
-2(-2x³ + 4x) + 2
-2(-2x³ + 4x) - 2
Find (f ∘ g)(t) if f(t) = 3t - 3 and g(t) = -2t² + t.
3(-2t² + t) - 3
3(-2t² + t) + 3
3(-2t² - t) - 3
3(-2t² - t) + 3
Find (g ∘ h)(a) if g(a) = a - 1 and h(a) = a² - 4a.
(a² - 4a) - 1
(a² - 4a) + 1
(a² + 4a) - 1
(a² + 4a) + 1
Find (f ∘ g)(x) if f(x) = 3x + 2 and g(x) = x³ + 2x².
3(x³ + 2x²) + 2
3(x³ + 2x²) - 2
3(x³ - 2x²) + 2
3(x³ - 2x²) - 2
Find (g ∘ h)(t) if g(t) = 4t + 5 and h(t) = -2t.
4(-2t) + 5
4(-2t) - 5
4(2t) + 5
4(2t) - 5
Find (h ∘ g)(t) if h(t) = 3t - 1 and g(t) = t + 2.
3(t + 2) - 1
3(t + 2) + 1
3(t - 2) - 1
3(t - 2) + 1
Find (g ∘ f)(n) if g(n) = 2n - 4 and f(n) = 4n + 4.
2(4n + 4) - 4
2(4n + 4) + 4
2(4n - 4) - 4
2(4n - 4) + 4
Find (g ∘ h)(n) if g(n) = n - 5 and h(n) = n² + 2n.
(n² + 2n) - 5
(n² + 2n) + 5
(n² - 2n) - 5
(n² - 2n) + 5
Find (h ∘ g)(x) if h(x) = -x and g(x) = 2x - 3.
-(2x - 3)
-(2x + 3)
(2x - 3)
(2x + 3)
Which of the following equations represents a parabola that opens downwards?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations has a vertex at the point (4, -4)?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations represents a parabola with a minimum value?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations represents a parabola that opens upwards?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations has a vertex at the point (-1, -2)?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations has a vertex at the point (4, 1)?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Which of the following equations represents a parabola with a maximum value?
y = -2x^2 - 8x - 12
y = 3x^2 - 24x + 44
y = 3x^2 + 6x + 1
y = 2x^2 - 16x + 33
Identify the vertex and axis of symmetry of the quadratic function y = -2x^2 + 8x - 6. Then sketch the graph.
Vertex: (2, 2), Axis of symmetry: x = 2
Vertex: (1, 0), Axis of symmetry: x = 1
Vertex: (3, -1), Axis of symmetry: x = 3
Vertex: (4, 4), Axis of symmetry: x = 4
Identify the vertex and axis of symmetry of the quadratic function y = x^2 + 6x + 7. Then sketch the graph.
Vertex: (-3, -2), Axis of symmetry: x = -3
Vertex: (-2, -1), Axis of symmetry: x = -2
Vertex: (-1, 0), Axis of symmetry: x = -1
Vertex: (0, 1), Axis of symmetry: x = 0
Identify the vertex and axis of symmetry of the quadratic function x = -2y^2 + 4y + 4. Then sketch the graph.
Vertex: (3, 1), Axis of symmetry: y = 1
Vertex: (2, 2), Axis of symmetry: y = 2
Vertex: (1, 1), Axis of symmetry: y = 1
Vertex: (0, 0), Axis of symmetry: y = 0
Identify the vertex and axis of symmetry of the quadratic function x = y^2 - 10y + 28. Then sketch the graph.
Vertex: (3, 5), Axis of symmetry: y = 5
Vertex: (2, 4), Axis of symmetry: y = 4
Vertex: (1, 3), Axis of symmetry: y = 3
Vertex: (0, 2), Axis of symmetry: y = 2
Which of the following is the inverse of the function f(x) = sqrt((-x + 3) / 2)?
A) f^-1(x) = 2x^2 - 3
B) f^-1(x) = -2x^2 + 3
C) f^-1(x) = 2x^2 + 3
D) f^-1(x) = -2x^2 - 3
Which of the following is the inverse of the function f(x) = -3 / x - 2?
A) f^-1(x) = -3 / (x + 2)
B) f^-1(x) = 3 / (x + 2)
C) f^-1(x) = -3 / (x - 2)
D) f^-1(x) = 3 / (x - 2)
Which of the following is the inverse of the function g(x) = (4 - sqrt(16x)) / 2?
A) g^-1(x) = (4 - 2x) / 16
B) g^-1(x) = (4 - 2x^2) / 16
C) g^-1(x) = (4 - 4x) / 16
D) g^-1(x) = (4 - 4x^2) / 16
Which of the following is the inverse of the function f(x) = -4 / (x + 1) - 3?
A) f^-1(x) = -4 / (x + 3) - 1
B) f^-1(x) = -4 / (x - 3) - 1
C) f^-1(x) = -4 / (x + 3) + 1
D) f^-1(x) = -4 / (x - 3) + 1
Which of the following is the inverse of the function f(x) = (-15 + 3x) / 5?
A) f^-1(x) = (5x + 15) / 3
B) f^-1(x) = (5x - 15) / 3
C) f^-1(x) = (3x + 15) / 5
D) f^-1(x) = (3x - 15) / 5
Which of the following is the inverse of the function h(x) = 1 / (-x - 3) + 2?
A) h^-1(x) = 1 / (-x + 2) - 3
B) h^-1(x) = 1 / (-x - 2) + 3
C) h^-1(x) = 1 / (-x + 2) + 3
D) h^-1(x) = 1 / (-x - 2) - 3
Which of the following is the inverse of the function g(x) = -x - 1?
A) g^-1(x) = -x + 1
B) g^-1(x) = -x - 1
C) g^-1(x) = x - 1
D) g^-1(x) = x + 1
