Free Printable Algebra and Vectors Assessment

1.

What is the solution to the system of equations?

a)

(5, 2)

b)

(2, 5)

c)

(-5, 2)

d)

(-2, -5)

2.

What is the solution to the system of equations?

a)

(3, -2)

b)

(3, 2)

c)

(2, 3)

d)

(2, -3)

3.

What is the solution to the system of equations?

a)

(-3, -4)

b)

(-4, 3)

c)

(4, -3)

d)

(-3, 4)

4.

What is the solution to the system of equations?

a)

(-5, -2)

b)

(2, -5)

c)

(2, 5)

d)

(-5, 2)

5.

What is the solution to the system of equations?

a)

(4, 1)

b)

(-4, -1)

c)

(1, 4)

d)

(-1, 4)

6.

What is the solution to the system of equations?

a)

(2, 3)

b)

(-3, 2)

c)

(2, -3)

d)

(3, 2)

7.

What is the solution to the system of equations?

a)

(-7, -5)

b)

(5, 7)

c)

(-5, -7)

d)

(-7, 5)

8.

What is the solution to the system of equations?

a)

(-3, 4)

b)

(3, 4)

c)

(-4, 3)

d)

(4, 3)

9.

$4x-3y=18$
$5x\ +2y=11$

4 lines

10.

$2x\ -3y\ =9$
$5x\ +y=9$

4 lines

11.

$3x\ -y=13$
$2x\ +3y=5$

4 lines

12.

$2x\ -5y=24$
$7x+8y=33$

4 lines

13.

$x+2y=-5$
$3x-y=13$

4 lines

14.

$3x+2y=17$
$2x+5y=4$

4 lines

15.

$10x-6y=52$
$12x+6y=102$

4 lines

16.

$8x+9y=3$
$x+y=0$

4 lines

17.

$2x+13y=36$
$13x+2y=69$

4 lines

18.

$7x-y=15$
$3x-2y=19$

4 lines

19.

Two pencils and a ruler cost 49 cents in total. One pencil and two rulers cost 62 cents in total. Find the cost of each item.

a)

pencil: 13 cents

ruler: 23 cents

b)

pencil: 15 cents

ruler: 23.50 cents

c)

pencil: 12 cents

ruler: 25 cents

d)

pencil: 18 cents

ruler: 26 cents

20.

Write an equation. Chelsea buys 8 packs of markers. Each pack contains the same number of markers. Chelsea gave 10 markers to her brother. Then, she has 54 markers left. How many markers were in each pack?

a)

8 - 10 = 54

b)

8p - 10 = 54

c)

8p + 10 = 54

d)

54 + 8p = 10

21.

Write and solve an equation. Chelsea buys 8 packs of markers. Each pack contains the same number of markers. Chelsea gave 10 markers to her brother. Then, she has 54 markers left. How many markers were in each pack?

a)

7 markers

b)

8 markers

c)

9 markers

d)

10 markers

22.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

23.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

24.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

25.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

26.

Solve the simultaneous equations $y = x^2 + 3x + 2$ and $y = 2x + 4$ .

a)

$(1, 6)$ and $(-2, 0)$

b)

$(0, 2)$ and $(1, 6)$

c)

$(2, 8)$ and $(-1, 2)$

d)

$(1, 6)$ and $(-2, 4)$

27.

Find the solution for the equations $x^2 + y^2 = 25$ and $x - y = 1$ .

a)

$(3, 4)$ and $(-4, -3)$

b)

$(4, 3)$ and $(-3, -4)$

c)

$(5, 0)$ and $(0, 5)$

d)

$(3, 2)$ and $(-2, -3)$

28.

Solve the pair of equations $x^2+y^2=20$ and $x + y = 6$ .

a)

$(3, 3)$ and $(4, 2)$

b)

$(3, 3)$ only

c)

$(4, 2)$ and $(2, 4)$

d)

No solution

29.

Given the equations $y = 3x^2 + 12x + 9$ and $y = 6x + 9$ , find the points of intersection.

a)

$(0, 9)$ and $(-4, -15)$

b)

$(1, 24)$ and $(-3, 9)$

c)

$(0, 9)$ and $(-2,-3)$

d)

$(1, 24)$ and $(-4, -15)$

30.

Solve the simultaneous equations $x^2 + 4x - y = 0$ and $2y-8x=8$ .

a)

$(2, 12)$ and $(-6, -16)$

b)

$(4, 32)$ and $(-2, 0)$

c)

$(2, 12)$ and $(-2,-4)$

d)

$(4, 32)$ and $(-6, -16)$

31.

Solve the equations $x^2 + 2x + y = 7$ and $y = x + 3$ .

a)

$(1, 4)$ and $(-4, -1)$

b)

$(2, 5)$ and $(-3, 0)$

c)

$(1, 4)$ and $(-3, 0)$

d)

$(2, 5)$ and $(-4, -1)$

32.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

33.

Find the vertex of
f(x) = -x²- 4x + 12

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

34.

What direction is the following equation opening?
y=-3x²-7x+8

a)

Up

b)

Down

c)

Left

d)

Right

35.

Does
y = -4x²
have a maximum or minimum value?

a)

maximum

b)

minimum

36.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

37.

What is the minimum value of the quadratic function

f(x) = x² - 2x + 7

a)

6

b)

7

38.

How does the parabola open? y = 4x - x² - 1

a)

up

b)

down

c)

left

d)

right

39.

Which graph shows y = x² + 5x + 4 ?

a)

b)

c)

d)

40.

Which graph shows y = x² - 5x + 4 ?

a)

b)

c)

d)

41.

Which value is the vertex?

a)

(-4, 0)

b)

(-1, -9)

c)

(0, -8)

d)

(2, 0)

42.

What is the equation of the graph?

a)

-(x-1)²-2

b)

(x-2)²+1

c)

-(x+2)²+1

d)

-(x+4)^2-1

43.

Which point is an example of a y-intercept?

a)

(3,4)

b)

(-2,8)

c)

(0,4)

d)

(5,0)

44.

Which equation could match the graph?

a)

y = (x + 2)²- 1

b)

y = (x - 2)²- 1

c)

y = (x + 2)²+ 1

d)

y = (x - 2)²+ 1

45.

Which equation could match the graph?

a)

y = (x + 2)²- 1

b)

y = (x - 2)²- 1

c)

y = (x + 2)²+ 1

d)

y = (x - 2)²+ 1

46.

What are the solutions to the parabola?

a)

(5, 0), (2, 0)

b)

(0, -10)

c)

(0, -5), 90, 2)

d)

(- 5, 0), (2, 0)

47.

What is the y-intercept of

$y=2x^2-x-10$

a)

-10

b)

-1

c)

2

d)

$-\frac{5}{2}$

48.

What are the x-intercepts of

$y=2x^2+15x-8$

a)

$\left(8,0\right)\ \&\ \left(\frac{1}{2},0\right)$

b)

$\left(-8,0\right)\ \&\ \left(\frac{1}{2},0\right)$

c)

$\left(8,0\right)\ \&\ \left(-\frac{1}{2},0\right)$

d)

$\left(-8,0\right)\ \&\ \left(-\frac{1}{2},0\right)$

49.

Convert to vertex form:

f(x) = x² + 10x + 24

a)

f(x) = ( x - 5 )² + 1

b)

f(x) = ( x + 5 )² - 1

c)

f(x) = ( x - 5 )² - 1

d)

f(x) = ( x + 5 )² + 1

50.

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

51.

What piece of information does c identify in the following equation?
y=ax²+bx+c

a)

Zeroes

b)

Axis of Symmetry

c)

Direction

d)

y-intercept

52.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

53.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

54.

What is the vertex of function

f(x) = 3(x+4)²-8? Write your answer as a coordinate (x,y)

(a)

55.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

both

d)

neither

56.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

57.

An Arrow with a Magnitude and Direction

a)

Scalar

b)

Vector

c)

Refractor

d)

Tip to Tail

58.

A method used to add vectors together

a)

Tip to Tail Method

b)

Resultant Vector

c)

Pythagorean Theorem

d)

$a^2+b^2=c^2$

59.

Which one of these does not show an example of Tip to Tail method?

a)

b)

c)

d)

60.

Velocity is an example of a

a)

Vector

b)

Scalar

61.

Time is an example of a

a)

Vector

b)

Scalar

62.

What is the sum of multiple vectors called?

a)

Scalar

b)

Vector Combination

c)

Resultant Vector

d)

Force

63.

Find the magnitude of this vector (each square is 1 unit long)

a)

4

b)

5

c)

3

d)

square root of 5

64.

If a car moves 12 miles North, 19 miles East, and 12 miles South, what is its displacement?

a)

12 miles

b)

19 miles, East

c)

31 miles

d)

43 miles, East

65.

A quantity that has only magnitude is known as a

a)

Scalar

b)

Vector

66.

A quantity that has a magnitude and a direction is known as a

a)

Scalar

b)

Vector

67.

Which of the following is NOT a scalar quantity?

a)

Momentum

b)

Length

c)

Mass

d)

Energy

68.

Which of the following is NOT a vector quantity?

a)

Density

b)

Displacement

c)

Acceleration

d)

Force

69.

Which of the following is NOT a contact force?

a)

Friction

b)

Spring Force

c)

Tension Force

d)

Gravity

70.

Which of the following is NOT a non-contact force?

a)

Friction

b)

Magnetic Force

c)

Electric Force

d)

Gravity

71.

The resultant of 5N East and 12 N East is...

a)

17 N East

b)

13 N East

c)

13 N West

d)

7 N East

72.

The resultant of 15N East and 8N West is...

a)

23 N East

b)

17 N East

c)

7 N West

d)

7 N East

73.

The resultant magnitude of 3N South and 4N West is...

a)

7 N

b)

5 N

c)

1 N

d)

12 N

74.

The horizontal component of the 150N force is

a)

150N x sin 60

b)

150N x cos 60

c)

150N x tan 60

75.

The vertical component of the 150N force is

a)

150N x sin 60

b)

150N x cos 60

c)

150N x tan 60

76.

The vertical component of the 150N force is

a)

150N

b)

130N

c)

75N

d)

50N

77.

The horizontal component of the 150N force is

a)

150N

b)

130N

c)

75N

d)

50N

78.

The resultant of the forces shown is

a)

30 N to the left

b)

30 N to the right

c)

90 N to the left

d)

90 N to the right

79.

The resultant of the forces shown is

a)

20 N to the left

b)

20 N to the right

c)

40 N to the left

d)

40 N to the right

Algebra and Vectors Assessment

Total questions: 79

Worksheet time: 4hrs 54mins

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