Algebraic Expressions
Write an expression that represents: "Seven times the sum of x and 4"?
7(x + 4)
Solve: −3x + 5 + 7x − 9 = 20
x = 6
The following hours of TV watched per week were recorded: 3, 7, 3, 5, 8, 4. What is the mean?
Mean = 5 hours
Using the rule y = 0.50x + 3, where x is the number of episodes downloaded through a streaming service, and y is the cost, how much would it cost to download 24 episodes of a show?
$15.00
A triangular prism has equilateral triangle bases with a base of 6 cm and height 5.2 cm. The prism's length is 10 cm. What is the area of one triangular base?
15.6
Given x = 5, what is the value of 2x² - 3x + 7?
42
Solve: 4y + 6 = 5(y − 3)
y = 21
A distribution of quiz scores has a mean of 72. Six of the seven scores are: 85, 60, 75, 68, 90, 55. What is the missing score?
Missing score = 67
A streaming service charges a $6.00 setup fee plus $0.75 per episode downloaded. Write the rule for total cost y based on number of episodes x.
y = 0.75x + 6
A cylinder has a diameter of 10 cm and a height of 15 cm. What is the total surface area? (Use π ≈ 3.14)
628 cm²
Simplify: -3(2x - 5) + 4x
-2x + 15
Marcus has 35 red and blue markers. The number of red markers is 3 more than twice the number of blue markers. How many blue markers are there?
Blue = 8
A data set has a mean of 55. The known values are: 40, 70, 62, x, x, 48. What is the value of x?
x = 55
A swimming pool contains water described by the rule y = −12x + 360, where x = minutes and y = litres. How many litres were there at the start?
360 litres
A square-based pyramid has a base side of 6 m and a slant height of 8 m. What is the total surface area (including base)?
132 m²
Write an expression that represents: "One-half of the difference between y and 11"
(y-11)/2
If you subtract 14 cm from the perimeter of a regular pentagon, you are left with 51 cm. What is the length of each side?
Each side = 13 cm
In a survey, 180 students were asked about their favourite season. The "Winter" section of a circle graph has a central angle of 60°. How many students chose winter?
30 students
Find the rule of a line that passes through points (-4, 8) and (0, 26)
y= 4.5x + 26
A rectangular prism has dimensions 5 cm × 4 cm × 3 cm. What is its total surface area?
94 cm²
Simplify
(12x² - 18x)/(6x) + 5
2x + 2
A triangle has a base of (x − 4) cm and a height of 50 cm. Its area is 600 cm². What is the value of x?
x = 28
48 students said "swimming" was their favourite activity. On the circle graph, the swimming section has an angle of 72°. How many students were surveyed in total?
240 students
Sofia rented a bike. She paid a $5.00 flat fee and a per-km rate. After biking 20 km, she paid $12. How much would 50 km cost?
$22.50
A regular hexagonal prism has a base with side length 4 cm, apothem 3.5 cm, and height 9 cm. What is the lateral area?
216 cm²