Number & Operations
Simplify: 3/4+1/8
7/8
If the ratio of blue marbles to red marbles is 2: 5, how many red marbles are there when there are 4 blue marbles?
5 red marbles
Evaluate the expression when 𝑥 = 3: 2𝑥 + 5
2(3) + 5 = 11
Find the area of a rectangle with length 6 cm and width 4 cm.
24 cm2
A spinner has equal sectors numbered 1–4. What is the probability of landing on 3?
1/4
Subtract: −5−8
A recipe calls for 3 cups of flour for every 2 cups of sugar. How much flour is needed for 8 cups of sugar?
12 cups of flour
Solve the onevariable two-step equation: 3𝑥 − 4 = 11
𝑥 = 5
***DOUBLE POINTS***
Find the circumference of a circle with radius 3 cm.
2𝜋𝑟 = 6𝜋 cm
Given data set: {2, 3, 3, 5, 7}, find the mode.
3
Multiply: 2/3 × 9/4
3/2 OR 1 1/2
**DOUBLE POINTS**
Find the unit rate: 150 miles in 3 hours
50 miles/hour
Write an equation for: "Seven less than twice a number is thirty-one."
2𝑛 − 7 = 31 → 𝑛 = 19
The volume of a rectangular prism is 120 cm3 . If the base area is 20 cm2 , find the height.
Height = 120 20 = 6 cm
A random sample of students shows that 40% prefer chocolate ice cream. If the total population is large, what inference can be tentatively made about the population preference?
We can tentatively infer about 40% of the population prefers chocolate, noting sample limitations.
Write 0.375 as a fraction in simplest form.
3/8
A map scale says 1 inch represents 12 miles. How many miles are represented by 3.5 inches?
42 miles
Solve and check: 1/2𝑥 + 7 = 19
1/2𝑥 = 12 ⇒ 𝑥 = 24
Find the area of a composite figure made of a rectangle 8 cm × 5 cm attached to a semicircle with diameter 5 cm.
Rectangle area = 40.
Semicircle area = 1/2𝜋𝑟^2 = 1 2𝜋(2.5)^2 = 6.25^2 𝜋 = 3.125𝜋.
Total = 40 + 3.125 (PI SIGN)
Calculate sales tax: An item costs $45. Sales tax rate is 6%. What is the total cost?
Tax = $45 × 0.06 = $2.70; Total = $47.70
A number is multiplied by −6 to give 54. What is the number?
-9
A quantity increases by 25% and becomes 50. What was the original amount?
40
Write and solve an equation using geometry: The sum of the angles in a triangle is 180∘ . Two angles measure 4𝑥∘ and 3𝑥∘ . Find 𝑥 and the angles.
Sum: 4𝑥 + 3𝑥 + 𝑥 = 180 ⇒ 8𝑥 = 180 ⇒ 𝑥 = 22.5; Angles: 90∘ , 67.5∘ , 22.5∘
Solve a similarity/scale problem: Two similar triangles have corresponding sides in ratio 2: 5. If the smaller triangle's area is 18 cm2 , what is the area of the larger triangle?
Scale factor for area = (5/2)^2 = (2.5)^2 = 6.25. Larger area = 18 × 6.25 = 112.5 cm2
A family budget allocates 15% to savings. If the monthly income is $3, 200, how much is planned for savings? (Also state this amount as a percentage of the total budget if the family decides to increase savings to 20%.)
Savings at 15%: $3, 200 × 0.15 = $480. If increased to 20%: $3, 200 × 0.20 = $640 (this is 20% of the total; $640 as a percent of total is 20%