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MB Essential Math 40S study materials
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MB Essential Math 40S practice questions

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Question 1Essential Mathematics 40S (domain structure not enumerated in source)

A shirt priced at $48 is discounted by 25%. What is the sale price?

  1. $12
  2. $23
  3. $60
  4. $36 Correct answer.

Explanation

A 25% discount removes one quarter of the price, and 25% of $48 equals $12. Subtracting the discount from the original price gives $48 − $12 = $36. Equivalently, the buyer pays 75% of $48, which is also $36.

Question 2Essential Mathematics 40S (domain structure not enumerated in source)

A recipe uses 3 cups of flour for every 2 cups of milk. How many cups of flour are needed with 5 cups of milk?

  1. 10
  2. 6.5
  3. 7.5 Correct answer.
  4. 4

Explanation

Set up the proportion 3/2 = x/5 and cross-multiply to get 2x = 15. Dividing both sides by 2 gives x = 7.5 cups of flour. The ratio of flour to milk must stay constant as the milk increases.

Question 3Essential Mathematics 40S (domain structure not enumerated in source)

A car travels 150 km in 2 hours. At this same average speed, how far does it travel in 5 hours?

  1. 375 km Correct answer.
  2. 450 km
  3. 300 km
  4. 325 km

Explanation

Average speed equals distance divided by time, so 150 km ÷ 2 h = 75 km/h. Multiplying this rate by 5 hours gives 75 × 5 = 375 km. The distance grows in direct proportion to the travel time.

Question 4Essential Mathematics 40S (domain structure not enumerated in source)

Which statement correctly describes the slope of a horizontal line on a Cartesian graph?

  1. The slope equals one.
  2. The slope is undefined.
  3. The slope is negative.
  4. The slope is zero. Correct answer.

Explanation

Slope measures vertical change divided by horizontal change. A horizontal line has no vertical change, so the numerator is zero and the slope is zero. A vertical line, by contrast, has zero horizontal change and an undefined slope.

Question 5Essential Mathematics 40S (domain structure not enumerated in source)

A savings account holds $800 and earns 5% simple interest per year. How much interest is earned after 3 years?

  1. $120 Correct answer.
  2. $126
  3. $240
  4. $40

Explanation

Simple interest is calculated as principal × rate × time. Here that is 800 × 0.05 × 3 = $120. The interest is not compounded, so each year adds the same $40.

Question 6Essential Mathematics 40S (domain structure not enumerated in source)

A bag contains 4 red marbles and 6 blue marbles. What is the probability of drawing a red marble at random?

  1. 0.44
  2. 0.4 Correct answer.
  3. 0.6
  4. 0.25

Explanation

Probability equals favourable outcomes divided by total outcomes. There are 4 red marbles out of 4 + 6 = 10 total, so the probability is 4/10 = 0.4. The blue probability would be 0.6.

Question 7Essential Mathematics 40S (domain structure not enumerated in source)

The mean of five test scores is 72. What is the sum of the five scores?

  1. 350
  2. 144
  3. 360 Correct answer.
  4. 72

Explanation

The mean equals the sum divided by the count. Rearranging gives sum = mean × count = 72 × 5 = 360. Checking back, 360 divided by 5 returns the original mean of 72.

Question 8Essential Mathematics 40S (domain structure not enumerated in source)

A rectangular room measures 4 m by 6 m. What is its area?

  1. 20 m²
  2. 48 m²
  3. 10 m²
  4. 24 m² Correct answer.

Explanation

The area of a rectangle equals length × width. Multiplying 4 m by 6 m gives 24 square metres. The units are squared because two length dimensions are multiplied.

Question 9Essential Mathematics 40S (domain structure not enumerated in source)

A jacket costs $80 before tax and the tax rate is 7%. What is the total cost including tax?

  1. $87.00
  2. $74.40
  3. $85.60 Correct answer.
  4. $5.60

Explanation

Tax equals 7% of $80, which is 0.07 × 80 = $5.60. Adding the tax to the base price gives $80 + $5.60 = $85.60. Multiplying $80 by 1.07 gives the same result directly.

Question 10Essential Mathematics 40S (domain structure not enumerated in source)

A population grows by 10% in one year and then by 10% the next year. What is the overall percent increase over the two years?

  1. 21% Correct answer.
  2. 20%
  3. 22%
  4. 10%

Explanation

Successive percentage changes multiply rather than add. After two years the multiplier is 1.10 × 1.10 = 1.21, which represents a 21% increase. The second 10% applies to an already larger base.

Question 11Essential Mathematics 40S (domain structure not enumerated in source)

Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has an area of 12 cm², what is the area of the larger triangle?

  1. 48 cm²
  2. 75 cm² Correct answer.
  3. 30 cm²
  4. 60 cm²

Explanation

Areas of similar figures scale with the square of the side ratio. The area ratio is 2²:5² = 4:25, so the larger area is 12 × 25/4 = 75 cm². Using the linear ratio directly would give the wrong answer.

Question 12Essential Mathematics 40S (domain structure not enumerated in source)

A line passes through the points (2, 3) and (6, 11). What is the slope of the line?

  1. 2 Correct answer.
  2. 4
  3. 0.5
  4. 8

Explanation

Slope equals the change in y divided by the change in x. Here the rise is 11 − 3 = 8 and the run is 6 − 2 = 4, so the slope is 8/4 = 2. The line rises two units for every one unit to the right.

Question 13Essential Mathematics 40S (domain structure not enumerated in source)

A monthly budget of $2,400 is split so that 35% goes to rent. How much is left for all other expenses?

  1. $1,560 Correct answer.
  2. $1,460
  3. $840
  4. $1,700

Explanation

Rent takes 35% of $2,400, which is $840, so the remaining share is 65%. Calculating 0.65 × 2,400 gives $1,560. Alternatively, subtract $840 from $2,400 to reach the same amount.

Question 14Essential Mathematics 40S (domain structure not enumerated in source)

A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning a number greater than 5?

  1. 0.25
  2. 0.375 Correct answer.
  3. 0.5
  4. 0.625

Explanation

The numbers greater than 5 are 6, 7, and 8, giving three favourable outcomes. With eight equally likely sections, the probability is 3/8 = 0.375. Numbers 1 through 5 do not qualify.

Question 15Essential Mathematics 40S (domain structure not enumerated in source)

The median of a data set with an even number of values is found by taking the average of which values?

  1. The first and last values as listed
  2. The most frequent values
  3. The largest and smallest values
  4. The two middle values after sorting Correct answer.

Explanation

The median is the middle value of an ordered data set. When the count is even, there is no single middle, so the two central values are averaged. Sorting the data first is essential before locating those middle values.

Question 16Essential Mathematics 40S (domain structure not enumerated in source)

A loan of $5,000 charges 6% annual interest compounded yearly. What is the amount owed after 2 years, to the nearest dollar?

  1. $5,600
  2. $5,300
  3. $5,612
  4. $5,618 Correct answer.

Explanation

Compound interest uses the formula A = P(1 + r)^t. Substituting gives 5000 × 1.06² = 5000 × 1.1236 = $5,618. The compounding adds interest on the first year's interest as well.

Question 17Essential Mathematics 40S (domain structure not enumerated in source)

A cylindrical tank has a radius of 2 m and a height of 5 m. Using π ≈ 3.14, what is its volume?

  1. 20 m³
  2. 125.6 m³
  3. 62.8 m³ Correct answer.
  4. 31.4 m³

Explanation

The volume of a cylinder is V = πr²h. Substituting gives 3.14 × 2² × 5 = 3.14 × 4 × 5 = 62.8 m³. Squaring the radius before multiplying by height is essential.

Question 18Essential Mathematics 40S (domain structure not enumerated in source)

A store marks up a wholesale item by 40% and later offers a 40% discount on the marked price. Compared with the original wholesale price, the final price is:

  1. Lower by 16% Correct answer.
  2. The same
  3. Higher by 16%
  4. Lower by 40%

Explanation

A 40% markup multiplies the price by 1.40, and a 40% discount multiplies by 0.60. The combined factor is 1.40 × 0.60 = 0.84, which is 16% below the original. The two percentages apply to different bases, so they do not cancel.

Question 19Essential Mathematics 40S (domain structure not enumerated in source)

A commuter's monthly transit pass costs $110. A single fare is $3.25. How many single fares must be taken in a month for the pass to save money?

  1. At least 25
  2. At least 30
  3. At least 40
  4. At least 34 Correct answer.

Explanation

Divide the pass cost by the fare: 110 ÷ 3.25 ≈ 33.8. Since fares are whole trips, 33 fares cost about $107.25, still below the pass, while 34 fares cost $110.50 and exceed it. So the pass saves money from 34 fares onward.

Question 20Essential Mathematics 40S (domain structure not enumerated in source)

A data set of 10 values has a mean of 50. If one value of 30 is removed, what is the mean of the remaining 9 values?

  1. 55
  2. 53.3
  3. 50
  4. 52.2 Correct answer.

Explanation

The original total is 50 × 10 = 500. Removing 30 leaves 470 spread over 9 values, so the new mean is 470 ÷ 9 ≈ 52.2. Removing a value below the old mean raises the mean.

Question 21Essential Mathematics 40S (domain structure not enumerated in source)

A 12 m ladder leans against a wall with its base 5 m from the wall. How high up the wall does the ladder reach?

  1. √119 m Correct answer.
  2. 13 m
  3. 7 m
  4. √169 m

Explanation

The ladder, wall, and ground form a right triangle with the ladder as hypotenuse. Using the Pythagorean theorem, height² = 12² − 5² = 144 − 25 = 119, so the height is √119 ≈ 10.9 m. Subtracting squares, not the lengths themselves, is required.

Question 22Essential Mathematics 40S (domain structure not enumerated in source)

A car depreciates by 15% each year. To the nearest dollar, what is a $20,000 car worth after 3 years?

  1. $14,450
  2. $13,000
  3. $11,000
  4. $12,283 Correct answer.

Explanation

Depreciation by a fixed percent uses the multiplier (1 − 0.15) = 0.85 each year. After three years the value is 20000 × 0.85³ = 20000 × 0.614125 ≈ $12,283. Straight-line subtraction of 15% of the original each year would be incorrect.

Question 23Essential Mathematics 40S (domain structure not enumerated in source)

Two investment plans are compared. Plan A pays 5% simple interest on $1,000 for 4 years. Plan B pays 5% interest compounded annually on $1,000 for 4 years. How much more does Plan B earn, to the nearest dollar?

  1. $0
  2. $215
  3. $50
  4. $16 Correct answer.

Explanation

Plan A earns 1000 × 0.05 × 4 = $200 in interest. Plan B grows to 1000 × 1.05⁴ ≈ $1,215.51, earning about $215.51, so the difference is roughly $16. Compounding earns interest on previously earned interest.

Question 24Essential Mathematics 40S (domain structure not enumerated in source)

A survey of 200 people found that 60% prefer tea and the rest prefer coffee. Of the tea drinkers, 25% also drink coffee. How many people drink only tea?

  1. 150
  2. 90 Correct answer.
  3. 30
  4. 120

Explanation

Tea drinkers number 0.60 × 200 = 120. Of these, 25% also drink coffee, which is 0.25 × 120 = 30 people. Those who drink only tea are 120 − 30 = 90. The overlap must be subtracted from the tea total.

Question 25Essential Mathematics 40S (domain structure not enumerated in source)

A rectangular garden is enlarged so that both its length and width increase by 20%. By what percent does its area increase?

  1. 20%
  2. 44% Correct answer.
  3. 24%
  4. 40%

Explanation

Each dimension is multiplied by 1.20, so the area is multiplied by 1.20 × 1.20 = 1.44. That represents a 44% increase in area. The percentage increases do not simply add because both factors apply to the area.

Question 26Essential Mathematics 40S (domain structure not enumerated in source)

A savings account earns 4% simple interest per year. How much interest is earned on $1,500 after 3 years?

  1. $1,680
  2. $180 Correct answer.
  3. $187
  4. $60

Explanation

Simple interest is calculated as principal times rate times time, so 1500 × 0.04 × 3 = 180 dollars. Simple interest is charged only on the original principal each year, not on accumulated interest.

Question 27Essential Mathematics 40S (domain structure not enumerated in source)

Which measure of central tendency is most affected by a single extremely large outlier?

  1. The mode
  2. The mean Correct answer.
  3. The median
  4. The range

Explanation

The mean is computed from the sum of all values, so one very large value pulls the sum and therefore the mean upward. The median and mode depend on position or frequency, so they resist a single extreme value.

Question 28Essential Mathematics 40S (domain structure not enumerated in source)

A fair six-sided die is rolled once. What is the probability of rolling an even number or a number greater than 4?

  1. 1/6
  2. 1/2
  3. 5/6
  4. 2/3 Correct answer.

Explanation

The even outcomes are 2, 4 and 6, and the outcomes greater than 4 are 5 and 6. Combining without double-counting gives 2, 4, 5, 6, which is 4 of 6 outcomes, or 2/3.

Question 29Essential Mathematics 40S (domain structure not enumerated in source)

A recipe uses flour and sugar in the ratio 5:2. If 350 g of flour is used, how much sugar is needed?

  1. 175 g
  2. 250 g
  3. 700 g
  4. 140 g Correct answer.

Explanation

Set up the proportion 5/2 = 350/x and solve for x. Cross-multiplying gives 5x = 700, so x = 140 grams of sugar.

Question 30Essential Mathematics 40S (domain structure not enumerated in source)

A rectangular prism has length 5 cm, width 3 cm, and height 4 cm. What is its surface area?

  1. 120 cm²
  2. 60 cm²
  3. 94 cm² Correct answer.
  4. 47 cm²

Explanation

Surface area of a rectangular prism is 2(lw + lh + wh). Substituting gives 2(15 + 20 + 12) = 2(47) = 94 square centimetres.

Question 31Essential Mathematics 40S (domain structure not enumerated in source)

A worker earns $18.50 per hour and works 38 hours in a week. What is the gross pay for that week?

  1. $665.00
  2. $720.50
  3. $740.00
  4. $703.00 Correct answer.

Explanation

Gross pay equals the hourly rate multiplied by the hours worked. Multiplying 18.50 by 38 gives 703.00 dollars before any deductions.

Question 32Essential Mathematics 40S (domain structure not enumerated in source)

A triangle has a base of 10 cm and a height of 6 cm. What is its area?

  1. 36 cm²
  2. 16 cm²
  3. 60 cm²
  4. 30 cm² Correct answer.

Explanation

The area of a triangle is one-half times base times height. Substituting gives 0.5 × 10 × 6 = 30 square centimetres.

Question 33Essential Mathematics 40S (domain structure not enumerated in source)

In a right triangle, the two legs measure 9 cm and 12 cm. What is the length of the hypotenuse?

  1. 13 cm
  2. 15 cm Correct answer.
  3. 21 cm
  4. 16 cm

Explanation

By the Pythagorean theorem, the hypotenuse squared equals 9² + 12² = 81 + 144 = 225. The square root of 225 is 15 centimetres.

Question 34Essential Mathematics 40S (domain structure not enumerated in source)

A bicycle priced at $450 is discounted by 20%, and then 5% tax is added to the sale price. What is the final cost?

  1. $472.50
  2. $360.00
  3. $378.00 Correct answer.
  4. $382.50

Explanation

First apply the discount: 450 × 0.80 = 360. Then add 5% tax: 360 × 1.05 = 378.00 dollars. Applying operations in sequence this way keeps the discount and tax separate.

Question 35Essential Mathematics 40S (domain structure not enumerated in source)

A data set contains the values 4, 7, 7, 9, 12, 15, 20. What is the interquartile range?

  1. 5.5
  2. 9
  3. 16
  4. 8 Correct answer.

Explanation

With seven ordered values, the median is 9. The lower half (4, 7, 7) has median 7 and the upper half (12, 15, 20) has median 15. The interquartile range is 15 − 7 = 8.

Question 36Essential Mathematics 40S (domain structure not enumerated in source)

A credit card balance of $2,000 grows at 1.5% interest per month, compounded monthly. To the nearest dollar, what is the balance after 4 months if no payments are made?

  1. $2,120
  2. $2,090
  3. $2,240
  4. $2,123 Correct answer.

Explanation

Use the compound interest formula A = P(1 + r)^n with P = 2000, r = 0.015, and n = 4. Computing 2000 × (1.015)^4 gives approximately 2122.73, which rounds to 2123 dollars.

Question 37Essential Mathematics 40S (domain structure not enumerated in source)

Two events A and B are independent, with P(A) = 0.4 and P(B) = 0.5. What is the probability that both A and B occur?

  1. 0.2 Correct answer.
  2. 0.9
  3. 0.45
  4. 0.1

Explanation

For independent events, the probability of both occurring is the product of their individual probabilities. Multiplying 0.4 × 0.5 gives 0.2.

Question 38Essential Mathematics 40S (domain structure not enumerated in source)

A car travels 240 km on 20 litres of fuel. At the same rate, how many litres are needed for a 360 km trip?

  1. 18 L
  2. 36 L
  3. 24 L
  4. 30 L Correct answer.

Explanation

The car uses 20 L per 240 km, which is 1 litre per 12 km. For 360 km, divide 360 by 12 to get 30 litres.

Question 39Essential Mathematics 40S (domain structure not enumerated in source)

A cone has a radius of 3 cm and a height of 7 cm. Using π ≈ 3.14, what is its volume, to the nearest cubic centimetre?

  1. 132 cm³
  2. 66 cm³ Correct answer.
  3. 594 cm³
  4. 198 cm³

Explanation

The volume of a cone is one-third of the base area times height: V = (1/3)πr²h. Substituting gives (1/3)(3.14)(9)(7) ≈ 65.9, which rounds to 66 cubic centimetres.

Question 40Essential Mathematics 40S (domain structure not enumerated in source)

A student's scores on four tests are 68, 75, 82 and 91. What score is needed on a fifth test to have a mean of 80?

  1. 90
  2. 84 Correct answer.
  3. 85
  4. 80

Explanation

A mean of 80 over five tests requires a total of 400 points. The four known scores sum to 316, so the fifth score must be 400 − 316 = 84.

Question 41Essential Mathematics 40S (domain structure not enumerated in source)

A map uses a scale of 1:25,000. A distance of 8 cm on the map represents what actual distance in kilometres?

  1. 2 km Correct answer.
  2. 20 km
  3. 0.2 km
  4. 200 km

Explanation

Multiply the map distance by the scale factor: 8 cm × 25,000 = 200,000 cm. Since 100,000 cm equals 1 km, this is 2 kilometres.

Question 42Essential Mathematics 40S (domain structure not enumerated in source)

A population of 5,000 decreases by 8% each year. To the nearest whole number, what is the population after 3 years?

  1. 3,800
  2. 3,894 Correct answer.
  3. 4,600
  4. 3,860

Explanation

Repeated percent decrease uses the multiplier (1 − 0.08) = 0.92 each year. Computing 5000 × (0.92)^3 gives approximately 3893.4, which rounds to 3894.

Question 43Essential Mathematics 40S (domain structure not enumerated in source)

In a group of 50 students, 30 play soccer, 20 play basketball, and 10 play both. How many play neither sport?

  1. 10 Correct answer.
  2. 0
  3. 20
  4. 30

Explanation

By the inclusion-exclusion principle, the number playing at least one sport is 30 + 20 − 10 = 40. Therefore 50 − 40 = 10 students play neither sport.

Question 44Essential Mathematics 40S (domain structure not enumerated in source)

A loan of $3,000 is repaid with simple interest over 18 months at an annual rate of 8%. What is the total amount repaid?

  1. $3,240
  2. $3,360 Correct answer.
  3. $3,720
  4. $3,180

Explanation

Convert 18 months to 1.5 years, then compute interest: 3000 × 0.08 × 1.5 = 360. Adding this to the principal gives 3,360 dollars total.

Question 45Essential Mathematics 40S (domain structure not enumerated in source)

A company's revenue rose from $40,000 to $52,000 in one year. What was the percent increase?

  1. 130%
  2. 12%
  3. 23%
  4. 30% Correct answer.

Explanation

Percent increase equals the change divided by the original amount, times 100. The change is 12,000, and 12,000 ÷ 40,000 = 0.30, or 30%.

Question 46Essential Mathematics 40S (domain structure not enumerated in source)

A bag holds 5 red, 3 green, and 2 yellow balls. Two balls are drawn without replacement. What is the probability that both are red?

  1. 1/4
  2. 1/2
  3. 1/5
  4. 2/9 Correct answer.

Explanation

The probability the first ball is red is 5/10, and after removing one red the second is 4/9. Multiplying gives (5/10)(4/9) = 20/90 = 2/9.

Question 47Essential Mathematics 40S (domain structure not enumerated in source)

A cylindrical container of radius 4 cm is filled with water to a height of 10 cm. A solid sphere of radius 3 cm is fully submerged. Using π ≈ 3.14, by how much does the water level rise, to the nearest tenth of a centimetre?

  1. 0.8 cm
  2. 2.3 cm Correct answer.
  3. 1.5 cm
  4. 3.0 cm

Explanation

The sphere displaces its own volume, (4/3)π(3)³ ≈ 113.0 cm³. Dividing by the cylinder's base area π(4)² ≈ 50.24 cm² gives a rise of about 2.25 cm, which rounds to 2.3 cm.

Question 48Essential Mathematics 40S (domain structure not enumerated in source)

A town's population grows by 6% in year one, then declines by 6% in year two. Compared with the starting population, what is the net result?

  1. A slight decrease Correct answer.
  2. No change
  3. A slight increase
  4. A 12% increase

Explanation

Apply multipliers in sequence: 1.06 × 0.94 = 0.9964, which is less than 1. The 6% decline is taken from a larger base, so the net effect is a decrease of about 0.36%.

Question 49Essential Mathematics 40S (domain structure not enumerated in source)

A data set of 9 values has a mean of 40 and a median of 42. If the largest value is increased by 18, what are the new mean and median?

  1. Mean 42, median 42 Correct answer.
  2. Mean 40, median 42
  3. Mean 42, median 44
  4. Mean 42, median 46

Explanation

Increasing one value by 18 raises the total by 18, so the mean rises by 18 ÷ 9 = 2, giving 42. The median depends on position, and the largest value stays largest, so the median remains 42.

Question 50Essential Mathematics 40S (domain structure not enumerated in source)

Two similar cylindrical cans have heights in the ratio 3:4. If the smaller can holds 540 mL, what is the capacity of the larger can?

  1. 720 mL
  2. 1,280 mL Correct answer.
  3. 960 mL
  4. 1,080 mL

Explanation

For similar solids, volumes scale as the cube of the linear ratio. The ratio (4/3)³ = 64/27, so the larger capacity is 540 × 64/27 = 1,280 millilitres.