Free Printable Algebraic Reasoning OCL Cumulative Review

1.

What is the rule for the given table?

a)

Multiply by 2

b)

Multiply by 3

c)

Add 3

d)

Add 4

2.

Which equation represents the relationship of the values in the table?

a)

$y=x+6$

b)

$y=6-x$

c)

$y=x+3$

d)

$y=3x$

3.

Identify the type of function shown on the given graph.

a)

Linear

b)

Quadratic

c)

Exponential

4.

Identify the type of function shown on the given graph.

a)

Linear

b)

Quadratic

c)

Exponential

5.

Which linear equation matches the given table?

a)

$f\left(x\right)=3x+9$

b)

$f\left(x\right)=x+9$

c)

$f\left(x\right)=x+3$

d)

$f\left(x\right)=12x-3$

6.

What algebraic equation shows the relationship between the independent and dependent variables?

a)

$y=ax$

b)

$y=x+12$

c)

$y=-3x$

d)

$y=x$

7.

Compare the function y = 5x² to the parent function y = x²

a)

Wider

b)

More Narrow

8.

Describe the transformation of y = (x - 4)²

a)

Shift Up

b)

Shift Down

c)

Shift Left

d)

Shift Right

9.

Describe the transformation of y = 3(x - 3)² + 3

a)

Narrow, Right, Up

b)

Narrow, Left, Down

c)

Wide, Right, Up

d)

Wide, Left Down

10.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, 4)

11.

True or false:

The solution, root, x-intercept, and zero of a problem are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

12.

What is the y-intercept of the following cubic function?

a)

(1, 0)

b)

(0, 2)

c)

(-1, 0)

d)

(2, 0)

13.

Determine the roots of the polynomial.
$f\left(x\right)=\left(x+1\right)\left(x-4\right)\left(x+2\right)$

a)

1, 4, 2

b)

1, -4, 2

c)

-1, -4, -2

d)

-1, 4, -2

14.

Describe the transformation of the graph y = -(x - 4)³ + 5

a)

Up 5 and Left 4

b)

Reflect x-axis, Left 4, Up 5

c)

Reflect x-axis, Right 4, Up 5

d)

Right 4 and up 5

15.

Determine the transformation:
$y=\left|x-3\right|+2$

a)

left 3, up 2

b)

right 3, up 2

c)

left 3, down 2

d)

right 3, down 2

16.

Describe the transformation:
$y=\frac{1}{4}\left|x+3\right|-1$

a)

stretch by factor of 1/4, right 3, down 1

b)

stretch by factor of 1/4, right 3, up 1

c)

stretch by factor of 1/4, left 3, down 1

d)

stretch by factor of 1/4, left 3, up 1

17.

Determine the domain of the given function.
$f\left(x\right)=\left|x+5\right|+1$

a)

$x>5$

b)

$x>-5$

c)

$x>1$

d)

All real numbers

18.

Determine the range of the given function.
$y=2\left|x-3\right|$

a)

$y>2$

b)

$y<2$

c)

$y>0$

d)

$y<0$

19.

Add the polynomials.

(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

20.

Subtract: (2a² + 5a + 3) -(a² - 3a - 4)

a)

3a² + 2a - 1

b)

a²+ 8a + 7

c)

3a²+ 8a + 7

d)

a² + 2a - 1

21.

Find f(n)+g(n)

f(n)=2n+1

g(n)=3n

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

22.

Find f(n)-g(n)

f(n)=x²+1

g(n)=2x-5

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

23.

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

24.

f(x) = 3 and g(x) = -2x + 5
Find $f\left(x\right)\cdot g\left(x\right)$

a)

6x+15

b)

6x-15

c)

-6x+15

d)

6x-8

25.

Find the product.

(2y - 7)(3y + 5)

a)

y²+ 2y + 4

b)

6y² -11y -35

c)

-35 -11y + 6y²

d)

2y²-17y +30

26.

f(x) = 6x² + 3x + 2 and g(x) = x - 7

Find f(x) * g(x)

a)

6x³ - 39x² - 19x + 14

b)

6x³ - 39x² - 21x - 14

c)

6x³ - 39x² - 19x - 14

d)

6x³ - 45x² - 19x + 14

27.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

28.

Simplify the rational function.

a)

$\frac{1}{\left(x+5\right)}$

b)

$\frac{1}{\left(x-5\right)}$

c)

$\left(x+5\right)\left(x-5\right)$

d)

$\frac{\left(x-5\right)}{\left(x+5\right)\left(x-5\right)}$

29.

Factor and cancel out in order to simplify.

a)

$\frac{1}{\left(n-7\right)}$

b)

$\left(n-7\right)$

c)

$\frac{\left(n-6\right)}{\left(n-7\right)}$

d)

$\left(n-6\right)$

30.

What is the GCF of $5x^2+20x$

a)

5

b)

x

c)

5x

d)

20x

31.

Factor the GCF: 4b⁵+ 4b³+ 16b²

a)

4b³(b⁴+ b²+ 4b)

b)

4b³(b⁴+ 4b + 5)

c)

4(b⁵+ b³+ 4b²)

d)

4b²(b³+ b + 4)

32.

Using the graph of the function $h\left(x\right)=-x^2+4x$
find the solution(s). Choose all that apply.

a)

(0, 4)

b)

(0, 0)

c)

(4, 0)

d)

(4, 4)

33.

Using the table, find the solutions for the given function. Choose all that apply.

a)

(-4, 0)

b)

(-1, 0)

c)

(1, 0)

d)

(4, 0)

Algebraic Reasoning OCL Cumulative Review

Total questions: 33

Worksheet time: 3hrs 45mins

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