A Basic Math Skills Assessment PDF with the Working Shown

People look for a basic math skills assessment PDF when an arithmetic check stands between them and a job offer, a training program, or a first college course. Most of the ones online give you questions with a bare answer letter, or no key at all. Download the PDF and you get the full practice set with the questions first and a separate answer key that shows the working for every item. The arithmetic does not change whether the official test comes from an employer's HR office or a college testing center.

The three skill buckets every basic math test draws from

Almost every basic math screen pulls from the same three groups of skills. The first is whole numbers and fractions: adding, subtracting, multiplying and dividing, plus the order of operations. The second is decimals and percents, which on a hiring test usually means money: change, discounts, sales tax, and "what percent of" questions. The third is applied word problems, where you read a short work situation and decide which operation to use: rates, area and perimeter, and converting units.

You can see the pattern in the tests themselves. Algonquin College's sample question sheet for its Basic Math Skills Assessment gives 17 Accuplacer-style Arithmetic questions sorted into exactly those three types. The Hampton Roads Sanitation District sample math skills test, a Virginia utility's 30-item hiring screen, runs pure computation first and word problems second, with no calculator allowed. So if your practice covers all three buckets, it covers what a math skills assessment is likely to ask. Algebra, geometry proofs, and statistics mostly live on other tests.

Why employers and colleges still screen for basic math

Everyone carries a calculator, so why test by hand? Because the screen is really checking whether you notice when a number is wrong. A cashier who keys $6.30 instead of $63.00, or an installer who cuts a run 12 inches short, had a calculator within reach. Employers in trades, retail, health care, and utilities use a short math screen because a slip on the job costs them money, material, or safety. Colleges have a gentler reason: placement puts you in a course you can pass, so a weak spot does not sink your first term. Adult number skills get measured at national scale as well. The United States takes part in PIAAC, an international survey of adult skills that tests numeracy alongside reading.

Which Basic Math Skills Assessment You Will Face: Tests Side by Side

Here are the tests people meet most often, with the rules that change how you should practise. Where a pass mark is published, it is listed. Where the employer or college sets it, the table says so rather than guessing.

Test

Who gives it

Questions

Time

Calculator

Passing bar

Accuplacer Arithmetic (Next-Generation)

College placement offices

20 multiple choice

Untimed

No handheld; an on-screen one appears on some items

No pass or fail; scores run 200 to 300 and each college sets placement cut-offs

CBEST Mathematics

California teacher candidates

50 multiple choice

Shared session with the reading and writing sections

Not allowed

Scaled 41, or as low as 37 if all three sections total 123

GED Mathematical Reasoning

Adults earning a high school equivalency

Varies by form

115 minutes

On-screen calculator for most items, not all

145

Wonderlic Basic Skills Test, math part

Employers and trade schools

45

20 minutes

Check your invitation

Set by each employer or school

HRSD Math Skills Test

Hampton Roads Sanitation District job applicants

30

Not stated on the sample

Not allowed

Not published

Short numeracy check

Employers and training providers

About 12

About 5 minutes

Usually none

Often around 65%, but ask whoever sets it

The Accuplacer figures come from the College Board's Next-Generation Accuplacer test specifications. The CBEST figures come from the official CBEST test page, and the GED rules from the GED math subject page, which flags the sample items where no calculator is available. The Wonderlic counts are from a college fact sheet on the Wonderlic Basic Skills Test. For a deeper look at hiring screens in particular, see our guide to employment math aptitude tests.

This sample math skills test follows the order most real screens use. Set a timer for 30 minutes, put the calculator in a drawer, and use a pencil and scrap paper. Pick one letter per question. The answer key and the working come after question 20, so you can finish the whole set before you check anything. If you would rather work on paper, download the PDF: it prints the questions first and the answer key on a separate page.

Whole numbers, fractions and order of operations

1. 4,208 minus 1,739(A) 2,469; (B) 2,579; (C) 3,531; (D) 2,531
2. 36 × 24(A) 764; (B) 864; (C) 854; (D) 144
3. 1,512 ÷ 18(A) 74; (B) 94; (C) 84; (D) 804
4. 3/4 + 2/3(A) 5/7; (B) 5/12; (C) 1 1/12; (D) 1 5/12
5. 2 1/2 × 1 3/5(A) 4; (B) 2 3/10; (C) 3 1/2; (D) 5
6. 5/6 ÷ 5/12(A) 1/2; (B) 2; (C) 25/72; (D) 2 1/2
7. 18 minus 3 × (4 + 2)² ÷ 12(A) 45; (B) 0; (C) 9; (D) 15

Decimals and percents, including discount and sales tax problems

1. 12.6 + 4.75 minus 3.08(A) 14.27; (B) 13.37; (C) 14.37; (D) 20.43
2. 0.35 × 1.2(A) 4.2; (B) 0.042; (C) 0.42; (D) 0.402
3. 7.2 ÷ 0.08(A) 0.9; (B) 9; (C) 90; (D) 900
4. What is 15% of 260?(A) 3.9; (B) 39; (C) 36; (D) 390
5. A jacket priced at $84 is 25% off, and 7% sales tax is charged on the sale price. What do you pay?(A) $63.00; (B) $67.41; (C) $68.88; (D) $62.37
6. 18 is what percent of 72?(A) 18%; (B) 25%; (C) 40%; (D) 4%

Workplace word problems: rates, area and perimeter, units

1. A crew lays 45 feet of pipe an hour. How long will 405 feet take?(A) 8 hours; (B) 9 hours; (C) 9.5 hours; (D) 10 hours
2. A storeroom floor measures 14 feet by 11 feet. How many square feet of flooring does it need?(A) 50 square feet; (B) 144 square feet; (C) 154 square feet; (D) 164 square feet
3. A yard is 30 meters by 18 meters. How much fencing goes around it?(A) 48 meters; (B) 96 meters; (C) 540 meters; (D) 78 meters
4. You cut three pieces of 26 inches each from a 7-foot board. How much is left?(A) 6 inches; (B) 1 foot 6 inches; (C) 4 inches; (D) Nothing
5. A tank holds 12 gallons. How many quarts is that?(A) 3; (B) 24; (C) 48; (D) 96
6. A van uses 8 gallons of fuel for 256 miles. How many gallons will a 400-mile route need?(A) 10 gallons; (B) 12.5 gallons; (C) 13 gallons; (D) 15 gallons
7. You earn $18.50 an hour and work 46 hours in a week. Overtime is paid at time and a half after 40 hours. What is your gross pay?(A) $851.00; (B) $906.50; (C) $1,276.50; (D) $795.50

Answer key with worked solutions

1. A: 2,469. Subtract column by column, borrowing where the top digit is smaller, then check by adding back: 2,469 + 1,739 = 4,208.
2. B: 864. 36 × 20 is 720, 36 × 4 is 144, and 720 + 144 is 864.
3. C: 84. 18 goes into 151 eight times (144), leaving 7; bring down the 2 to make 72, and 18 goes into 72 four times.
4. D: 1 5/12. The common denominator is 12: 9/12 + 8/12 = 17/12, which is 1 5/12.
5. A: 4. Turn both into improper fractions first: 5/2 × 8/5 = 40/10 = 4.
6. B: 2. Flip the second fraction and multiply: 5/6 × 12/5 = 60/30 = 2.
7. C: 9. Brackets first (6), then the square (36), then multiply and divide left to right (3 × 36 = 108, then 108 ÷ 12 = 9), and subtract last: 18 minus 9. Choice A comes from subtracting first.
8. A: 14.27. Line up the decimal points: 12.60 + 4.75 = 17.35, then 17.35 minus 3.08.
9. C: 0.42. 35 × 12 = 420, and the two factors carry three decimal places between them.
10. C: 90. Move both decimal points two places right: 720 ÷ 8.
11. B: 39. 10% is 26 and 5% is 13, so 26 + 13.
12. B: $67.41. 25% of 84 is 21, so the sale price is $63. Tax is 63 × 0.07 = $4.41, and $63 + $4.41 = $67.41. Choice C is the usual trap: tax taken on the original $84.
13. B: 25%. 18 ÷ 72 = 0.25.
14. B: 9 hours. 405 ÷ 45.
15. C: 154 square feet. Area is length times width. Choice A is the perimeter, a different measure.
16. B: 96 meters. Perimeter is 2 × (30 + 18).
17. A: 6 inches. 7 feet is 84 inches, and 3 × 26 is 78.
18. C: 48. There are 4 quarts in a gallon.
19. B: 12.5 gallons. 256 ÷ 8 = 32 miles per gallon, then 400 ÷ 32.
20. B: $906.50. 40 × 18.50 = $740. The overtime rate is $27.75, and 6 × 27.75 = $166.50. Add them. Choice A forgets the overtime rate.

If the fraction items felt rusty, the maths aptitude test guide has more timed practice at a step up in difficulty.

Give yourself one point per correct final answer, with no half marks: an official screen will not give you credit for the right method and the wrong number. Then read your total against this table. It is our own study guide for this practice set, not any test's official scale.

Your score out of 20

Where you stand

What to do next

18 to 20

Ready

Book the official test and keep one mixed practice session a week until then

14 to 17

Close

Find the bucket you missed most, spend a week on it, and retake this set

10 to 13

Not yet

Follow the two-week plan below before you book

0 to 9

Start from the ground floor

Rebuild whole numbers and fractions first; the other buckets depend on them

Your misses also tell you where to look. Items 1 to 7 are whole numbers, fractions, and order of operations. Items 8 to 13 are decimals and percents. Items 14 to 20 are word problems. Missing two or more in one group points to that group, not to math in general. Missing only the word problems usually means the arithmetic is fine and the reading is the issue: underline what the question asks for before you start calculating.

What score counts as passing on common math screens

It depends on who is testing you. The CBEST publishes its bar, a scaled 41 on the math section, and the GED passes at 145 on each subject. Accuplacer has no pass or fail at all; your college decides which course each score band leads to. Most employers keep their cut score private. If yours will not say, aim for at least 18 of 20 here before you sit it. That margin is our suggestion, built to leave room for nerves and a clock.

Practising with and without a calculator

Do your first practice run without a calculator, even when the official test offers one. A calculator on the screen is slower than it looks, and the tests that provide one still hold back some items, as the GED does. Mental arithmetic also gives you a way to check your answer: if 15% of 260 comes out as 3.9 or 390, you should feel it is wrong before you move on. Once your hand scores are steady, do a second timed run with a basic calculator to practise speed. We cover the rules test by test in our calculator rules guide.

Turning missed questions into a two-week study plan

Here is how to prepare for a basic math screen in two weeks, using nothing but this sheet and scrap paper. Days 1 to 4: take your weakest bucket and write ten fresh problems like the ones you missed, changing the numbers each time. Days 5 to 7: repeat with your second-weakest bucket. Day 8: retake the whole set on the clock. Days 9 to 13: work only on the items you missed on day 8, saying the steps aloud as you go. Day 14: one final timed run. If you are heading into a certificate or trade program that uses the TABE instead, our CTE basic skills assessment guide maps its scores by grade level.

Three groups go looking for a printable math test like this one, and each wants something slightly different from it.

Job applicants. Utilities, trades apprenticeships, warehouses, hospitals, and retail chains often send a short math test, on paper or on screen, before an interview. These readers want to know what is on the test and whether they will pass. Cashier and stock roles lean on the money problems in items 8 to 13; see our free cashier aptitude test for more of that style.

Adults going back to school. Community colleges place new students with tests like Accuplacer, and adult education programs use short numeracy checks to decide where a learner starts. For this group, falling short means a different starting course, not a rejection, and a few weeks of practice can lift you a level.

Career changers checking a baseline. Someone moving from office work into a trade, or from retail into health care, often has not done long division since school. A private practice run tells them how much rust there is before an employer sees it. If you are not sure which kind of skills test your situation calls for, our guide to free skills assessment test PDFs sorts them by why you are testing.

This page is built for adults. If you are assessing a child's math by grade level, a school-focused tool will serve you better than a hiring screen.

A pass on a math screen shows an employer that the numbers in the job will not trip you up. It does not tell you whether a job built around numbers is where you do your best work. Two people can both score 20 of 20. One enjoys a day of reconciling invoices; the other finishes it flat and counting the hours. The test cannot see that difference.

If this practice run is part of a bigger move, like leaving one line of work for another, it is worth asking that second question on purpose. Pigment's career test is one way to do it. Its questions are forced-choice with no right answers, so there is nothing to study for and nothing to game. If you are weighing an office job against a trade, for example, the career section shows which kinds of roles line up with the way you already like to work. It costs $79.99 and it is built for your own planning, never for an employer deciding between applicants.

After the Math Screen, Choose Where to Aim

You have practised the arithmetic. Now see which kinds of work suit how you operate, in a 36-page report. $79.99.

See where your strengths point