6th Grade Math Test
Print your 6th grade math test before you start. Try to answer all the questions.
On this page, you will learn
- How well you know the main 6th grade skills: expressions and equations, statistics, probability, fractions, decimals, ratios, percents and geometry
- How to use the order of operations to evaluate an expression
- Which skills you have mastered and which ones need more practice
Before You Start: Order of Operations, a Worked Example
This example is not part of the test. It shows how to work through a problem step by step, so you are ready for the questions below.
- Parentheses first: 6 − 2 = 4, so the expression becomes 3 + 4 × 4.
- Multiply before you add: 4 × 4 = 16, so it becomes 3 + 16.
- Add: 3 + 16 = 19.
3 + 4 × (6 − 2) = 19
Working from left to right. 3 + 4 = 7 and 7 × 4 = 28 is wrong, because multiplication comes before addition.
Evaluate 2 × (5 + 3) − 4.
Show answer
12. 5 + 3 = 8, then 2 × 8 = 16, then 16 − 4 = 12.
Problems 1–10: Equations, Expressions, Statistics and Probability
Name Date:
Solve the following problems
1. In the equation below, what is the value of x?
20 = x + (2 × 8) − 6
2. Sarah has 30 pencils. Her friend Sylvia has k fewer pencils. Which expression shows the number of pencils Sylvia has?
A. 30 + kB. k − 30C. 30 − kD. 30 − 2k
3. Triangle ABC is similar to triangle DEF.
What is the length of DF?
A. 2 inchesB. 1 inchC. 3 inchesD. 1.5 inches
4. What is the value of the expression below?
53
A. 15B. 8C. 25D. 125
5. Use the following list to find the average or mean, the median, the mode, and the range
10, 15, 5, 8, 6, 6, 2
Average =
Median =
Mode =
Range =
6.
−5 − 8 =
5 − 8 =
−8 − 5 =
7. Draw a coordinate system in the space below and then plot (2, 5) and (−4, 2)
8. Find the perimeter and area of the rectangle below:
Perimeter = units
Area = square units
9. Get a die and throw it.
The different outcomes are
Write the probability of getting an even number
Write the probability of getting an odd number
Write the probability of getting a prime number
10. Add 35 and 27
Problems 11–20: Place Value, Ordering Numbers, Primes, Circles and Proportions
11. For the number 76.2345, the value of the digit 4 is
A. 4 tensB. 4 tenthsC. 4 thousandthsD. 4 ten-thousandths
12. If 9450 ÷ x equals 21, what is x?
13. Put the following numbers in order from least to greatest
−14, 74, 0.90, −24, 0.20, 34, 1.50, −0.50
, , , , , , ,
14. a. You want to save money to buy a bike. You start with 50 dollars and you save 4 dollars each day. Which expression shows the amount of money you have after x days?
50 − 4x4x − 504x + 5050 + 4 × 10
b. How much money do you have after 20 days?
A. 120 dollarsB. 130 dollarsC. 110 dollarsD. 200 dollars
15. a. Write down all composite numbers bigger than 10 and smaller than 20 (Hint: there are 5 of them)
, , , ,
Pick a composite number and write down all the factors in the space below
b. Write down all prime numbers bigger than 10 and smaller than 20 (Hint: there are 4 of them)
, , ,
16. How many lines of symmetry does a square have?
17. The diameter of a circle is 8 inches.
The perimeter and area are:
A. P = 4π and A = 12πB. P = 16π and A = 8πC. P = 8π and A = 16πD. P = 16π and A = 4π
18. John and Peter have 40 dollars together. If John has 4 times as much money as Peter, how much money does each have? (Hint: try trial and error)
John has dollars
Peter has dollars
19. A machine produces 5000 items in 6 minutes. Which proportion cannot be used to find how many minutes it takes to produce 15000 items?
A. 50006 = 15000xB. 50006 = x15000C. 6x = 500015000D. 65000 = x15000
20. You go to the restaurant and buy food for 120 dollars. The restaurant requires a 15% tip. What is your total?
Problems 21–30: Scale, Probability, Geometry and Measurement
21. On a map, 1 inch represents 30 miles. How many inches will show a distance of 120 miles?
22. A box contains 6 blue marbles, 4 yellow marbles, and 10 red marbles.
What is the probability of choosing a red marble?
A. 420B. 320C. 620D. 1020
Which color is least likely to be picked?
23. a. Write down a brief definition of congruence
Make a drawing to show two shapes that are congruent
b. Write down a brief definition of similarity
Make a drawing to show two shapes that are similar
24. Spin each spinner once and list all possible outcomes (Hint: one outcome is 2 and white)
What is the probability of getting 1 and red?
25. Evaluate the numerical expression below:
(8 + 2)[(7 − 3) × 5]
A. 100B. 150C. 300D. 200
26. What is the sum of the angles in a pentagon? (Hint: divide the pentagon into triangles. A triangle is 180 degrees)
27. a. How many inches are in 3 and 12 feet?
b. How many meters are in 500 centimeters?
28. What are the volume and surface area of the following rectangular prism?
Volume =
Surface area =
29. a. The shape of a swimming pool is more like a
A. Rectangular prismB. CircleC. PyramidD. Sphere
b. Look up a soccer field online. Then, identify 4 geometric figures
, , ,
30. You go shopping and you see a sign that says, "Buy 1 T-shirt and get 20% off on the second T-shirt." Each T-shirt costs 30 dollars and you buy 2 T-shirts. What is your total?
Something to Keep in Mind About the 6th Grade Math Test
A score of 25 or more on this 6th grade math test is a good indication that most skills taught in 6th grade were mastered.
If you struggled a lot on this 6th grade math test, get someone to help you.
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Summary
- This test checks the main 6th grade skills: expressions and equations, statistics, probability, fractions, decimals, ratios, percents and geometry.
- Use the order of operations: parentheses first, then multiplication and division, then addition and subtraction.
- Show your work for each problem, and give fraction answers in lowest terms.
- A score of 25 or more out of 30 shows that most 6th grade skills are mastered.
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