CAEC Mathematics Preparation: Lessons 2026

Lesson 1: The Mathematics test and problem-solving strategy

The Canadian Adult Education Credential (CAEC) is a high school equivalency for adults who do not have a high school diploma. It replaced the GED® in 2024. Completed GED® credentials stay valid.

There are five tests: Reading, Writing, Mathematics, Science and Social Studies. To earn the CAEC you must pass all five (or meet Prior Learning and Achievement Recognition, or PLAR, rules for some of them). Your province or territory then issues the credential. Tests are in English and French, on computer or paper, at a testing centre.

The tests are run by the CAEC testing service, which operates out of Alberta Education and Childcare's Provincial Assessment Sector. Provinces and territories that have an agreement with Alberta offer the tests, for example Ontario, Nova Scotia, New Brunswick, and Newfoundland and Labrador. Check your own province or territory's CAEC page for its rules on age, fees and test centres.

How the Mathematics test is set up

Part I checks that you can compute with fractions, decimals, percentages and integers, use the order of operations and solve simple equations, all without a calculator. Part II is about 75% of the test and covers four strands:

In Part II you may use an approved calculator, such as the TI-30XS or the Casio fx-260. Graphing calculators are not allowed, and neither are calculators with stored formulas or notes, or remote communication.

Pass mark and result levels

You need 55% to pass each CAEC test. Results come in four levels:

You may write a subject test once per calendar month, and up to 3 times per calendar year. Some provinces add their own rules, so check locally. You cannot rewrite a test you have passed. Mathematics results are usually ready in about 2 business days (Writing takes about 20).

The formula sheet

A formula sheet appears automatically on any question that has no information on the left side of the screen. It covers perimeter, circumference, area, surface area, volume, distance, simple interest, probability of independent and mutually exclusive events, and the Pythagorean theorem.

It does not list metric conversions, the mean or slope, so learn those. Questions that use imperial or U.S. units (feet, pounds, gallons) give you the conversion rate. Metric (SI) conversions, such as kilometres to metres, are not given.

A plan for every word problem

1. Read the whole question. Find exactly what it asks for.
2. Pick out the numbers you need. Some questions include extra numbers.
3. Estimate: round the numbers and get a rough answer.
4. Solve step by step. Write each step down.
5. Check the units (m, m², m³, $, hours).
6. Ask: is the answer reasonable and close to my estimate?

Example: $19.85 + $40.10 + $29.95 is about $20 + $40 + $30 = $90, and the exact total is $89.90. If a family's weekly groceries come out at $2,450, that is not reasonable: check your work.

Watch the clock. Part I gives you 30 ÷ 12 = 2.5 minutes per question, and Part II gives you 90 ÷ 30 = 3 minutes per question. If a question takes too long, skip it and come back.

Temaquiz 1: The Mathematics test and problem-solving strategy

Lesson 2: Part I – computing without a calculator

Fractions

• Add or subtract: use a common denominator. 3/4 + 1/8 = 6/8 + 1/8 = 7/8. Never add the denominators.
• Multiply: top × top and bottom × bottom. 3/4 × 1/2 = 3/8. "Half of" means "× 1/2".
• Divide: multiply by the reciprocal (flip the second fraction). 4 ÷ 2/3 = 4 × 3/2 = 6.
• Mixed numbers: change them to improper fractions first. 2 1/2 = 5/2 and 1 1/3 = 4/3, so 2 1/2 × 1 1/3 = 20/6 = 3 1/3.

To subtract mixed numbers, change both to improper fractions with the same denominator: 5 3/4 − 2 7/8 = 46/8 − 23/8 = 23/8 = 2 7/8.

Decimals and percentages

• Add or subtract: line up the decimal points. Write 12.4 as 12.40, then 12.40 − 3.75 = 8.65.
• Multiply: multiply as whole numbers, then count the decimal places. 0.6 × 0.4: 6 × 4 = 24, two decimal places, so 0.24.
• Fraction to percent: divide, then × 100. 2/5 = 0.4 = 40%.
• Percent of a number in your head: 10% of 80 is 8, 5% is half of that (4), so 15% of 80 is 12.

Integers (positive and negative numbers)

• Subtracting a negative is the same as adding: −7 + 12 − (−3) = −7 + 12 + 3 = 8.
• Same signs multiply or divide to a positive: (−4) × (−6) = 24.
• Different signs give a negative: 24 ÷ (−3) = −8.

Order of operations (BEDMAS)

Work in this order: Brackets, Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right).

• 3 + 4 × 2² = 3 + 4 × 4 = 3 + 16 = 19
• 18 − 6 ÷ 3 + 2 = 18 − 2 + 2 = 18
• 1/2 + 3/4 × 2 = 1/2 + 1 1/2 = 2

Simple equations

To solve x + a + b = c, first combine the numbers on the left, then do the opposite operation on both sides.

• x + 3.5 + 1.5 = 12 → x + 5 = 12 → x = 7
• x + (−4) + 9 = 2 → x + 5 = 2 → x = −3

Temaquiz 2: Part I: computing without a calculator

Lesson 3: Number sense – money, percentages, rates and ratios

Percentages in everyday money

To find a percent of an amount, change the percent to a decimal and multiply: 15% = 0.15.

• Tip: 15% of a $64.00 bill = 0.15 × 64 = $9.60.
• Discount: 25% off $120: discount = $30, sale price = $90. A shortcut is $120 × 0.75.
• Tax: 5% tax on $80 = $4, so the total is $84. Shortcut: $80 × 1.05.
• Discount, then tax: do them in order. $200 at 30% off = $140, then $140 × 1.05 = $147.
• Commission: 4% of $8,500 in sales = $340.

Wages and salary

Pay = hourly rate × hours. For overtime at 1.5 times, find the overtime rate first: $20 × 1.5 = $30. With 40 regular hours and 6 overtime hours, pay = 40 × $20 + 6 × $30 = $980. A yearly salary ÷ 12 gives a monthly amount.

Simple interest

Use I = Prt: I is interest, P is the principal (amount borrowed or saved), r is the yearly rate as a decimal, and t is the time in years. $2,000 at 3% for 4 years: I = 2,000 × 0.03 × 4 = $240. For 18 months, use t = 1.5. The total paid back is P + I.

Rates and unit prices

To compare prices, find the unit price: price ÷ quantity. $4.20 for 1.5 L is $2.80 per litre; $5.30 for 2 L is $2.65 per litre, so the 2 L size is the better buy.

• Speed: time = distance ÷ speed. 405 km at 90 km/h takes 4.5 h = 4 h 30 min.
• Fuel use: 8.5 L/100 km over 340 km uses 8.5 × 340 ÷ 100 = 28.9 L. At $1.55 per litre, that costs $44.80.

Ratios, proportions and scale

A ratio of 1 : 4 (concentrate to water) means 5 parts in total. For 2.5 L of juice, each part is 0.5 L. In a proportion, find the amount for one, then multiply: 300 g of pasta for 4 people is 75 g each, so 10 people need 750 g.

A map scale of 1 : 50 000 means 1 cm on the map is 50 000 cm in real life. 6 cm → 300 000 cm = 3 km (100 000 cm = 1 km).

Percent change

Percent change = (new − original) ÷ original × 100. Rent going from $1,400 to $1,505 is a change of $105, and 105 ÷ 1,400 × 100 = 7.5%. Always divide by the original amount.

Temaquiz 3: Number sense: money, percentages, rates and ratios

Lesson 4: Patterns and relations

Patterns

In a pattern that adds the same amount each time (4, 9, 14, 19 …), find the difference: +5. In a pattern that multiplies (3, 6, 12, 24 …), find the factor: × 2.

For an adding pattern, term n = first term + difference × (n − 1). A savings balance of $150, $175, $200 … in week 8 is 150 + 25 × 7 = $325. For tiles: figure 1 has 5, figure 2 has 8, figure 3 has 11. The rule is 3n + 2, so figure 20 has 62 tiles.

Writing a linear equation

Many costs are a fixed amount plus a rate: total = fixed + rate × amount. A taxi with a $4.00 flat fee and $2.10 per km costs C = 4.00 + 2.10d. A plumber with a $75 call-out fee and $90 per hour costs C = 75 + 90h.

Solving two-step equations

Undo the addition first, then the multiplication. For a $25 taxi ride: 25 = 4 + 2.10d → 21 = 2.10d → d = 10 km. For a $300 plumber bill: 300 = 75 + 90h → 225 = 90h → h = 2.5 hours. For flyers costing C = 0.15n + 12, $87 buys (87 − 12) ÷ 0.15 = 500 flyers.

To find when two plans cost the same, set them equal. Gym A: 40 + 25m. Gym B: 35m. So 40 + 25m = 35m → 40 = 10m → m = 4 months.

Use a letter for an unknown amount. If two friends each pay x and Sam pays x + 12 on a $96 bill: 3x + 12 = 96, so x = 28 and Sam pays $40.

Using and rearranging formulas

• To use a formula, put in the numbers and follow BEDMAS. F = 1.8C + 32: at 25 °C, F = 45 + 32 = 77 °F.
• C = (F − 32) ÷ 1.8: at 50 °F, C = 18 ÷ 1.8 = 10 °C. Do the brackets first.
• To rearrange, do the same thing to both sides. From d = rt, divide by r: t = d ÷ r.
• From I = Prt, r = I ÷ (P × t). A $90 interest charge on $1,500 over 2 years gives r = 90 ÷ 3,000 = 0.03 = 3%.

Logical reasoning

Put facts in order. If Ana is older than Ben, Ben is older than Cal, and Dee is younger than Cal, the order is Ana, Ben, Cal, Dee.

Think about what the answer means. If each shelf holds 12 boxes and you have 75 boxes, 75 ÷ 12 = 6.25. You cannot use part of a shelf and 6 shelves hold only 72, so you need 7.

Temaquiz 4: Patterns and relations

Lesson 5: Geometry and measurement

Metric units (you must know these)

Change to the same unit before you calculate. A 3.6 kg bag holds 3,600 g, so it makes 3,600 ÷ 450 = 8 batches of 450 g. For imperial units, the question gives the rate. With 1 inch = 2.54 cm, 55 inches = 139.7 cm. With 1 kg ≈ 2.2 lb, divide pounds by 2.2: 48 lb ≈ 21.8 kg.

Perimeter and area

A 12 m by 8.5 m yard needs 2 × (12 + 8.5) = 41 m of fence. A circle with a 6 m diameter has a 3 m radius, so its area is π × 9 ≈ 28.3 m².

For a composite shape, split it into rectangles, or take the big rectangle and subtract the missing piece. A 6 m by 4 m room missing a 2 m by 1.5 m corner has 24 − 3 = 21 m².

The Pythagorean theorem

In a right triangle, a² + b² = c², where c is the longest side (the hypotenuse). A 30 m by 40 m lot has a diagonal of √(900 + 1,600) = 50 m. For a 5 m ladder with its foot 1.5 m from the wall, height = √(25 − 2.25) ≈ 4.77 m. Subtract when you know the hypotenuse.

Similar shapes and scale factor

Scale factor = new length ÷ old length. A 10 cm by 15 cm photo enlarged to 25 cm wide has a factor of 2.5, so the height is 37.5 cm. Shadows work the same way: if a 2 m post casts a 1.5 m shadow, a tree with a 9 m shadow is 9 × 2 ÷ 1.5 = 12 m tall.

Volume and surface area

• Box (rectangular prism): length × width × height. A 1.2 m × 0.5 m × 0.4 m planter holds 0.24 m³ = 240 L.
• Cylinder: π × radius² × height. A tank with r = 0.5 m and h = 1.2 m holds about 0.942 m³ ≈ 942 L.
• Wall area for paint: perimeter of the room × wall height. A 4 m by 3 m room with 2.5 m walls has 2 × (4 + 3) × 2.5 = 35 m² of wall. Two coats = 70 m². At 10 m² per litre, you need 7 L.

For flooring, find the area, add extra for waste (often 10%), divide by what one box covers, and round up. For 14.7 m²: 14.7 × 1.10 = 16.17 m², and 16.17 ÷ 2.2 ≈ 7.35, so buy 8 boxes.

Temaquiz 5: CAEC geometry and measurement

Lesson 6: Data management and probability

Reading tables and graphs

Data may be shown in tables, spreadsheets or graphs. Read the title, labels and units first.

• A bar graph or table compares amounts, such as calls per month. A change from 120 to 150 is +30, and 30 ÷ 120 = 25%.
• A circle graph shows parts of a whole as percentages. If food is 15% of $3,800, food is $570.
• A histogram groups data into ranges, such as ages 30–39. For "30 or older", add every group from 30 up.
• A scatterplot shows two values for each person or item. If points rise from left to right, the relationship is positive; if they fall, it is negative.

Mean, median, mode and range

With an even number of values, the median is the mean of the two middle values: for 9, 11, 12, 15, 18, 20 it is (12 + 15) ÷ 2 = 13.5. Always sort first. With negative numbers, range = highest − lowest: 8 − (−12) = 20.

An outlier is a value far from the others. It pulls the mean toward it but hardly moves the median. For wages of $16, $17, $17, $18 and $52, the mean is $24 but the median is $17. When data has an outlier, the median usually shows the typical value better.

Probability

Probability = number of favourable outcomes ÷ total number of outcomes. A bag with 3 red, 5 blue and 2 green marbles gives P(blue) = 5/10 = 1/2.

• Mutually exclusive events cannot happen at the same time. Add: P(A or B) = P(A) + P(B). Rolling a 2 or a 5 on a die: 1/6 + 1/6 = 1/3. If you hold 4 and a friend holds 6 of 500 raffle tickets, P(one of you wins) = 10/500 = 2%.
• Independent events do not affect each other. Multiply: P(A and B) = P(A) × P(B). Heads and a 6: 1/2 × 1/6 = 1/12. A bus late 20% of days, late two days in a row: 0.2 × 0.2 = 0.04 = 4%.

Temaquiz 6: Data management and probability