Equations
Solve: 3x + 5 = 20
x = 5
Are these proportional: 2/3 and 4/6? Explain quickly.
Yes; 2/3 = 4/6
(equivalent fractions).
Name the shape with 4 equal sides and 4 right angles.
What is a square.
If you roll a fair six-sided die, what is the probability of rolling a 4? Give as a fraction.
Probability = 1/6
If a movie ticket is $8 and Mia has $50, how many tickets can she buy? How much money will remain?
50 ÷ 8 = 6 with remainder 2 →
buy 6 tickets, $2 left.
Solve and check: 4(2x − 3) = 20
4(2x − 3) = 20
→ 8x − 12 = 20
→ 8x = 32
→ x = 4
Find the unit rate: 45 miles in 3 hours (miles per hour).
Unit rate = 45 ÷ 3 = 15 mph.
Find the area of a rectangle with length 9 cm and width 4 cm.
Area = 9 × 4 = 36 cm2
Find the mean of: 6, 8, 10, 10, 6.
Mean = (6+8+10+10+6)/5 = 40/5 = 8.
A salesperson earns $40 per week plus $6 per sale. Write an inequality for the number of sales s needed so that pay is at least $100, and solve. (Write and solve inequality.)
Pay = 40 + 6s ≥ 100
→ 6s ≥ 60
→ s ≥ 10 sales.
Solve: 1/3x+7=16
1/3x+7=16
1/3x=9
x=27
Solve: If 5 pens cost $12.50, how much do 8 pens cost?
5 pens = $12.50 → unit price = $2.50 per pen → 8 pens = $20.00
Two similar triangles have corresponding side lengths 3 and 9. If the smaller triangle’s perimeter is 24, what is the larger triangle’s perimeter?
Scale factor from 3 to 9 is 3, so perimeter scales by 3: 24 × 3 = 72.
Create a simple sample space for flipping two coins. List all outcomes. Then find probability of getting exactly one head.
Sample space: {HH, HT, TH, TT}. Exactly one head: {HT, TH} → probability 2/4 = 1/2.
A bike is on sale for 25% off the $160 price. What is the sale price?
25% of 160 = 40
→ sale price = 160 − 40 = $120.
Write an equation and solve: A number decreased by 9 equals 4 times the number plus 3
Let number = n.
n − 9 = 4n + 3
→ −9 − 3 = 4n − n
→ −12 = 3n
→ n = −4
A map uses scale 1 inch : 25 miles. On the map two cities are 3.2 inches apart. How many miles apart are the cities?
1 in : 25 miles → 3.2 in = 3.2 × 25 = 80 miles.
Find the circumference of a circle with radius 7 cm. Use π.
Circumference = 2πr
2π(7)=
14π cm.
Given data set: 3, 7, 7, 8, 10 — find the mean, median, mode and range.
100 pts each correct
Mean = 7
Median = 7
Mode = 7
Range = 7
A classroom has a ratio of boys to girls 3:4. If there are 21 boys, how many students total?
Boys = 21 corresponds to 3 parts,
1 part = 7, total parts 7
→ total students = 7 × 7 = 49.
Solve the inequality: 5x − 2 > 18.
Bonus points: Then give one integer solution.
5x − 2 > 18
→ 5x > 20
→ x > 4.
One integer solution: 5
A recipe for 6 muffins uses 2/3 cup of sugar. How much sugar is needed per muffin?
Bonus: Then scale the recipe to make 15 muffins (give total cups).
Sugar per muffin = (2/3)÷6=2/18=1/9(2/3)÷6=2/18=
1/9 cup per muffin.
For 15 muffins: 15 × 1/9 = 15/9 = 5/3 = 1 2/3 cups for 15 muffins.
A right rectangular prism has dimensions 4 cm by 3 cm by 5 cm. Find its volume.
V= l x w x h
Volume = 4 × 3 × 5 = 60 cm3
If a six sided dice is thrown what is the chance that the number is a multiple of 3? Give as a fraction.
3, 6
So 2 out of 6 or 2/6 which simplifies to 1/3.
A container is being filled at a rate of 2.5 liters per minute. The container's capacity is 18 liters and it already has 3 liters. Write and solve an equation to find how many minutes more are needed to fill the container.
Let t = minutes needed. 3 + 2.5t = 18 → 2.5t = 15 → t = 6. So 6 minutes to fill the container.