K–12 Four-Operations Inventory — 48 problems per grade
Purpose / notes:
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This document is a Brigance-style criterion-referenced inventory focused only on the four operations (addition, subtraction, multiplication, division).
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Each grade (K–12) contains 48 computation items arranged in a consistent, printable graphic format: a 4-column table (Addition, Subtraction, Multiplication, Division) with 12 items in each column (12 × 4 = 48).
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Items are grade-appropriate and organized to align with Common Core end-of-grade expectations where applicable. Some grades include extension items when requested (for example: grade 4 includes both 4‑digit × 1‑digit and 3×3 style multiplication by request).
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No answers are provided here; this is a teacher/assessor inventory for administration as a timed or untimed probe.
How to use this document
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Print one grade at a time. Present the page to the student and ask them to compute each expression (written or oral) into the blank provided.
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Scoring: each correct computation = 1 point (adapt as needed). Use Brigance/criterion-referenced interpretation to decide mastery levels.
Kindergarten
| Addition | Subtraction | Multiplication (conceptual/repeated-addition) | Division (conceptual/sharing) |
|---|---|---|---|
| 1) 1 + 1 = ___ | 1) 2 - 1 = ___ | 1) 2 groups of 1 = ___ | 1) Share 2 apples between 2 friends: ___ each |
| 2) 2 + 1 = ___ | 2) 3 - 1 = ___ | 2) 2 + 2 + 2 = ___ (three 2s) | 2) Share 4 crackers between 2 friends: ___ each |
| 3) 2 + 2 = ___ | 3) 4 - 1 = ___ | 3) 3 groups of 1 = ___ | 3) Share 6 candies among 3 friends: ___ each |
| 4) 3 + 1 = ___ | 4) 5 - 1 = ___ | 4) 1 + 1 + 1 + 1 = ___ | 4) If 4 toys are put into 2 equal piles, each pile has ___ |
| 5) 3 + 2 = ___ | 5) 5 - 2 = ___ | 5) 2 groups of 2 = ___ | 5) Share 3 cookies between 3 friends: ___ each |
| 6) 4 + 1 = ___ | 6) 6 - 1 = ___ | 6) 4 is 2 + 2, so 2 groups of 2 = ___ | 6) Share 8 stickers between 4 friends: ___ each |
| 7) 5 + 0 = ___ | 7) 6 - 2 = ___ | 7) 3 groups of 2 (use drawings) = ___ | 7) Put 6 crayons into 2 equal piles: ___ in each pile |
| 8) 4 + 2 = ___ | 8) 7 - 2 = ___ | 8) 0 + 0 + 0 = ___ | 8) 2 friends share 10 grapes equally: ___ each |
| 9) 5 + 1 = ___ | 9) 8 - 3 = ___ | 9) Show 2 groups of 3; total = ___ | 9) 5 items shared by 5 friends: ___ each |
| 10) 3 + 3 = ___ | 10) 9 - 4 = ___ | 10) 4 groups of 1 = ___ | 10) 9 objects shared into 3 equal piles: ___ each |
| 11) 4 + 3 = ___ | 11) 10 - 1 = ___ | 11) 2 + 2 + 2 + 2 = ___ | 11) Share 12 beads among 3 children: ___ each |
| 12) 5 + 4 = ___ | 12) 10 - 5 = ___ | 12) 2 groups of 5 (use fingers) = ___ | 12) If 8 apples split into 4 groups, each gets ___ |
Grade 1
| Addition | Subtraction | Multiplication (equal groups / arrays) | Division (sharing / partition) |
|---|---|---|---|
| 1) 7 + 5 = ___ | 1) 9 - 4 = ___ | 1) 2 × 3 = ___ | 1) 6 ÷ 2 = ___ |
| 2) 8 + 6 = ___ | 2) 10 - 7 = ___ | 2) 3 × 2 = ___ | 2) 9 ÷ 3 = ___ |
| 3) 5 + 9 = ___ | 3) 12 - 5 = ___ | 3) 4 × 1 = ___ | 3) 8 ÷ 4 = ___ |
| 4) 11 + 6 = ___ | 4) 14 - 6 = ___ | 4) 5 groups of 2 = ___ | 4) Share 10 cookies among 5: ___ each |
| 5) 13 + 4 = ___ | 5) 15 - 8 = ___ | 5) 2 + 2 + 2 + 2 = ___ | 5) 12 ÷ 4 = ___ |
| 6) 9 + 9 = ___ | 6) 18 - 9 = ___ | 6) 3 groups of 4 = ___ | 6) 15 ÷ 3 = ___ |
| 7) 10 + 7 = ___ | 7) 17 - 9 = ___ | 7) 4 × 3 = ___ | 7) Share 16 pencils among 4 students: ___ each |
| 8) 6 + 8 = ___ | 8) 13 - 6 = ___ | 8) 2 × 5 = ___ | 8) 14 ÷ 7 = ___ |
| 9) 7 + 7 = ___ | 9) 11 - 3 = ___ | 9) 1 × 7 = ___ | 9) 20 ÷ 5 = ___ |
| 10) 12 + 8 = ___ | 10) 16 - 8 = ___ | 10) 5 × 4 = ___ | 10) Share 18 marbles among 3 friends: ___ each |
| 11) 14 + 3 = ___ | 11) 19 - 9 = ___ | 11) 6 × 1 = ___ | 11) 21 ÷ 7 = ___ |
| 12) 15 + 5 = ___ | 12) 20 - 10 = ___ | 12) 2 × 6 = ___ | 12) 24 ÷ 6 = ___ |
Grade 2
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
| 1) 34 + 12 = ___ | 1) 45 - 23 = ___ | 1) 3 × 4 = ___ | 1) 12 ÷ 3 = ___ |
| 2) 27 + 18 = ___ | 2) 58 - 19 = ___ | 2) 6 × 5 = ___ | 2) 18 ÷ 2 = ___ |
| 3) 49 + 26 = ___ | 3) 63 - 27 = ___ | 3) 7 × 3 = ___ | 3) 20 ÷ 4 = ___ |
| 4) 56 + 13 = ___ | 4) 80 - 32 = ___ | 4) 8 × 2 = ___ | 4) 24 ÷ 6 = ___ |
| 5) 71 + 19 = ___ | 5) 90 - 41 = ___ | 5) 9 × 6 = ___ | 5) 30 ÷ 5 = ___ |
| 6) 38 + 47 = ___ | 6) 66 - 34 = ___ | 6) 4 × 7 = ___ | 6) 28 ÷ 7 = ___ |
| 7) 22 + 33 = ___ | 7) 55 - 20 = ___ | 7) 5 × 5 = ___ | 7) 36 ÷ 6 = ___ |
| 8) 14 + 86 = ___ | 8) 72 - 18 = ___ | 8) 3 × 9 = ___ | 8) 10 ÷ 2 = ___ |
| 9) 99 + 0 = ___ | 9) 100 - 1 = ___ | 9) 2 × 8 = ___ | 9) Share 27 items into 9 groups: ___ each |
| 10) 67 + 22 = ___ | 10) 48 - 17 = ___ | 10) 6 × 6 = ___ | 10) 45 ÷ 5 = ___ |
| 11) 31 + 69 = ___ | 11) 84 - 39 = ___ | 11) 7 × 4 = ___ | 11) 40 ÷ 8 = ___ |
| 12) 25 + 25 = ___ | 12) 95 - 46 = ___ | 12) 9 × 9 = ___ | 12) 32 ÷ 4 = ___ |
Grade 3
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
| 1) 123 + 234 = ___ | 1) 543 - 321 = ___ | 1) 6 × 7 = ___ | 1) 56 ÷ 7 = ___ |
| 2) 207 + 189 = ___ | 2) 802 - 475 = ___ | 2) 8 × 9 = ___ | 2) 81 ÷ 9 = ___ |
| 3) 345 + 456 = ___ | 3) 700 - 199 = ___ | 3) 4 × 12 = ___ (array) | 3) 72 ÷ 8 = ___ |
| 4) 412 + 389 = ___ | 4) 1,000 - 123 = ___ | 4) 3 × 11 = ___ | 4) 90 ÷ 9 = ___ |
| 5) 678 + 212 = ___ | 5) 634 - 318 = ___ | 5) 7 × 8 = ___ | 5) 48 ÷ 6 = ___ |
| 6) 299 + 101 = ___ | 6) 558 - 247 = ___ | 6) 9 × 6 = ___ | 6) 63 ÷ 7 = ___ |
| 7) 501 + 379 = ___ | 7) 444 - 188 = ___ | 7) 5 × 9 = ___ | 7) 36 ÷ 4 = ___ |
| 8) 230 + 467 = ___ | 8) 321 - 115 = ___ | 8) 12 × 4 = ___ | 8) 99 ÷ 11 = ___ |
| 9) 175 + 125 = ___ | 9) 888 - 333 = ___ | 9) 7 × 7 = ___ | 9) 27 ÷ 3 = ___ |
| 10) 389 + 611 = ___ | 10) 999 - 501 = ___ | 10) 8 × 8 = ___ | 10) 54 ÷ 6 = ___ |
| 11) 256 + 256 = ___ | 11) 762 - 444 = ___ | 11) 3 × 3 × 3 (compute) = ___ | 11) 24 ÷ 3 = ___ |
| 12) 410 + 590 = ___ | 12) 820 - 268 = ___ | 12) 11 × 9 = ___ | 12) 100 ÷ 4 = ___ |
Grade 4
This grade is aligned to CCSS Grade 4 expectations (focus: multi-digit multiplication and introductory fraction operations). Per request, this set includes both 4‑digit × 1‑digit items and 3×3 style multi-digit multiplication problems, plus mixed-number fraction items for extension.
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
| 1) 1,234 + 2,345 = ___ | 1) 5,678 - 2,345 = ___ | 1) 4,321 × 8 = ___ (4×1) | 1) 4,568 ÷ 8 = ___ |
| 2) 2,019 + 3,981 = ___ | 2) 9,000 - 3,456 = ___ | 2) 123 × 456 = ___ (3×3) | 2) 1,234 ÷ 6 = ___ |
| 3) 6,789 + 1,111 = ___ | 3) 7,032 - 2,718 = ___ | 3) 2,345 × 7 = ___ (4×1) | 3) 999 ÷ 3 = ___ |
| 4) 3,456 + 4,444 = ___ | 4) 8,210 - 4,567 = ___ | 4) 321 × 123 = ___ (3×3) | 4) 2,400 ÷ 6 = ___ |
| 5) 7,777 + 222 = ___ | 5) 6,543 - 1,234 = ___ | 5) 3,210 × 9 = ___ (4×1) | 5) 1,005 ÷ 5 = ___ |
| 6) 4,008 + 2,992 = ___ | 6) 5,005 - 2,002 = ___ | 6) 234 × 345 = ___ (3×3) | 6) 2,520 ÷ 7 = ___ |
| 7) 5,123 + 3,877 = ___ | 7) 7,000 - 1,111 = ___ | 7) 3,999 × 6 = ___ (4×1) | 7) 3,333 ÷ 9 = ___ |
| 8) 8,888 + 111 = ___ | 8) 9,876 - 4,321 = ___ | 8) 456 × 234 = ___ (3×3) | 8) 4,500 ÷ 5 = ___ |
| 9) 2,222 + 1,778 = ___ | 9) 3,210 - 1,209 = ___ | 9) 2,107 × 4 = ___ (4×1) | 9) 6,048 ÷ 8 = ___ |
| 10) 6,111 + 3,889 = ___ | 10) 10,000 - 4,444 = ___ | 10) 789 × 321 = ___ (3×3) | 10) 7,200 ÷ 9 = ___ |
| 11) 1,500 + 8,500 = ___ | 11) 2,999 - 1,444 = ___ | 11) 9,001 × 3 = ___ (4×1) | 11) 5,005 ÷ 5 = ___ |
| 12) 3,333 + 6,667 = ___ | 12) 8,000 - 2,222 = ___ | 12) 101 × 909 = ___ (3×3) | 12) 8,888 ÷ 8 = ___ |
Fraction/mixed-number extension (choose some items to include on a separate fraction page):
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Multiply: 1) 1 1/2 × 3 = ___; 2) 2 2/3 × 4 = ___; 3) 3/4 × 8 = ___; 4) 5 × 2 1/5 = ___ (convert to improper fractions and multiply).
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Add/Sub: 1) 2 1/3 + 1 2/3 = ___; 2) 4 1/2 - 1 3/4 = ___; 3) 3 3/5 + 2 1/5 = ___; 4) 5 2/3 - 2 2/3 = ___.
Grade 5
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
| 1) 12,345 + 9,876 = ___ | 1) 15,432 - 8,765 = ___ | 1) 234 × 56 = ___ | 1) 5,688 ÷ 24 = ___ |
| 2) 8,908 + 7,092 = ___ | 2) 20,000 - 7,777 = ___ | 2) 3,210 × 12 = ___ | 2) 9,999 ÷ 27 = ___ |
| 3) 23,456 + 7,654 = ___ | 3) 30,123 - 14,321 = ___ | 3) 1,234 × 45 = ___ | 3) 12,345 ÷ 15 = ___ |
| 4) 45,678 + 12,322 = ___ | 4) 40,000 - 19,876 = ___ | 4) 4,567 × 23 = ___ | 4) 6,048 ÷ 16 = ___ |
| 5) 11,111 + 22,222 = ___ | 5) 55,555 - 11,111 = ___ | 5) 2,050 × 25 = ___ | 5) 8,640 ÷ 18 = ___ |
| 6) 9,900 + 100 = ___ | 6) 24,689 - 12,345 = ___ | 6) 999 × 11 = ___ | 6) 14,400 ÷ 60 = ___ |
| 7) 6,543 + 7,457 = ___ | 7) 72,000 - 36,000 = ___ | 7) 5,432 × 21 = ___ | 7) 10,001 ÷ 17 = ___ |
| 8) 3,210 + 4,789 = ___ | 8) 88,888 - 44,444 = ___ | 8) 7,777 × 12 = ___ | 8) 99,999 ÷ 9 = ___ |
| 9) 17,890 + 2,110 = ___ | 9) 100,000 - 55,555 = ___ | 9) 1,111 × 13 = ___ | 9) 81,000 ÷ 27 = ___ |
| 10) 29,999 + 10,001 = ___ | 10) 60,060 - 30,030 = ___ | 10) 6,250 × 16 = ___ | 10) 72,000 ÷ 25 = ___ |
| 11) 14,321 + 5,679 = ___ | 11) 37,800 - 18,900 = ___ | 11) 4,444 × 14 = ___ | 11) 25,000 ÷ 50 = ___ |
| 12) 50,000 + 1 = ___ | 12) 99,000 - 48,999 = ___ | 12) 8,000 × 9 = ___ | 12) 16,032 ÷ 32 = ___ |
(Grade 5 includes decimals & place-value operations when teacher adds context — consider adding decimal versions on a separate page.)
Grade 6
| Addition (integers/decimals) | Subtraction | Multiplication (fractions/decimals) | Division (fractions/decimals) |
|---|---|---|---|
| 1) 123,456 + 78,912 = ___ | 1) 234,567 - 98,765 = ___ | 1) 3/4 × 8 = ___ | 1) (2/3) ÷ (3/4) = ___ |
| 2) 1,234 + 5,678 = ___ | 2) 9,876 - 4,321 = ___ | 2) 12.34 × 5 = ___ | 2) 7.2 ÷ 0.8 = ___ |
| 3) 45.67 + 89.33 = ___ | 3) 123.45 - 23.45 = ___ | 3) 2 1/2 × 3 = ___ | 3) 3/5 ÷ 1/5 = ___ |
| 4) 987 + 654 = ___ | 4) 1,000 - 457 = ___ | 4) 0.6 × 0.25 = ___ | 4) 4 1/2 ÷ 3 = ___ |
| 5) 12,345 + 67,890 = ___ | 5) 5,678 - 2,345 = ___ | 5) (5/6) × 12 = ___ | 5) 0.75 ÷ 0.25 = ___ |
| 6) 3,210 + 4,790 = ___ | 6) 8,000 - 3,333 = ___ | 6) 14 × 0.6 = ___ | 6) 15 ÷ 3/5 = ___ |
| 7) 456.78 + 123.22 = ___ | 7) 600 - 275 = ___ | 7) 7/8 × 16 = ___ | 7) 2/3 ÷ 1/6 = ___ |
| 8) 2,999 + 1 = ___ | 8) 999 - 1 = ___ | 8) 0.125 × 8 = ___ | 8) 9 ÷ 2.25 = ___ |
| 9) 71.5 + 28.5 = ___ | 9) 100.0 - 33.3 = ___ | 9) 3 × 2/5 = ___ | 9) 7 1/2 ÷ 5 = ___ |
| 10) 4,444 + 5,556 = ___ | 10) 777 - 333 = ___ | 10) 6.4 × 10 = ___ | 10) 4 ÷ 1/8 = ___ |
| 11) 8,001 + 1,199 = ___ | 11) 2,222 - 1,111 = ___ | 11) 5/9 × 18 = ___ | 11) 0.36 ÷ 0.12 = ___ |
| 12) 100,000 + 9 = ___ | 12) 10,000 - 9,999 = ___ | 12) 2 2/3 × 6 = ___ | 12) (7/8) ÷ (1/4) = ___ |
Grade 7
| Addition (integers & rationals) | Subtraction | Multiplication (rational & negative) | Division (rational & negative) |
|---|---|---|---|
| 1) -12 + 25 = ___ | 1) 34 - (-8) = ___ | 1) (-6) × 7 = ___ | 1) -48 ÷ 6 = ___ |
| 2) 3/4 + 1/2 = ___ | 2) -5 - 9 = ___ | 2) (-3) × (-4) = ___ | 2) 7/8 ÷ 1/4 = ___ |
| 3) 12.5 + (-3.5) = ___ | 3) 0 - (-12) = ___ | 3) 2/3 × 3/5 = ___ | 3) -27 ÷ (-3) = ___ |
| 4) -7 + (-9) = ___ | 4) 5.25 - 2.75 = ___ | 4) (-2.5) × 4 = ___ | 4) 0.9 ÷ 0.3 = ___ |
| 5) 5 1/2 + 2 2/3 = ___ | 5) 7 1/4 - 2 3/4 = ___ | 5) 3/7 × 14 = ___ | 5) -3/5 ÷ 1/5 = ___ |
| 6) 0 + (-15) = ___ | 6) -100 - 25 = ___ | 6) (-1/2) × 8 = ___ | 6) 4 ÷ (-1/2) = ___ |
| 7) 123 + (-23) = ___ | 7) 200 - 333 = ___ | 7) 4 1/2 × 2 = ___ | 7) 5.4 ÷ (-0.9) = ___ |
| 8) 7/10 + 2/5 = ___ | 8) -2/3 - 1/3 = ___ | 8) (-7) × 6 = ___ | 8) 2/9 ÷ 1/3 = ___ |
| 9) -0.75 + 1.25 = ___ | 9) 1.0 - (-0.5) = ___ | 9) 11 × (-3) = ___ | 9) -5 ÷ 0.2 = ___ |
| 10) 9 2/3 + 1 1/3 = ___ | 10) 8 3/4 - 4 1/2 = ___ | 10) (-2/3) × (-3/4) = ___ | 10) 7 ÷ -7 = ___ |
| 11) 2.25 + 3.75 = ___ | 11) -6 - (-6) = ___ | 11) 1 2/5 × 5 = ___ | 11) (3/10) ÷ (3/5) = ___ |
| 12) -50 + 100 = ___ | 12) 0 - 45 = ___ | 12) (-4) × (-4) = ___ | 12) -1 ÷ 1/2 = ___ |
Grade 8
| Addition (rationals & scientific notation) | Subtraction | Multiplication (rationals & exponents context) | Division (rationals & exponents context) |
|---|---|---|---|
| 1) 3.21 + 7.79 = ___ | 1) 100 - 37.5 = ___ | 1) 0.002 × 3,000 = ___ | 1) 6.4 ÷ 0.8 = ___ |
| 2) -3/5 + 4/5 = ___ | 2) -7/8 - (-1/8) = ___ | 2) 1.5 × 2.4 = ___ | 2) 10^-3 ÷ 10^-5 = ___ |
| 3) 1.2 × 10^3 + 3.8 × 10^2 = ___ | 3) 2.75 - 1.125 = ___ | 3) (-0.4) × (-2.5) = ___ | 3) 0.00036 ÷ 0.004 = ___ |
| 4) 5 3/4 + 2 1/2 = ___ | 4) 7.2 - (-3.4) = ___ | 4) 7/12 × 24 = ___ | 4) (3/4) ÷ (1/8) = ___ |
| 5) -123 + 456 = ___ | 5) -200 - 100 = ___ | 5) 1 1/3 × 3/4 = ___ | 5) 9 ÷ (-3/2) = ___ |
| 6) 0.333 + 0.667 = ___ | 6) 1.234 - 0.234 = ___ | 6) 2.5 × 4 = ___ | 6) -0.81 ÷ 0.9 = ___ |
| 7) 4.5 + (-2.25) = ___ | 7) -0.5 - 0.75 = ___ | 7) 125 × 8 = ___ | 7) 144 ÷ 12 = ___ |
| 8) 9 7/8 + 0 1/8 = ___ | 8) 3/10 - 1/20 = ___ | 8) 0.125 × 0.25 = ___ | 8) (5/6) ÷ (5/9) = ___ |
| 9) -7.5 + 17.5 = ___ | 9) 0 - 0.0001 = ___ | 9) 2.02 × 100 = ___ | 9) 3.6 ÷ 0.6 = ___ |
| 10) 6.02 + 0.98 = ___ | 10) 6 2/3 - 2 1/3 = ___ | 10) 4 1/4 × 8 = ___ | 10) 5 ÷ 2.5 = ___ |
| 11) 10^4 + 2,345 = ___ | 11) 10,000 - 9,876 = ___ | 11) (-3)^2 × (-3) = ___ (careful sign) | 11) 1000 ÷ 250 = ___ |
| 12) 0.012 + 0.088 = ___ | 12) -1.2 - 3.8 = ___ | 12) (2/5) × (5/3) = ___ | 12) -27 ÷ 4 = ___ |
Grade 9 (Intro to algebraic numeric operations)
Focus: arithmetic with integers, rationals, and simple polynomial arithmetic (add/sub/mult/div as numeric or symbolic computational skill practice).
| Addition (numbers & polynomials) | Subtraction | Multiplication (numbers & polynomials) | Division (numbers & polynomials) |
|---|---|---|---|
| 1) 12,345 + 98,765 = ___ | 1) 75,000 - 12,345 = ___ | 1) (x + 2) + (x - 5) rewrite & add like terms (=___) | 1) (x^2 - 1) ÷ (x - 1) = ___ (polynomial divide) |
| 2) -123 + 456 = ___ | 2) -500 - (-125) = ___ | 2) (x + 3)(x - 2) multiply = ___ | 2) 1,234 ÷ 7 = ___ |
| 3) 0.75 + 1.25 = ___ | 3) 3/4 - 1/2 = ___ | 3) (2x)(3x) = ___ | 3) (2x^2 + 5x) ÷ x = ___ |
| 4) 123.45 + 876.55 = ___ | 4) 1000 - 333 = ___ | 4) 45 × 32 = ___ | 4) 9,999 ÷ 27 = ___ |
| 5) (2x + 3) + (x - 1) = ___ | 5) (5x - 2) - (3x + 4) = ___ | 5) Multiply: (x + 1)(x^2 - x + 1) = ___ | 5) Divide: 144 ÷ 12 = ___ |
| 6) 5 2/3 + 4 1/3 = ___ | 6) -7 - 19 = ___ | 6) 123 × 456 = ___ | 6) (x^3 - x) ÷ x = ___ |
| 7) 10,000 + 2,345 = ___ | 7) 7.5 - 2.5 = ___ | 7) (3x + 2)(2x - 1) = ___ | 7) 2,016 ÷ 32 = ___ |
| 8) -2/3 + 5/6 = ___ | 8) 0 - (-1) = ___ | 8) Multiply: (x - 4)(x + 4) = ___ | 8) (x^2 + 5x + 6) ÷ (x + 2) = ___ |
| 9) 999 + 1 = ___ | 9) 1,234 - 987 = ___ | 9) 7 × (-8) = ___ | 9) 1,000,000 ÷ 125 = ___ |
| 10) (3/4 + 1/4) + 2 = ___ | 10) 6 3/4 - 2 1/2 = ___ | 10) 0.125 × 0.8 = ___ | 10) -144 ÷ 12 = ___ |
| 11) (x + 2) + (2x - 5) = ___ | 11) (4x - 3) - (x + 7) = ___ | 11) (2x^2)(3x) = ___ | 11) (6x^2) ÷ (2x) = ___ |
| 12) 7,321 + 2,679 = ___ | 12) -1,000 - 500 = ___ | 12) 234 × 89 = ___ | 12) (x^2 - 4x + 4) ÷ (x - 2) = ___ |
Grade 10
| Addition (complex numbers & polynomials) | Subtraction | Multiplication (polynomials & rationals) | Division (polynomials & rationals) |
|---|---|---|---|
| 1) (3 + 2i) + (1 - 5i) = ___ | 1) (3 + 4) - (5 + 6) = ___ | 1) (x + 2)(x^2 - x + 3) multiply = ___ | 1) (x^3 + x^2 - x) ÷ x = ___ |
| 2) 12,345 + 67,890 = ___ | 2) 10^5 - 3,456 = ___ | 2) (2 + 3i)(1 - i) = ___ | 2) 3,456 ÷ 12 = ___ |
| 3) -123 + (-456) = ___ | 3) (2x + 5) - (x - 3) = ___ | 3) (x^2 + 2x + 1)(x - 1) = ___ | 3) (x^2 - 1) ÷ (x - 1) = ___ |
| 4) (5 - 3i) + (2 + 7i) = ___ | 4) 1,000 - 999 = ___ | 4) Multiply: (3x)(4x^2) = ___ | 4) 10,000 ÷ 25 = ___ |
| 5) 234,567 + 89,123 = ___ | 5) -2 - (-8) = ___ | 5) (1/2) × (3/4) = ___ | 5) (x^3 + 8) ÷ (x + 2) (synthetic or long) = ___ |
| 6) (x^2 + 3x) + (2x^2 - x) = ___ | 6) (a+b) - (b+a) = ___ | 6) (2x + 3)(x - 4) multiply = ___ | 6) 7,200 ÷ 45 = ___ |
| 7) 0.001 + 0.999 = ___ | 7) 5/6 - 1/3 = ___ | 7) (3 + 2i)^2 = ___ | 7) (-36) ÷ 6 = ___ |
| 8) (2 + i) + (2 - i) = ___ | 8) 200 - 150 = ___ | 8) 125 × 64 = ___ | 8) (x^3 - 27) ÷ (x - 3) = ___ |
| 9) 99,999 + 1 = ___ | 9) 1/2 - 1/4 = ___ | 9) (x + 1)^2 multiply = ___ | 9) 81,000 ÷ 90 = ___ |
| 10) (4 - 2i) + ( -4 + 8i) = ___ | 10) 1,000,000 - 999,999 = ___ | 10) (x^2 - 1)(x + 2) multiply = ___ | 10) 123,456 ÷ 12 = ___ |
| 11) 7,777 + 22,223 = ___ | 11) -500 - 250 = ___ | 11) Multiply: (1/3) × (9) = ___ | 11) (6x^2 + x) ÷ (2x) = ___ |
| 12) (6 + 4i) + ( -6 - 4i) = ___ | 12) 3.5 - 1.25 = ___ | 12) (x + 3)(x^2 - 3x + 9) = ___ | 12) 2,000 ÷ 125 = ___ |
Grade 11
| Addition (advanced numeric & algebraic) | Subtraction | Multiplication (polynomials & rational expressions) | Division (polynomials & rational expressions) |
|---|---|---|---|
| 1) (5 + 7i) + ( -2 + 3i) = ___ | 1) (x^3 + 2) - (x^2 + 1) = ___ | 1) Multiply: (x^2 + x + 1)(x - 1) = ___ | 1) (x^3 - 8) ÷ (x - 2) = ___ |
| 2) 1,234,567 + 987,654 = ___ | 2) 10,000 - 7,777 = ___ | 2) (3/4)(16/9) = ___ | 2) (x^2 - 4) ÷ (x - 2) = ___ |
| 3) -3.141 + 2.718 = ___ | 3) -1,000 - (-500) = ___ | 3) (x^2)(x^3) = ___ | 3) 5,000 ÷ 40 = ___ |
| 4) (2x^2 + 3x) + (x^2 - x) = ___ | 4) (4x^2 - 2x) - (x^2 + x) = ___ | 4) Multiply: (2x + 3)(x - 4) = ___ | 4) (2x^3 + x^2) ÷ x = ___ |
| 5) 123,321 + 456,654 = ___ | 5) 999,999 - 111,111 = ___ | 5) (3x^2)(2x) = ___ | 5) 6,048 ÷ 16 = ___ |
| 6) (7 + 2i) + (1 - 2i) = ___ | 6) 4.5 - 1.25 = ___ | 6) (x^2 + 2x + 1)(x + 1) = ___ | 6) (x^4 - 1) ÷ (x^2 - 1) = ___ |
| 7) 0.0001 + 0.9999 = ___ | 7) 2/3 - 1/4 = ___ | 7) (5/8) × 64 = ___ | 7) 30,000 ÷ 125 = ___ |
| 8) (x^3 + x) + ( -x^2 + 2x) = ___ | 8) (a+b) - (b-a) = ___ | 8) (x + 2)(x^2 - 2x + 4) = ___ | 8) (x^3 + 3x^2 + 3x + 1) ÷ (x + 1) = ___ |
| 9) 1,000,000 + 2,000,000 = ___ | 9) -10 - 90 = ___ | 9) 0.45 × 0.2 = ___ | 9) 144,000 ÷ 600 = ___ |
| 10) (6 - i) + ( -6 + 2i) = ___ | 10) 7.75 - 2.5 = ___ | 10) (x^2 - 9)(x + 3) multiply = ___ | 10) (3x^2 - 6x) ÷ 3x = ___ |
| 11) 123,456 + 654,321 = ___ | 11) 9 - (-9) = ___ | 11) (2/5) × (25/2) = ___ | 11) 2,500 ÷ 25 = ___ |
| 12) (3x + 2) + (4x - 5) = ___ | 12) 1,000 - 0 = ___ | 12) Multiply: (x - 1)^3 expand = ___ | 12) (x^3 - 8x) ÷ (x) = ___ |
Grade 12
High school senior-level practice — computational fluency with large numeric values, rational expressions, polynomial arithmetic, complex numbers, and rational function division.
| Addition (large & symbolic) | Subtraction | Multiplication (polynomial & rational expressions) | Division (polynomial & rational expressions, complex quotients) |
|---|---|---|---|
| 1) 12,345,678 + 9,876,543 = ___ | 1) 23,456,789 - 12,345,678 = ___ | 1) (x^2 + 3x + 2)(x - 1) multiply = ___ | 1) (x^4 - 1) ÷ (x^2 - 1) = ___ |
| 2) (5 + 6i) + ( -2 - 3i) = ___ | 2) (2x^3 + x^2) - (x^3 - x) = ___ | 2) (x^2 + 1)(x^2 - 1) multiply = ___ | 2) Divide: (3x^3 + 6x^2) ÷ 3x = ___ |
| 3) 123,456 + 876,544 = ___ | 3) 1,000,000 - 123,456 = ___ | 3) (3/7) × (14/3) = ___ | 3) (x^3 + 8) ÷ (x + 2) = ___ |
| 4) (10 - 4i) + (4 + 10i) = ___ | 4) -5,000 - 7,500 = ___ | 4) (x^2 - x + 1)(x + 2) = ___ | 4) (x^3 - 3x^2 + 3x - 1) ÷ (x - 1) = ___ |
| 5) 9,999,999 + 1 = ___ | 5) 10^6 - 10^3 = ___ | 5) Multiply: (2x)(x^2 - 1) = ___ | 5) 1,000,000 ÷ 250 = ___ |
| 6) (7i) + (5i) = ___ | 6) (x^4 + x^2) - (x^3 + x) = ___ | 6) (x - 1)^2 (x + 1) multiply = ___ | 6) (2x^4 + x^3) ÷ x^2 = ___ |
| 7) 123,123 + 321,321 = ___ | 7) -1,234 - 5,678 = ___ | 7) (4/9) × (81/2) = ___ | 7) (x^3 - x) ÷ (x - 1) = ___ |
| 8) (2 + 3i) + (2 - 3i) = ___ | 8) (a+b+c) - (b+c) = ___ | 8) Multiply: (x^3 - 1)(x + 1) = ___ | 8) Complex divide: (3 + 4i) ÷ (1 - 2i) = ___ |
| 9) 1,111,111 + 2,222,222 = ___ | 9) 2,000,000 - 1,111,111 = ___ | 9) (5x^2)(2x - 1) = ___ | 9) 250,000 ÷ 125 = ___ |
| 10) (1/2 + 1/3) + (1/4) = ___ | 10) 3/4 - 1/6 = ___ | 10) (x^2 + 2x + 1)(x - 2) = ___ | 10) (x^4 - 16) ÷ (x^2 - 4) = ___ |
| 11) 10^7 + 10^6 = ___ | 11) 10^8 - 10^4 = ___ | 11) (9/16) × (64/3) = ___ | 11) (x^5 - x) ÷ x = ___ |
| 12) (6 + i) + ( -6 + 4i) = ___ | 12) -100,000 - 200,000 = ___ | 12) Multiply: (1/5) × (500) = ___ | 12) (x^3 + 3x^2 + 3x + 1) ÷ (x + 1) = ___ |
End of document — notes:
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This inventory can be printed grade-by-grade and used as a Brigance-style criterion probe.
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If you want answer keys, timed versions, randomized item banks, or PDFs formatted for single-sided testing, tell me and I will produce them.
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If you want the inventory strictly limited to only CCSS-required items (no extensions), I can produce a variant showing which items are core vs extension per grade.
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