In the gold-foil experiment, nearly all alpha particles passed straight through the foil, but about 1 in 8000 was deflected by more than 90°. Which conclusion about atomic structure do these results most directly support?

The atom's positive charge and most of its mass are concentrated in a tiny central region

Gold atoms are packed with large gaps between neighboring atoms in the foil

Electrons occupy quantized orbits with fixed energies around the nucleus

Positive charge is spread uniformly throughout the atom with electrons embedded in it

A runner completes exactly one lap of a 400 m oval track in 80 s, finishing where she started. What are her average speed and the magnitude of her average velocity for the lap?

Average speed 5.0 m/s; average velocity 0

Average speed 2.5 m/s; average velocity 0

Average speed 0; average velocity 5.0 m/s

Average speed 5.0 m/s; average velocity 5.0 m/s

Trial Time (s) 1 2.31 2 2.28 3 2.35 4 2.30 5 2.26 A student times a cart over the same distance in five trials, as shown in the table. Which result best reports the time with an appropriate uncertainty?

2.30 ± 0.05 s, the mean with half the range of the trials

2.3 s exactly, because averaging removes the uncertainty

2.300 ± 0.001 s, matching the stopwatch's resolution

2.26 s, the smallest value, because it has the least reaction delay

GACE Physics (6–12) (718)

Free GACE Physics (6–12) (718) Practice Questions

10 sample questions for the GACE Physics (6–12) (718), with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.

Sections covered on the exam: Mechanics (Motion, Forces, Energy), Data Analysis, Graphs, and Problem Solving, Foundations of Scientific Inquiry and Measurement, Electricity and Magnetism, Instructional and Pedagogical Content, Waves and Optics, Modern Physics, Thermodynamics.

Question 1 · Mechanics (Motion, Forces, Energy)
Time (s) Position (m)
0 0
2.0 3.0
4.0 10.0
6.0 21.0
8.0 36.0
The table shows the position of a cart moving along a straight track. What is the cart's average velocity between t = 2.0 s and t = 6.0 s?
- A.9.0 m/s
- B.3.5 m/s
- C.5.3 m/s
- D.4.5 m/s
Show answer and explanation
Answer: D. 4.5 m/s
Average velocity is Δx/Δt = (21.0 m − 3.0 m)/(6.0 s − 2.0 s) = 18.0 m/4.0 s = 4.5 m/s. Dividing the final position by the total elapsed time from zero (21.0 m/6.0 s = 3.5 m/s) ignores the starting point of the interval, and dividing 21.0 m by 4.0 s uses a position rather than a displacement.
Question 2 · Mechanics (Motion, Forces, Energy)
A uniform solid disk of mass 2.0 kg and radius 0.30 m can rotate freely about a fixed axle through its center. A 5.0 N force is applied tangentially at its rim. What is the disk's angular acceleration? (For a solid disk, I = ½MR².)
- A.0.75 rad/s²
- B.33 rad/s²
- C.17 rad/s²
- D.8.3 rad/s²
Show answer and explanation
Answer: C. 17 rad/s²
The torque is τ = FR = (5.0 N)(0.30 m) = 1.5 N·m and I = ½(2.0 kg)(0.30 m)² = 0.090 kg·m², so α = τ/I = 17 rad/s². Using I = MR² (a hoop) gives 8.3 rad/s², and dividing the torque by the mass instead of the moment of inertia gives 0.75, which has the wrong units.
Question 3 · Electricity and Magnetism
Current I (A) Terminal voltage V (V)
0.50 5.75
1.00 5.50
1.50 5.25
2.00 5.00
To find the emf and internal resistance of a battery, a student connects it to different load resistors and records the terminal voltage and current shown in the table. What are the emf and internal resistance?
- A.5.75 V and 11.5 Ω
- B.6.00 V and 2.0 Ω
- C.6.00 V and 0.50 Ω
- D.5.00 V and 0.50 Ω
Show answer and explanation
Answer: C. 6.00 V and 0.50 Ω
The data fit V = ε − Ir: V drops 0.25 V for every 0.50 A, so r = 0.25 V/0.50 A = 0.50 Ω, and extrapolating to I = 0 gives ε = 5.75 V + (0.50 A)(0.50 Ω) = 6.00 V. Dividing a single voltage by its current (5.75 V/0.50 A) gives the load resistance, not r, and 2.0 Ω inverts the slope.
Question 4 · Waves and Optics
An FM radio station broadcasts at a frequency of 98.7 MHz. What is the wavelength of its signal in air?
- A.3.04 m
- B.0.304 m
- C.30.4 m
- D.0.329 m
Show answer and explanation
Answer: A. 3.04 m
λ = c/f = (3.00 × 10⁸ m/s) ÷ (98.7 × 10⁶ Hz) ≈ 3.04 m. Dividing f by c instead gives 0.329 m, and slipping a power of ten in the megahertz conversion gives 0.304 m or 30.4 m.
Question 5 · Modern Physics
In the gold-foil experiment, nearly all alpha particles passed straight through the foil, but about 1 in 8000 was deflected by more than 90°. Which conclusion about atomic structure do these results most directly support?
- A.Gold atoms are packed with large gaps between neighboring atoms in the foil
- B.Electrons occupy quantized orbits with fixed energies around the nucleus
- C.Positive charge is spread uniformly throughout the atom with electrons embedded in it
- D.The atom's positive charge and most of its mass are concentrated in a tiny central region
Show answer and explanation
Answer: D. The atom's positive charge and most of its mass are concentrated in a tiny central region
Large-angle scattering requires a strong repulsive force from a concentrated positive charge, while the rarity of such events shows that this charge occupies a tiny fraction of the atom's volume. A uniform spread of positive charge, as in the plum-pudding model, could not reverse an alpha particle, and quantized orbits come from spectral evidence rather than from this scattering data.
Question 6 · Mechanics (Motion, Forces, Energy)
A runner completes exactly one lap of a 400 m oval track in 80 s, finishing where she started. What are her average speed and the magnitude of her average velocity for the lap?
- A.Average speed 5.0 m/s; average velocity 0
- B.Average speed 2.5 m/s; average velocity 0
- C.Average speed 0; average velocity 5.0 m/s
- D.Average speed 5.0 m/s; average velocity 5.0 m/s
Show answer and explanation
Answer: A. Average speed 5.0 m/s; average velocity 0
Average speed is total distance over time, 400 m/80 s = 5.0 m/s, while average velocity is displacement over time, and the displacement for a full lap is zero. Equating the two quantities treats velocity as a scalar, and 2.5 m/s halves the distance for no reason.
Question 7 · Foundations of Scientific Inquiry and Measurement
Trial Time (s)
1 2.31
2 2.28
3 2.35
4 2.30
5 2.26
A student times a cart over the same distance in five trials, as shown in the table. Which result best reports the time with an appropriate uncertainty?
- A.2.3 s exactly, because averaging removes the uncertainty
- B.2.300 ± 0.001 s, matching the stopwatch's resolution
- C.2.30 ± 0.05 s, the mean with half the range of the trials
- D.2.26 s, the smallest value, because it has the least reaction delay
Show answer and explanation
Answer: C. 2.30 ± 0.05 s, the mean with half the range of the trials
The mean is (2.31 + 2.28 + 2.35 + 2.30 + 2.26)/5 = 2.30 s, and half the range, (2.35 − 2.26)/2 ≈ 0.05 s, is a reasonable estimate of the random uncertainty. The trial-to-trial spread is much larger than the stopwatch's resolution, so ±0.001 s overstates the precision, and picking one trial discards data without justification.
Question 8 · Electricity and Magnetism
A straight wire segment 0.50 m long carries a current of 8.0 A in a uniform 0.40 T magnetic field. The wire makes an angle of 30° with the field direction. What is the magnitude of the magnetic force on the segment?
- A.1.60 N
- B.1.39 N
- C.0.80 N
- D.0.40 N
Show answer and explanation
Answer: C. 0.80 N
F = ILB sin θ = (8.0 A)(0.50 m)(0.40 T)(sin 30°) = 0.80 N. Using cos 30° gives 1.39 N, ignoring the angle gives 1.60 N, and using sin²30° gives 0.40 N.
Question 9 · Waves and Optics
Source Frequency (Hz)
P 2.45 × 10⁹
Q 3.0 × 10¹³
R 5.5 × 10¹⁴
S 3.0 × 10¹⁸
The table lists the frequency of the electromagnetic radiation emitted by each of four sources. Which source emits radiation in the infrared band?
- A.Source Q
- B.Source S
- C.Source P
- D.Source R
Show answer and explanation
Answer: A. Source Q
λ = c/f gives 12 cm for P (microwave), 10 μm for Q (infrared), 545 nm for R (visible green), and 0.10 nm for S (X-ray). Only Q lies between about 700 nm and 1 mm, the infrared range.
Question 10 · Modern Physics
A sample of hydrogen atoms is excited so that every atom starts in the n = 4 level. As the atoms return to the ground state by every possible route, how many distinct wavelengths of emission lines can be observed?
- A.10
- B.3
- C.4
- D.6
Show answer and explanation
Answer: D. 6
Any pair of the four levels can produce a line, giving 4 × 3/2 = 6 distinct transitions (4→3, 4→2, 4→1, 3→2, 3→1, 2→1). Counting only the single-step cascade 4→3→2→1 gives 3, and 10 would require five levels.

Time (s)	Position (m)
0	0
2.0	3.0
4.0	10.0
6.0	21.0
8.0	36.0

Current I (A)	Terminal voltage V (V)
0.50	5.75
1.00	5.50
1.50	5.25
2.00	5.00

Trial	Time (s)
1	2.31
2	2.28
3	2.35
4	2.30
5	2.26

Source	Frequency (Hz)
P	2.45 × 10⁹
Q	3.0 × 10¹³
R	5.5 × 10¹⁴
S	3.0 × 10¹⁸

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