Math 8 Fall Benchmark

Posljednje ažuriranje 7 months ago

Equations

8.EE.7.a

8.EE.7.b

Congruence

8.G.1.b

8.G.1.a

8.G.1.b

Dilations and scale factors

7.G.1

8.G.3

Rigid Transformations

8.G.2

8.G.3

8.G.2

Slope

8.EE.6

Linear Equations (Graph & Write)

8.EE.6

Angle pairs

8.G.5

Triangle angles

8.G.5

Math 8 Fall Benchmark

Posljednje ažuriranje 7 months ago

Equations

What is a reasonable first step for solving the equation
4x - 14 = 6

add 14 to both sides

divide by 14 on both sides

multiply by 14 on both sides

subtract 14 from both sides

8.EE.7.a

Which equation is equivalent to
14+7y-25=4y+10

3y-11=10

5y+11=30

3y+14=30

11y+10=39

8.EE.7.b

Solve:
6+10p=8p+12

p=1

p=-6

p=3

p=6

8.EE.7.b

Solve:
\frac{2}{3}x-1=17

x=12

x=24

x=\frac{1}{27}

x=27

8.EE.7.b

Solve:
2(5x-7)+4=-35

x=-3.8

x=-3.2

x=-2.5

x=-5.3

8.EE.7.b

Solve:
2m+5=5m-35-3m

no solution

m=-7

m=7

many solutions

8.EE.7.b

Congruence

\triangle ABC is congruent to \triangle QRS.
What angle is congruent to \angle A?

\angle Q

\angle S

\angle C

\angle R

8.G.1.b

\triangle ABC is congruent to \triangle QRS.
Which side is congruent to \overline{BC}?

\overline{AC}

\overline{SQ}

\overline{RQ}

\overline{RS}

8.G.1.a

Trapezoid ABCD is congruent to trapezoid EFGH.
What is the measure of side \overline{GF}?

9 \;cm

5 \;cm

4 \;cm

13 \;cm

8.G.1.a

Trapezoid ABCD is congruent to trapezoid EFGH.
Which angle in trapezoid EFGH is congruent to \angle D?

\angle E

\angle F

\angle H

\angle G

8.G.1.b

Dilations and scale factors

The two figures are similar.
What is the ratio of the small to large figure?

\frac{13}{5}

-\frac{5}{13}

\frac{5}{13}

7.G.1

The unshaded figure is a dilation of the shaded figure.
Find the scale factor.

-3

\frac{1}{6}

8.G.3

Find the coordinates of J after a dilation of 3.

J^{\prime}(-5,4)

J^{\prime}(3,-6)

J^{\prime}(-6,3)

J^{\prime}(-2,1)

8.G.3

Find the coordinates of G after a dilation of \frac{1}{2}.
I(1, -1), G(2, 4), L(3, 1)

G^{\prime}(1,2)

G^{\prime}(4,8)

G^{\prime}(2\frac{1}{2},4\frac{1}{2})

G^{\prime}(1\frac{1}{2},\frac{1}{2})

8.G.3

Rigid Transformations

Choose the best rule to describe the transformation of the figure shown.

Translation

Reflection

Rotation 90\degree clockwise

Rotation 90\degree counterclockwise

8.G.2

Choose the best rule to describe the transformation of the figure shown.

Rotation 90\degree clockwise

Reflection

Rotation 90\degree counterclockwise

Translation

8.G.2

Find the coordinates of vertex Y after a translation 2 units left and 3 units down.

Y^{\prime}(-4, -1)

Y^{\prime}(-3, -2)

Y^{\prime}(-1, 1)

Y^{\prime}(-1, 4)

8.G.3

Find the coordinates of vertex J after a reflection across the y-axis.

J^{\prime}(-2, 5)

J^{\prime}(2, -5)

J^{\prime}(2, 5)

J^{\prime}(-2, -5)

8.G.3

Find the coordinates of vertex I after a rotation of 180\degree about the origin.

I^{\prime}(-2, 1)

I^{\prime}(1, -2)

I^{\prime}(2, 1)

I^{\prime}(2, -1)

Find the coordinates of vertex D after a rotation of 90\degree counterclockwise about the origin.

D^{\prime}(3, 5)

D^{\prime}(-3, -5)

D^{\prime}(5, 3)

D^{\prime}(-5, 3)

8.G.3

Choose the best rule to describe the transformation of the figure shown.

Reflection

Translation

Rotation 90\degree clockwise

Rotation 90\degree counterclockwise

8.G.2

Choose the best rule to describe the transformation of the figure shown.

Translation 7 units right and 2 units down

Rotation 180\degree

Reflection over y-axis

Translation 7 units left and 2 units up

8.G.2

Slope

Find the growth rate (slope) shown in the table.

\frac{1}{3}

-3

8.EE.6

Find the slope of the line that passes through
(7,2) and (11, 5).

m=\frac{7}{18}

m=\frac{4}{3}

m=\frac{6}{5}

m=\frac{3}{4}

8.EE.6

A student finds the slope of the line between
(17, 19) and (22, 21).
He writes \frac{19-21}{22-17}. What mistake did he make?

He used y-values where he should have used x-values.

He should have added the values, not subtracted them.

He did not make a mistake.

He did not keep the order of the points the same in the numerator and the denominator.

8.EE.6

Find the slope of the line.

-\frac{1}{2}

\frac{1}{2}

-2

8.EE.6

Linear Equations (Graph & Write)

What is the equation of the line in the graph shown below?

y=\frac{2}{3}x+3

y=\frac{3}{2}x-2

y=-\frac{2}{3}x+2

y=-3x+2

8.EE.6

Which is the equation of the line with a slope of -\frac{1}{3} and a y-intercept at (0, -2)?

y=-\frac{1}{3}x-2

y=\frac{1}{3}x-2

y=\frac{1}{3}x+2

y=-\frac{1}{3}x+2

8.EE.6

What is the equation of the line?

y=x

y=3

x=3

y=3x

8.EE.6

Graph the linear equation y = 2x + 6.

null

8.EE.6

Graph the linear equation y=-\frac{4}{9}x+7.

null

8.EE.6

Angle pairs

If \angle f = x + 44 and \angle b = 2x - 17, then find the value of \angle f.

73\degree

95\degree

105\degree

107\degree

8.G.5

If \angle e=84\degree, then find the value of \angle c.

116\degree

84\degree

6\degree

96\degree

8.G.5

Name the angle relationship for angles a and h.

vertical angles

alternate exterior angles

corresponding angles

alternate interior angles

8.G.5

Name the angle relationship for angles c and g.

alternate exterior angles

vertical angles

corresponding angles

alternate interior angles

8.G.5

Triangle angles

Find the measure of \angle x.

26\degree

162\degree

64\degree

116\degree

8.G.5

The measures of three angles of a triangle are
(2x)\degree, (3x)\degree, and (x+60)\degree.
What is the value of x?

5\degree

12\degree

20\degree

10\degree

8.G.5

Find the measure of \angle BCD.

92\degree

90\degree

102\degree

88\degree

8.G.5

Find the value of x.

8.3

8.G.5

Math 8 Fall Benchmark

Math 8 Fall Benchmark

What is a reasonable first step for solving the equation 4x - 14 = 6

Which equation is equivalent to 14+7y-25=4y+10

Solve:6+10p=8p+12

Solve:\frac{2}{3}x-1=17

Solve:2(5x-7)+4=-35

Solve:2m+5=5m-35-3m

\triangle ABC is congruent to \triangle QRS.What angle is congruent to \angle A?

\triangle ABC is congruent to \triangle QRS.Which side is congruent to \overline{BC}?

Trapezoid ABCD is congruent to trapezoid EFGH.What is the measure of side \overline{GF}?

Trapezoid ABCD is congruent to trapezoid EFGH. Which angle in trapezoid EFGH is congruent to \angle D?

The two figures are similar. What is the ratio of the small to large figure?

The unshaded figure is a dilation of the shaded figure. Find the scale factor.

Find the coordinates of J after a dilation of 3.

Find the coordinates of G after a dilation of \frac{1}{2}.I(1, -1), G(2, 4), L(3, 1)

Choose the best rule to describe the transformation of the figure shown.

Choose the best rule to describe the transformation of the figure shown.

Find the coordinates of vertex Y after a translation 2 units left and 3 units down.

Find the coordinates of vertex J after a reflection across the y-axis.

Find the coordinates of vertex I after a rotation of 180\degree about the origin.

Find the coordinates of vertex D after a rotation of 90\degree counterclockwise about the origin.

Choose the best rule to describe the transformation of the figure shown.

Choose the best rule to describe the transformation of the figure shown.

Find the growth rate (slope) shown in the table.

Find the slope of the line that passes through (7,2) and (11, 5).

A student finds the slope of the line between(17, 19) and (22, 21).He writes \frac{19-21}{22-17}. What mistake did he make?

Find the slope of the line.

What is the equation of the line in the graph shown below?

Which is the equation of the line with a slope of -\frac{1}{3} and a y-intercept at (0, -2)?

What is the equation of the line?

Graph the linear equation y = 2x + 6.

Graph the linear equation y=-\frac{4}{9}x+7.

If \angle f = x + 44 and \angle b = 2x - 17, then find the value of \angle f.

If \angle e=84\degree, then find the value of \angle c.

Name the angle relationship for angles a and h.

Name the angle relationship for angles c and g.

Find the measure of \angle x.

The measures of three angles of a triangle are (2x)\degree, (3x)\degree, and (x+60)\degree.What is the value of x?

Find the measure of \angle BCD.

Find the value of x.

What is a reasonable first step for solving the equation 4x - 14 = 6

Which equation is equivalent to 14+7y-25=4y+10

Solve:6+10p=8p+12

Solve:\frac{2}{3}x-1=17

Solve:2(5x-7)+4=-35

Solve:2m+5=5m-35-3m

\triangle ABC is congruent to \triangle QRS.What angle is congruent to \angle A?

\triangle ABC is congruent to \triangle QRS.Which side is congruent to \overline{BC}?

Trapezoid ABCD is congruent to trapezoid EFGH.What is the measure of side \overline{GF}?

Trapezoid ABCD is congruent to trapezoid EFGH. Which angle in trapezoid EFGH is congruent to \angle D?

The two figures are similar. What is the ratio of the small to large figure?

The unshaded figure is a dilation of the shaded figure. Find the scale factor.

Find the coordinates of J after a dilation of 3.

Find the coordinates of G after a dilation of \frac{1}{2}.I(1, -1), G(2, 4), L(3, 1)

Choose the best rule to describe the transformation of the figure shown.

Choose the best rule to describe the transformation of the figure shown.

Find the coordinates of vertex Y after a translation 2 units left and 3 units down.

Find the coordinates of vertex J after a reflection across the y-axis.

Find the coordinates of vertex I after a rotation of 180\degree about the origin.

Find the coordinates of vertex D after a rotation of 90\degree counterclockwise about the origin.

Choose the best rule to describe the transformation of the figure shown.

Choose the best rule to describe the transformation of the figure shown.

Find the growth rate (slope) shown in the table.

Find the slope of the line that passes through (7,2) and (11, 5).

A student finds the slope of the line between(17, 19) and (22, 21).He writes \frac{19-21}{22-17}. What mistake did he make?

Find the slope of the line.

What is the equation of the line in the graph shown below?

Which is the equation of the line with a slope of -\frac{1}{3} and a y-intercept at (0, -2)?

What is the equation of the line?

Graph the linear equation y = 2x + 6.

Graph the linear equation y=-\frac{4}{9}x+7.

If \angle f = x + 44 and \angle b = 2x - 17, then find the value of \angle f.

If \angle e=84\degree, then find the value of \angle c.

Name the angle relationship for angles a and h.

Name the angle relationship for angles c and g.

Find the measure of \angle x.

The measures of three angles of a triangle are (2x)\degree, (3x)\degree, and (x+60)\degree.What is the value of x?

Find the measure of \angle BCD.

Find the value of x.

What is a reasonable first step for solving the equation
4x - 14 = 6

Which equation is equivalent to
14+7y-25=4y+10

Solve:
6+10p=8p+12

Solve:
\frac{2}{3}x-1=17

Solve:
2(5x-7)+4=-35

Solve:
2m+5=5m-35-3m

\triangle ABC is congruent to \triangle QRS.
What angle is congruent to \angle A?

\triangle ABC is congruent to \triangle QRS.
Which side is congruent to \overline{BC}?

Trapezoid ABCD is congruent to trapezoid EFGH.
What is the measure of side \overline{GF}?

Trapezoid ABCD is congruent to trapezoid EFGH.
Which angle in trapezoid EFGH is congruent to \angle D?

The two figures are similar.
What is the ratio of the small to large figure?

The unshaded figure is a dilation of the shaded figure.
Find the scale factor.

Find the coordinates of G after a dilation of \frac{1}{2}.
I(1, -1), G(2, 4), L(3, 1)

Find the slope of the line that passes through
(7,2) and (11, 5).

A student finds the slope of the line between
(17, 19) and (22, 21).
He writes \frac{19-21}{22-17}. What mistake did he make?

The measures of three angles of a triangle are
(2x)\degree, (3x)\degree, and (x+60)\degree.
What is the value of x?

What is a reasonable first step for solving the equation
4x - 14 = 6

Which equation is equivalent to
14+7y-25=4y+10

Solve:
6+10p=8p+12

Solve:
\frac{2}{3}x-1=17

Solve:
2(5x-7)+4=-35

Solve:
2m+5=5m-35-3m

\triangle ABC is congruent to \triangle QRS.
What angle is congruent to \angle A?

\triangle ABC is congruent to \triangle QRS.
Which side is congruent to \overline{BC}?

Trapezoid ABCD is congruent to trapezoid EFGH.
What is the measure of side \overline{GF}?

Trapezoid ABCD is congruent to trapezoid EFGH.
Which angle in trapezoid EFGH is congruent to \angle D?

The two figures are similar.
What is the ratio of the small to large figure?

The unshaded figure is a dilation of the shaded figure.
Find the scale factor.

Find the coordinates of G after a dilation of \frac{1}{2}.
I(1, -1), G(2, 4), L(3, 1)

Find the slope of the line that passes through
(7,2) and (11, 5).

A student finds the slope of the line between
(17, 19) and (22, 21).
He writes \frac{19-21}{22-17}. What mistake did he make?

The measures of three angles of a triangle are
(2x)\degree, (3x)\degree, and (x+60)\degree.
What is the value of x?