Module 01 of 06 · Full Teaching Edition
Data-analysis questions test whether you can extract numbers from pictures: bar graphs, line graphs, and pie charts. The math is light — the trap is misreading the axis, units, or percentage.
The graph shows the number of apples that each of five students ate during a week. Which student ate the greatest number of apples?
On a bar graph, the tallest bar represents the largest quantity.
Read each student's bar height against the y-axis; pick the maximum.
Don't confuse “greatest” with “least” — Vinh has the smallest bar.
A — Dae (6 apples)
The line graph shows the distance Andrew walked over time. How long did it take Andrew to walk the first 2 km?
On a distance-vs-time graph, to find the time for a given distance, draw a horizontal line at that distance and read where it meets the curve.
Don't read off “2 hours” from the x-axis. Always go from distance → time.
B — 1 hour, 15 minutes
The pie chart shows results of a survey asking students their favourite fruit. 100 students were surveyed. How many chose banana? Orange 40%, Apple 40%, Banana 20%.
Pie chart count = percentage × total respondents.
20% of 100 = 0.20 × 100 = 20 students.
D — 20 students
In the pie chart shown, 80 students chose juice. The juice slice has a right angle. How many students chose milk?
A right angle in a pie chart equals 90° / 360° = 1/4 of the total.
Use the juice fraction and its count to find the total, then identify the milk fraction from the chart.
Always identify all slices before subtracting. The “rest of the circle” may include a third category.
B — 160 students
Alexis took a total of 243,000 steps during the 30 days of April. What was her mean number of steps per day?
Mean = 243000 ÷ 30 = 8100.
Estimate: 240,000 ÷ 30 = 8,000. The exact answer must be slightly larger.
B — 8,100 steps/day
Five different integers in a list have a median of 10 and a range of 7. What is the smallest possible integer in the list?
For 5 sorted integers a < b < c < d < e, the median is c and the range is e − a.
Fix c = 10 and e − a = 7. Minimize a by making e as small as possible while keeping d strictly between 10 and e.
“Different integers” rules out repeats.
B — 5
Heights of 4 athletes are 135, 160, 170, 175 cm. Laurissa joins. On the new team of 5, mode = median = mean. How tall is Laurissa?
A mode requires at least one repeated value. Since the original four are all different, Laurissa must equal one of them.
Test each candidate that matches an existing height.
B — 160 cm
The mean of six numbers is 10. When 25 is removed, what is the mean of the remaining numbers?
Use sum = mean × count twice.
B — 7
P(A) = favorable outcomes / total outcomes
A circular spinner has 12 unshaded sections and 3 shaded sections. Each unshaded section is 3× the size of each shaded section. The arrow is spun once. What is the probability it lands in a shaded section?
Sections are not equal sized. You cannot just write 3/15.
Let one shaded section = 1 unit of area. Then each unshaded section = 3 units.
D — 1/13
A bag contains some candies. P(choosing a red candy) = 5/6. The total number of candies could be:
If P = 5/6 in lowest terms, the total candies must be a multiple of 6.
From the options, only 6 is a multiple of 6.
D — 6
A number is chosen from {1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the probability the chosen number is divisible by 2, or by 3, or by both?
Inclusion–Exclusion: |A ∪ B| = |A| + |B| − |A ∩ B|.
Forgetting to subtract the overlap double-counts 6.
C — 6/9
A standard fair coin is tossed three times. What is the probability that all three outcomes are the same?
List the sample space. There are 2³ = 8 outcomes.
C — 1/4
For two standard dice there are exactly 36 equally likely outcomes. Sum 7 is the most common; the extremes 2 and 12 are rarest.
Ways by sum: 2:1, 3:2, 4:3, 5:4, 6:5, 7:6, 8:5, 9:4, 10:3, 11:2, 12:1.
Two standard six-sided dice are rolled. If the two top-face numbers are added, which sum is least likely?
Sums closer to the extremes have fewer combinations. From the choices, 11 is farthest from the center.
Sum 7: 6 ways. Sum 8: 5 ways. Sum 9: 4 ways. Sum 10: 3 ways. Sum 11: 2 ways.
E — sum of 11
Two standard dice are rolled. What is the probability the sum is a prime number?
Prime sums possible: 2, 3, 5, 7, 11.
9 is not prime.
A — 5/12
Two standard dice are rolled. The product of the two numbers is computed. What is the probability that the ones digit of the product is 0?
Ones digit is 0 ⇔ product is a multiple of 10 ⇔ product has both a factor of 2 and a factor of 5.
Since 5 only appears on die face 5, at least one die must show 5. The other die must show 2, 4, or 6.
Order matters: (5,2) and (2,5) are separate outcomes.
D — 1/6
A special 6-sided die is rolled. P(multiple of 3) = 1/2, P(even) = 1/3. Which face-set works?
Out of 6 faces, need exactly 3 multiples of 3 and exactly 2 even faces.
Option B = {1, 2, 3, 3, 5, 6}. Multiples of 3: 3, 3, 6 → 3 faces. Even numbers: 2, 6 → 2 faces.
Each face is counted separately, even if the same number appears twice.
B — {1, 2, 3, 3, 5, 6}
A 10 × 10 grid is created using 100 points. Point P is given. One of the other 99 points is randomly chosen to be Q. What is the probability that segment PQ is vertical or horizontal?
PQ is horizontal ⇔ P and Q are in the same row. PQ is vertical ⇔ same column.
Count points in the same row as P plus points in the same column as P, excluding P itself.
This answer does not depend on where P sits in the grid.
For an n × n grid: P = 2(n−1)/(n²−1) = 2/(n+1). For n = 10, this gives 2/11.
A — 2/11
Based on the bar graph, which sport is played by the most students? Hockey 40, Basketball 30, Soccer 50, Volleyball 20, Badminton 10.
Soccer = 50 is the tallest bar.
C — Soccer
480 students voted for a favourite subject: Math 40%, Science 30%, Music 20%, Art 10%. How many voted for math?
Math voters = 0.40 × 480 = 192.
B — 192
The mean of the four integers 78, 83, 82, and x is 80. Which statement is true?
D — x is 3 less than the mean
The mean of the list 2, 9, 4, n, 2n is 6. What is n?
D — n = 5
The list of seven numbers 3, 15, 8, 8, 9, 9, n has exactly one mode, which is 8. What is n?
Currently 8 appears twice and 9 appears twice. To make 8 the unique mode, 8 must appear more times.
D — n = 8
Eloise bought water pumps for charity. Mean price was $85 per pump. Total spent was $765. How many pumps did she buy?
Count = total ÷ mean = 765 ÷ 85 = 9.
C — 9 pumps
An integer is randomly chosen from {10, 11, 12, …, 19}. What is the probability the chosen integer is even?
Even numbers: 10, 12, 14, 16, 18 → 5 numbers. P = 5/10.
C — 5/10
A spinner has 20 equal sections numbered 1–20. What is the probability the arrow stops in a section containing a divisor of 20?
Divisors of 20 divide 20 evenly.
Do not include numbers like 3, 6, 7, 8, or 9.
E — 6/20
A box contains 15 red, 20 blue, and 16 green jelly beans. Jack first picks and eats a green, then picks and eats a blue. What is the probability his next pick is red?
Conditional probability — update the counts after each removal.
The red count does not change; only the total changes.
C — 15/49
A dime = $0.10, a quarter = $0.25. Terry's jar contains $1.00 in dimes and $1.00 in quarters. He removes one coin at random. What is the probability it is a dime?
Equal dollar amounts do not mean equal coin counts.
If the jar had $1 in nickels and $1 in quarters: 20 nickels and 4 quarters → P(nickel) = 20/24 = 5/6.
E — 5/7