FREE 6th Grade SBAC Math Practice Test

1- A baker needs to pack 143 chocolate cookies and 55 vanilla cookies into boxes so that each box has the same number of cookies and only one type of cookie per box. What is the largest number of cookies that can be put in each box?

A. 5

B. 7

C. 9

D. 11

2- What is the value of \(2{,}205 \div 315\)?

A. 5

B. 6

C. 7

D. 8

3- If \(112=22+x\), what is the value of \(x\)?

A. 78

B. 90

C. 100

D. 134

4- Car A travels 221.5 km. Car B travels 1.2 times the distance of Car A. How far does Car B travel?

A. 184.6 km

B. 221.5 km

C. 242.8 km

D. 265.8 km

5- The perimeter of the trapezoid below is 38. What is its area?

A. 198 cm\(^2\)

B. 162 cm\(^2\)

C. 99 cm\(^2\)

D. 81cm\(^2\)

6- Which of the following expressions has the greatest value?

A. \( 3^1+12\)

B. \( 3^3-3^2\)

C. \( 3^4-60\)

D. \( 3^5-218\)

7- Alfred has \(x\) apples. Alvin has 40 apples, which is 15 apples less than the number of apples Alfred owns. If Baron has \(\frac{1}{5}\) times as many apples as Alfred has. How many apples does Baron have?

A. 5

B. 11

C. 55

D. 275

8- In the following triangle find \(α\).

A. \(100^\circ\)

B. \(90^\circ\)

C. \(60^\circ\)

D. \(30^\circ\)

9- The price of a laptop is decreased by \(15\%\) to $425. What is its original price?

A. $283

B. $430

C. $500

D. $550

10- Find the perimeter of the shape in the following figure. (all angles are right angles)

A. 21

B. 22

C. 24

D. 20

11- What are the values of mode and median in the following set of numbers?
\(1,3,3,6,6,5,4,3,1,1,2\)

A. Mode: 1, 2, Median: 2

B. Mode: 1, 3, Median: 3

C. Mode: 2, 3, Median: 2

D. Mode: 1, 3, Median: 2.5

12- Which expression equivalent to \(x × 92\)?

A. \((x×90)+2\)

B. \(x×9×2\)

C. \((x×90)+(x×2)\)

D. \((x×90)+2\)

13- The ratio of pens to pencils in a box is 3 to 5. If there are 96 pens and pencils in the box altogether, how many more pens should be put in the box to make the ratio of pens to pencils 1: 1?

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A. 22

B. 23

C. 24

D. 25

14- If point A placed at \(-\frac{24}{3}\) on a number line, which of the following points has a distance equal to 5 from point A?

A. \(-13\)

B. \(-3\)

C. \(-2\)

D. A and B

15- Which of the following shows the numbers in increasing order?

A. \(\frac{3}{13}, \frac{4}{11}, \frac{5}{14}, \frac{2}{5}\)

B. \(\frac{3}{13}, \frac{5}{14}, \frac{4}{11}, \frac{2}{5}\)

C. \(\frac{3}{13}, \frac{5}{14}, \frac{2}{5}, \frac{4}{11}\)

D. \(\frac{5}{14}, \frac{3}{13}, \frac{2}{5}, \frac{4}{11}\)

16- If \(x=- 4\), which of the following equations is true?

A. \(x(3x-1)=50\)

B. \(5(11-x^2 )=-25\)

C. \(3(-2x+5)=49\)

D. \(x(-5x-19)=-3\)

17- What is the missing prime factor of number 450?
\(450=2^1×3^2×…\) _________

18- What is the perimeter of the following shape? (it’s a right triangle)

A. 14 cm

B. 18 cm

C. 24 cm

D. 32 cm

19- 65 is what percent of 50?

A. \(50 \%\)

B. \(77 \%\)

C. \(130 \%\)

D. \(140 \%\)

20- Which of the following expressions has a value of \(-23\)?

A. \(-10+(-8)+ \frac{5}{2}×(-2)\)

B. \(5×3+(-2)×18\)

C. \(-10+6×8÷(-4)\)

D. \((-3) × (-7) + 2\)

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Answers:

2- C
\(2205÷315=\frac{2205}{315}=\frac{441}{63}=\frac{147}{21}= 7\)

3- B
\(112=22+x \)
Subtract 22 from both sides of the equation. Then:
\(x=112-22=90\)

4- D
Distance that car B travels \(=1.2 ×\) distance that car A travels
=\(1.2×221.5=265.8 \) km

5- D
The perimeter of the trapezoid is 38.
Therefore, the missing side (height) is \(= 38 – 8 – 10 – 11 = 9\)
Area of the trapezoid: \(A = \frac{1}{2} h (b_1 + b_2) = \frac{1}{2}1 (9) (8 + 10) = 81\)

6- D
A. \(3^1+12=3+12=15\)
B. \(3^3-3^2=27-9=18\)
C. \(3^4-60=81-60=21\)
D. \(3^5-218=243-218=25\)

7- B
Alfred has \(x\) apple which is 15 apples more than the number of apples Alvin owns. Therefore:
\(x-15=40→x=40+15=55\)
Alfred has 55 apples.
Let \(y\) be the number of apples that Baron has. Then: \(y=\frac{1}{5}×55=11\)

8- A
Complementary angles add up to 180 degrees.
\( β+150^\circ=180^\circ→β=180^\circ-150^\circ=30^\circ\)
The sum of all angles in a triangle is 180 degrees. Then:
\(α+β+50^\circ=180^\circ→α+30^\circ+50^\circ=180^\circ\)
\(→α+80^\circ=180^\circ→α=180^\circ-80^\circ=100^\circ\)

9- C
Let \(x\) be the original price.
If the price of a laptop is decreased by \(15\%\) to $425, then:
\(85 \% \space of \space x=425⇒ 0.85x=425 ⇒ x=425÷0.85=500\)

10- C
Let \(x\) and \(y\) be two sides of the shape. Then:
\(x+1=1+1+1→x=2\)
\(y+6+2=5+4→y+8=9→y=1\)
Then, the perimeter is:
\(1+5+1+4+1+2+1+6+2+1=24\)

11- B
First, put the numbers in order from least to greatest: \(1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 6\)
The Mode of the set of numbers is: 1 and 3 (the most frequent numbers)
The median is: 3 (the number in the middle)

12- C
\(x×92=x×(90+2)=(x×90)+(x×2)\)

13- C
The ratio of pens to pencils is \(3: 5\). Therefore there are 3 pens out of all 8 pens and pencils. To find the answer, first dived 96 by 8 then multiply the result by 3.
\(96÷8=12→12×3=36\)
There are 36 pens and 60 pencils \((96-36)\). Therefore, 24 more pens should be put in the box to make the ratio \(1: 1\)

14- D
If the value of point A is greater than the value of point B, then the distance of two points on the number line is: the value of A- the value of B
A. \(-\frac{24}{3}-(-13)=-8+13=5=5\)
B. \(-3-(-\frac{24}{3})=-3+8=5=5\)
C. \(-2-(-\frac{24}{3})=-2+8=6≠5\)

15- B
\(\frac{3}{13}≅0.23, \frac{5}{14}≅0.357, \frac{4}{11}≅0.36, \frac{2}{5}=0.4\)

16- B
Plugin the value of \(x\) in the equations. \(x = -4\), then:
A.\(x(3x-1)=50→-4(3(-4)-1)=-4(-12-1)=-4(-13)=52≠50\)
B. \(5(11-x^2 )=-25→5(11-(-4)^2 )= 5(11-16)=5(-5)=-25\)
C. \(3(-2x+5)=49→3(-2(-4)+5)=3(8+5)=39≠49\)
D. \(x(-5x-19)=-3→-4(-5(-4)-19=-4(20-19)=-4≠-3\)

17- 5
Let \(x\) be the missing prime factor of 450.
\(450= 2 × 3 × 3 × x ⇒ x =\frac{450}{18} ⇒ x = 25=5×5\)

18- C
Use the Pythagorean theorem to find the hypotenuse of the triangle.
\(a^2+b^2=c^2→6^2+8^2=c^2→36+64=c^2→100=c^2→c=10\)
The perimeter of the triangle is: \(6+8+10=24\)

19- C
Use the percent formula:
\(Part = \frac{percent}{100} × whole\)
\(65= \frac{percent}{100} × 50⇒ 65 = \frac{percent ×50}{100}⇒ 65=\frac{percent ×5}{10}\)
multiply both sides by 10.
\(650 =percent ×5, \space divide \space both \space sides \space by \space 5.\)
130 = percent
The answer is \(130\%\)

20- A
Let’s check the options provided.
A. \(-10+(-8)+ (\frac{5}{2})×(-2)=-10+(-8)+(-5)=-10-13=-23\)
B. \(5×3+(-2)×18=15+(-38)=-21\)
C. \(-10+6×8÷(-4)=-10+48÷(-4)=-10-12=-22\)
D. \((-3)× (-7)+ 2=21+2=23\)

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For a workbook your child can use alongside this practice test, the 6th Grade SBAC Math for Beginners walks through every topic on the test with worked examples. For full state-test prep with multiple practice tests, see the 6th Grade SBAC Math Test Prep Bundle.

Frequently Asked Questions

What is the SBAC math test?

The SBAC (Smarter Balanced Assessment Consortium) is a Common Core-aligned state assessment used by California, Washington, Oregon, Hawaii, Connecticut, Delaware, Idaho, Montana, Nevada, North Dakota, South Dakota, and several others. The grade 6 math test covers all five Common Core grade 6 domains and four SBAC “claims.”

What are the four SBAC math claims?

Claim 1: Concepts and Procedures (about 40% of the test). Claim 2: Problem Solving (about 20%). Claim 3: Communicating Reasoning (about 20%). Claim 4: Modeling and Data Analysis (about 20%). Claim 1 has no calculator; Claims 2-4 allow one.

Is a calculator allowed on the grade 6 SBAC math?

Partially. The Claim 1 (Concepts and Procedures) section is calculator-free. The Claim 2-4 sections and the Performance Task allow an on-screen calculator. Students should practice both with and without a calculator during prep.

Is the SBAC math test computer-adaptive?

Yes. The Computer Adaptive Test (CAT) portion adjusts question difficulty based on your child’s previous answers. The Performance Task portion (a multi-step real-world problem) is not adaptive. Together the CAT and Performance Task make up the full grade 6 SBAC math.

How long is the grade 6 SBAC math test?

About 2.5 to 3.5 hours total, usually split across two or three sessions. The CAT portion is around 1.5 to 2 hours, and the Performance Task adds another 1 to 1.5 hours. Time limits are flexible — most districts let students work until done.

When is the SBAC given?

Most SBAC states administer the test in March, April, or May. Exact dates vary by district. Your child’s teacher will share the schedule a few weeks before testing begins.

How is the SBAC scored?

Math gets a scaled score (roughly 2200-2900 for grade 6) and one of four achievement levels: Level 1 (not met), Level 2 (nearly met), Level 3 (met), Level 4 (exceeded). Most districts target Level 3 or better. Reports are sent home in late summer.

What grade 6 math topics show up most on the SBAC?

Ratios and unit rates, dividing fractions, expressions with variables, one-variable equations and inequalities, the coordinate plane with negative numbers, area of triangles and quadrilaterals, surface area of prisms, and statistical measures (mean, median, mean absolute deviation).

How long should we prep for the grade 6 SBAC math?

Most grade 6 students do well with 4 to 6 weeks of consistent practice (15 to 25 minutes per day). Start with this practice test as a diagnostic, drill the weakest claim area, then build up to mixed-topic timed practice in the final two weeks.

Where can I find more grade 6 SBAC math practice?

EffortlessMath has the 6th Grade SBAC Math for Beginners workbook covering every topic on the test and the 6th Grade SBAC Math Test Prep Bundle with multiple full-length practice tests and answer explanations.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to divide fractions
• Order of operations (PEMDAS)
• How to solve one-variable equations
• How to find the area of a triangle
• Rules of exponents