Grade 7 Math Practice Test: Scale Drawings and Scale Factors
- Scale Drawings
- 10 questions
- 15 minutes
This test covers reading map and blueprint scales, finding actual lengths and areas from a drawing and redrawing a figure at a different scale. Tip: find actual lengths first, then compute the area; never multiply an area by the length scale.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
On a map, 1 inch represents 25 miles. Two towns are 3.4 inches apart on the map. What is the actual distance?
Correct answer: D
3.4 × 25 = 85 miles. 28.4 adds 25 instead of multiplying.
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Question 2
A floor plan uses the scale 1 cm : 4 m. A room is 18 m long. How long is the room on the plan?
Correct answer: A
Each 4 m becomes 1 cm, so 18 ÷ 4 = 4.5 cm. 72 cm multiplies by 4 instead of dividing.
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Question 3
A garden is drawn as a 3 cm by 5 cm rectangle with the scale 1 cm : 2 m. What is the actual area of the garden?
Correct answer: C
The actual garden is 6 m by 10 m, so its area is 60 m2. 30 m2 multiplies the drawing area 15 by 2, but the area grows by 2 × 2 = 4.
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Question 4
A model car is built at a scale of 1 : 24. The model is 7.5 inches long. How long is the real car?
Correct answer: C
7.5 × 24 = 180 inches, and 180 ÷ 12 = 15 feet. 180 feet keeps the number of inches but changes the unit.
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Question 5
On a drawing with scale 1 in : 6 ft, a wall is 4 in long. The drawing is redone with scale 1 in : 8 ft. How long is the wall on the new drawing?
Correct answer: A
The real wall is 4 × 6 = 24 ft. On the new drawing it is 24 ÷ 8 = 3 in. 513 in multiplies by 8 and divides by 6, the reverse of what is needed.
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Question 6
A blueprint has a scale of 1 : 50. A wall measures 12 cm on the blueprint. How long is the actual wall?
Correct answer: B
12 × 50 = 600 cm, and 600 cm = 6 m. 60 m comes from dividing 600 by 10 instead of 100.
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Question 7
A 30 m swimming pool is drawn 6 cm long. What is the scale of the drawing?
Correct answer: D
6 cm stands for 30 m, so 1 cm stands for 30 ÷ 6 = 5 m. 1 cm : 0.2 m divides 6 by 30, the wrong way around.
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Question 8
A triangle with sides 2 cm, 4 cm and 5 cm is enlarged with a scale factor of 3. What is the perimeter of the new triangle?
Correct answer: A
The new sides are 6, 12 and 15 cm, so the perimeter is 33 cm (3 × 11). 14 cm adds 3 to the original perimeter instead of multiplying.
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Question 9
A square photo with 4-inch sides is enlarged with a scale factor of 2.5. What is the area of the enlarged photo?
Correct answer: C
The new side is 4 × 2.5 = 10 in, so the area is 10 × 10 = 100 in2. 40 in2 multiplies the old area 16 by 2.5 only once.
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Question 10
A map uses the scale 2 cm : 15 km. Two lakes are 7 cm apart on the map. What is the actual distance?
Correct answer: B
1 cm stands for 7.5 km, so 7 × 7.5 = 52.5 km. 105 km treats each centimeter as 15 km.
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