Grade 7 Mathematics Diagnostic
NC EOG-Aligned Readiness Assessment
Learning Objectives
Use unit rates, proportional relationships, and percents to solve real-world problems.
Add, subtract, multiply, and divide rational numbers to solve problems.
Generate equivalent linear expressions and solve multi-step equations and inequalities.
Solve problems involving scale, circles, angle relationships, area, and volume.
Draw inferences from samples and find probabilities of simple and compound events.
Directions
~3 minutesThis diagnostic screens all five Grade 7 math domains. Item counts follow the NC End-of-Grade weighting, so proportional reasoning, expressions and equations, and statistics and probability carry the most items. Read each question carefully and use scratch paper.
Ratios & Proportional Relationships
~16 minutesProportional relationship: hours worked and pay.
| Hours (x) | Pay in dollars (y) |
|---|---|
| 2 | 30 |
| 4 | 60 |
| 6 | 90 |
A runner jogs $\frac{1}{2}$ mile in $\frac{1}{4}$ hour at a steady pace. What is the unit rate in miles per hour?
Use the hours-and-pay table shown. What is the constant of proportionality (dollars per hour)?
Use the hours-and-pay table shown. How much is earned for 8 hours?
The graph shown passes through the origin and the point (1, 2). What is the unit rate?
A jacket costs $\$50$. With a 6% sales tax, what is the total cost?
A $\$80$ pair of shoes is marked 25% off. What is the sale price?
A plant grew from 40 cm to 50 cm. What was the percent increase?
A meal costs $\$60$. A 20% tip is added. What is the total bill?
The Number System
~6 minutesThe temperature is -4 degrees F at midnight and drops 9 degrees F by 3 a.m. What is the new temperature?
Evaluate $(-6) \times (-4)$.
A diver starts at -15 feet and rises 3 feet each second for 4 seconds. What is the diver's depth then?
Expressions & Equations
~14 minutesSimplify $3(2x + 4)$.
Factor the expression $6x + 9$ using the greatest common factor.
A shirt costs c dollars. After a 20% discount, which expression gives the new price?
Carla buys 3 notebooks at $\$2.50$ each and a pen for $\$1.75$. How much does she spend in all?
Solve $3x + 5 = 20$.
Solve $(\frac{1}{2})x - 3 = 4$.
Solve the inequality $2x + 3 > 11$.
Geometry
~12 minutesUse the circle shown with radius 5 cm. What is its area? Use 3.14 for $\pi$.
A circle has a radius of 5 cm. What is its circumference? Use 3.14 for $\pi$.
Use the diagram of angles on a straight line. If one angle is 130 degrees, what is x?
A scale drawing uses 1 cm = 4 m. A wall is 6 cm long in the drawing. What is its actual length?
A trapezoid has parallel bases of 6 cm and 10 cm and a height of 4 cm. What is its area?
A triangular prism has a triangular base with area 12 square cm and a length of 5 cm. What is its volume?
Statistics & Probability
~16 minutesA principal wants to know students' favorite lunch. Which sample is most likely to be representative?
In a random sample of 50 students, 8 are left-handed. About how many of the 400 students are likely left-handed?
Which probability describes an event that is unlikely but still possible?
Use the spinner shown with 8 equal sections, 3 shaded. What is the probability of landing on a shaded section?
A coin is flipped 20 times and lands on heads 12 times. What is the experimental probability of heads?
A coin is flipped and a number cube (1 to 6) is rolled. What is the probability of heads and a 4?
Use the box plot of quiz scores shown. What is the median score?
Match each statistics term with its meaning.