Rates & Ratio
A drink mix says “1 part syrup : 8 parts water.”
If you use 90 mL syrup, how many mL of final drink are produced?
810 mL
A bag has 6 red, 4 blue, 5 green marbles.
If one marble is drawn at random, what’s P (not green)?
2/3
Define the range of a data set.
(What's the formula?)
Max − min
The point (−4, 1) is reflected across the y-axis. What is the new point?
(4, 1)
Expand (x + 2)(x + 5)
x² + 7x + 10.
Two printers work at rates of 18 pages/min and 24 pages/min.
If they start together and must print 504 pages total, how long until both finish exactly together?
14 min
You roll two dice.
Find P(sum ≥ 10)
1/6
For {2, 4, 4, 6, 10}, find the mean and median.
Mean = 5.2;
Median = 4
Describe the transformation from y = x² to y = (x − 3)² + 2.
Right 3, up 2.
xpand (2x − 3)(x − 4)
2x² − 11x + 12
The ratio of girls : boys in a club is 5 : 7.
After 6 boys leave, the ratio becomes 5 : 4. How many girls are there?
50 girls
Two cards are drawn without replacement from a standard deck.
Find P(both red).
25/102
A class of 10 students has a mean of 65. After one new student joins with 85, find the new mean.
(10×65 + 85)/11 = 66.8
A triangle is translated 3 units right and 2 units down. Write the coordinate rule.
(x, y) → (x + 3, y − 2)
Simplify (x − 5)² − (x − 3)(x − 7)
4x − 4
A car travels at 90 km/h for x hours and 60 km/h for (5 − x) hours.
If its average speed for the trip is 72 km/h, find x.
2 hours
A jar contains 3 red and 2 blue marbles.
A marble is drawn without replacement, and then another is drawn.
Find P(the second marble is blue).
2/5
The mean of six numbers is 12. If one number, 18, is removed, the new mean is 10. Find the missing total of remaining five numbers.
50
A rotation of 90° clockwise about the origin transforms (x, y) to what new coordinates?
(y, −x)
Expand (x + 2y)(x − 2y)(x + 3y)
x³ + 3x²y − 4xy² − 6y³
The ratio of surface area : volume of a cube is 3 : 2.
Find the cube’s edge length.
9
A spinner is divided into 8 equal parts numbered 1–8.
Two spins are made.
Find P(the product is a multiple of 3 but not of 6)
3/16
The mean of five numbers is 20. When another number is added, the mean increases to 22.
Find the value of the new number.
Total of first 5 = 100; total of 6 numbers = 132; new number = 32
A triangle has vertices A(1, 2), B(3, 1), C(2, 4).
It is rotated 180° about the origin and then translated 2 units right and 1 unit up.
Find the coordinates of A″ after both transformations.
Rotation 180° → (−1, −2);
then translation → (1, −1).
Answer: A″ = (1, −1).
Expand and simplify: (3x − y + 2)(x − 2y + 1)
3x² − 7xy + x − 2y² + 5y + 2