40-Question Math Test: Inequalities, Proportions, Angles, Polygons, Circles, Pythagorean Theorem and Formula Transformation with Step-by-Step Answers

Published on November 9, 2026

Other

A comprehensive 40-question grade 7-8 math test covering graphing and solving inequalities, percent proportions, angle classification, polygon angle sums, circle measurements, the Pythagorean theorem, and transforming formulas, with full step-by-step solutions and an answer key.

Question

Please create a 40 questions test with the following lessons with answers and step by step processes show graphs Graphing and writing inequalities Solving inequalities by adding or subtracting Solving inequalities by multiplying or dividing Solving percent problems using proportions Proportions Measuring and classifying angles Quadrilaterals and other polygons Circles Pythagorean theorem interpreting Graphs Transforming formulas

Answer

Math Test: Grades 7–8 Review (40 Questions)

Part 1: Graphing and Writing Inequalities

1. Write an inequality for “x is at least 5,” and graph it on a number line.

2. Graph

on a number line.

3. Write the inequality shown by this graph:

<----------●-------------
           1

4. Write and graph the inequality: “The number of students

is more than 12 but at most 20.”

Part 2: Solving Inequalities by Adding or Subtracting

5. Solve

6. Solve

7. Solve

8. Solve

Part 3: Solving Inequalities by Multiplying or Dividing

9. Solve

10. Solve

11. Solve

12. Solve

Part 4: Solving Percent Problems Using Proportions

13. What is 35% of 80?

14. 18 is what percent of 60?

15. 45 is 75% of what number?

16. A shirt costs $40. The sales tax rate is 6%. How much is the tax?

Part 5: Proportions

17. Solve

18. Is

a true proportion?

19. A recipe uses 2 cups of flour for 12 muffins. How many cups of flour are needed for 30 muffins?

20. On a map, 1 inch represents 25 miles. How many miles are represented by 3.5 inches?

Part 6: Measuring and Classifying Angles

21. Find the complement of a

angle. Then classify the

angle.

22. Find the supplement of a

angle.

23. Two supplementary angles measure

and

. Find

and both angle measures.

24. Two vertical angles measure

and

. Find

and the angle measure.

Part 7: Quadrilaterals and Other Polygons

25. Find the sum of the interior angles of a hexagon.

26. Find the measure of each interior angle of a regular octagon.

27. Two consecutive angles of a parallelogram measure

and

. Find both angles.

28. How many diagonals does a pentagon have?

Part 8: Circles

29. A circle has a radius of 7 cm. Find its circumference and area in terms of

30. A circle has a diameter of 10 cm. Find its circumference to the nearest tenth. Use

31. A circle has a radius of 6 units. A sector has a central angle of

. Find the arc length and the area of the sector, both in terms of

32. Write the equation of a circle with center

and radius 4.

Part 9: Pythagorean Theorem and Interpreting Graphs

33. A right triangle has legs of 6 and 8. Find the hypotenuse.

34. A right triangle has a hypotenuse of 13 and a leg of 5. Find the other leg.

35. Find the distance between

and

36. The graph of a line passes through

and

. Find the slope and the equation of the line, and describe its graph.

Part 10: Transforming Formulas

37. Solve

for

38. Solve

for

39. Solve

for

40. Solve

for

Answer Key with Step-by-Step Solutions

Part 1: Graphing and Writing Inequalities

1. “At least 5” means 5 or more, so

.
Graph: closed dot at 5, arrow to the right.

  ----+----+----+----+----●=========>
     2    3    4    5    6

means values less than

. Use an open dot at

with an arrow to the left.

<=========○----+----+----+----+----
          -2   -1    0    1    2

3. The dot at 1 is closed (so

), and the shading goes left, so the values are less than or equal to 1.
Answer:

4. “More than 12 but at most 20” gives

.
Graph: open dot at 12, closed dot at 20, shaded segment between them.

----+----○=========●----+----
   10   12   14   16   18   20

Part 2: Solving by Adding or Subtracting

Add 7:

Subtract 4:

Add 4:

, which is the same as

Subtract 2.5:

Part 3: Solving by Multiplying or Dividing

Divide by 4 (positive, so no flip):

10.

Divide by

and flip the inequality:

11.

Multiply by 5:

12.

Multiply by

and flip:

Part 4: Percent Problems Using Proportions

13.

Cross-multiply:

, so

14.

Cross-multiply:

, so

. Answer: 30%

15.

Cross-multiply:

, so

16.

Cross-multiply:

, so

. Answer: $2.40

Part 5: Proportions

17.

Cross-multiply:

, so

18. Cross-multiply:

and

.
Since the products are equal, yes, it is a true proportion.

19.

Cross-multiply:

, so

. Answer: 5 cups

20.

Cross-multiply:

. Answer: 87.5 miles

Part 6: Measuring and Classifying Angles

21. Complement:

angle is less than

, so it is acute.

22. Supplement:

23. Supplementary angles sum to

, so

and

.
Angles:

and

24. Vertical angles are equal:

, so

.
Angle:

Part 7: Quadrilaterals and Other Polygons

25. Interior angle sum:

For

26. Sum for an octagon:

Each angle in a regular octagon:

27. Consecutive angles in a parallelogram are supplementary:

, so

.
Angles:

and

28. Diagonals:

For

diagonals.

Part 8: Circles

29. Circumference:

cm
Area:

cm²

30.

, so

31. A

central angle is

of the circle.
Arc length:

units
Sector area:

square units

32. Standard form:

With

Part 9: Pythagorean Theorem and Interpreting Graphs

33.

, so

34.

, so

35. Distance formula:

36. Slope:

The y-intercept is

, so

.
Equation:

Graph: a straight line rising from left to right, crossing the y-axis at 3, rising 2 units for every 1 unit to the right.

 y
 7 |                ●  (2, 7)
 5 |             /
 3 |●  (0, 3)  /
 1 |        /
   +--------------- x

Part 10: Transforming Formulas

37.

Divide by

38.

Subtract

Divide by 2:

39.

Multiply by 3:

Divide by

40.

Subtract 32:

Multiply by

Final Answers

#	#	Answer	#	Answer	#	Answer
1	11		21	, acute	31	;
2	12		22		32
3	13	28	23	; ,	33	10
4	14	30%	24	;	34	12
5	15	60	25		35	5
6	16	$2.40	26		36	;
7	17	15	27	,	37
8	18	Yes	28	5	38
9	19	5 cups	29	cm; cm²	39
10	20	87.5 mi	30	31.4 cm	40

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

40-Question Math Test: Inequalities, Proportions, Angles, Polygons, Circles, Pythagorean Theorem and Formula Transformation with Step-by-Step Answers

Question

Answer

Math Test: Grades 7–8 Review (40 Questions)

Part 1: Graphing and Writing Inequalities

Part 2: Solving Inequalities by Adding or Subtracting

Part 3: Solving Inequalities by Multiplying or Dividing

Part 4: Solving Percent Problems Using Proportions

Part 5: Proportions

Part 6: Measuring and Classifying Angles

Part 7: Quadrilaterals and Other Polygons

Part 8: Circles

Part 9: Pythagorean Theorem and Interpreting Graphs

Part 10: Transforming Formulas

Answer Key with Step-by-Step Solutions

Part 1: Graphing and Writing Inequalities

Part 2: Solving by Adding or Subtracting

Part 3: Solving by Multiplying or Dividing

Part 4: Percent Problems Using Proportions

Part 5: Proportions

Part 6: Measuring and Classifying Angles

Part 7: Quadrilaterals and Other Polygons

Part 8: Circles

Part 9: Pythagorean Theorem and Interpreting Graphs

Part 10: Transforming Formulas

Final Answers

Related math solutions

Unlock the Web Version Forever

Related math solutions