Robot Test Bench: Order and Decisions

Compare rational numbers to interpret a robotics club’s test results.

Claw Alignment

The robotics club is building a robot that picks up supply bins. Use the alignment records to answer Questions 1–5.

A claw height of 0 mm is exactly at the target. Negative values are below the target; positive values are above it.

Claw Height Relative to Target
Test	Height (mm)
A	−1.4
B	0.6
C	−3/4
D	0
E	−1.05

Which comparison correctly describes Tests A and E?

A. −1.4 > −1.05, so A is higher than E.B. −1.4 = −1.05, so A is as high as E.C. −1.4 < −1.05, so A is lower than E.D. −1.4 < −1.05, so A is higher than E.

What is the lowest recorded claw height relative to the target? mm

Which list puts all five tests in order from lowest claw position to highest?

A. A, E, C, D, BB. B, D, C, E, AC. C, E, A, D, BD. A, C, E, D, B

A test passes if the claw height is at least −1 mm and no more than 0.5 mm. Select all tests that pass.

The club adds a new test with a claw height of −0.9 mm.

What recorded height is immediately below −0.9 mm when all six heights are ordered? mm

Activation Timing

Use the timing records for Questions 6–10. Order the times, not their distances from zero.

The robot should start when a light flashes. A negative time means it starts before the flash. A positive time means it starts after the flash. A time of 0 seconds means it starts exactly at the flash.

Start Time Relative to the Flash
Program	Time (seconds)
P	−0.35
Q	1/5
R	−1/2
S	0
T	−0.08

Which program starts earliest?

A. Program P starts earliest.B. Program Q starts earliest.C. Program T starts earliest.D. Program R starts earliest.

What does −0.35 < −0.08 tell the club about Programs P and T?

A. P starts after T, and both start before the flash.B. P starts before T, and both start before the flash.C. P starts before T, and both start after the flash.D. P starts after T, and both start after the flash.

For a new demonstration, the robot must start strictly after −0.1 seconds but strictly before 1/4 second. Select all programs that meet this requirement.

Arrange all five recorded start times from earliest to latest.

What time is third in that order? seconds

10.

Luis says, “Program R starts later than Program P because 1/2 is greater than 0.35.” Is he correct? Write an inequality comparing their signed times and explain what it means.

Cold-Chamber Sensor Tests

The club checks the robot’s temperature sensor in a test chamber. Use each set of readings to answer Questions 11–14.

11.

Three chamber readings are −2.6°C, −2 1/4°C, and −2.08°C. Which inequality orders them from coldest to warmest?

A. −2.08 < −2 1/4 < −2.6B. −2 1/4 < −2.6 < −2.08C. −2.6 < −2 1/4 < −2.08D. −2.6 < −2.08 < −2 1/4

12.

The robot’s cold alert should turn on only when the temperature is below −1.5°C. The club tests readings of −1.6°C, −1 1/2°C, −1.45°C, and −1 3/4°C.

At how many of these readings should the alert turn on? readings

13.

The chamber must be warmer than −3/4°C but colder than 0°C for the next test. Which setting meets both conditions?

A. Set the chamber to −0.8°C.B. Set the chamber to −0.6°C.C. Set the chamber to 0°C.D. Set the chamber to 0.6°C.

14.

Amira records −0.4°C < 1/4°C < 0.7°C. Which statement correctly reads the full inequality in this testing situation?

A. 1/4°C is warmer than −0.4°C and colder than 0.7°C.B. 1/4°C is colder than −0.4°C and warmer than 0.7°C.C. 1/4°C is warmer than both −0.4°C and 0.7°C.D. 1/4°C is colder than both −0.4°C and 0.7°C.