Math 7 (Grade 7) Midterm — Full-Course Review

Math Grade 7 30 multiple choice + 2 written

Free printable Math 7 midterm (Grade 7): 30 multiple-choice questions plus 2 written responses covering Proportional Relationships, Operations with Rational Numbers, Expressions & Equations, Percent Applications, Geometry: Angles, Circles, Area & Volume, Probability & Statistics. Answer key included — customize it in the Midterm Maker.

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Directions: Read each question carefully and choose the best answer. Answer the written response in complete sentences.

Covers: Proportional Relationships · Operations with Rational Numbers · Expressions & Equations · Percent Applications · Geometry: Angles, Circles, Area & Volume · Probability & Statistics

Part 1: Multiple Choice

On a map, 1 inch represents 25 miles. Two towns are 3.5 inches apart on the map. What is the actual distance?
1. A. 75 miles
2. B. 100 miles
3. C. 28.5 miles
4. D. 87.5 miles
Which equation represents a proportional relationship?
1. A. y = x + 4
2. B. y = 4x + 1
3. C. y = 4x
4. D. y = x^2
Which description matches the graph of a proportional relationship?
1. A. A straight line that crosses the y-axis at 2
2. B. A horizontal line above the x-axis
3. C. A curve that passes through the origin
4. D. A straight line that passes through the origin
Maria walks 1/2 mile in 1/4 hour. What is her speed in miles per hour?
1. A. 4
2. B. 1/8
3. C. 3/4
4. D. 2
The cost y of x pounds of apples is given by y = 7x. What is the constant of proportionality?
1. A. 14
2. B. 1/7
3. C. 7
4. D. 0.7
A diver is at -30 feet. She rises 12 feet and then descends 7 feet. What is her new position?
1. A. -35 feet
2. B. -25 feet
3. C. -11 feet
4. D. -49 feet
What is -3/4 + 1/2?
1. A. -1/4
2. B. -2/6
3. C. -5/4
4. D. 1/4
What is (-2/3) ÷ (4/9)?
1. A. -3/2
2. B. -2/3
3. C. 3/2
4. D. -8/27
What is 5 - (-9)?
1. A. -4
2. B. 4
3. C. -14
4. D. 14
What is 3/8 written as a decimal?
1. A. 0.035
2. B. 0.83
3. C. 2.667
4. D. 0.375
Which expression is equivalent to 5a - 2b + 3a + 7b?
1. A. 13ab
2. B. 8a - 9b
3. C. 2a + 5b
4. D. 8a + 5b
Which inequality is the solution of -3x > 12?
1. A. x < -4
2. B. x < 4
3. C. x > -4
4. D. x > 4
A gym charges $25 to join plus $15 per month. Leo has paid $130 in total. For how many months has he been a member?
1. A. 7 months
2. B. 8 months
3. C. 10 months
4. D. 5 months
Solve: 4x - 7 = 21
1. A. x = 7
2. B. x = 5
3. C. x = 28
4. D. x = 3.5
Jada has $40 and saves $6 each week. She wants at least $100. Which inequality models the number of weeks w?
1. A. 40 + 6w ≤ 100
2. B. 40 + 6w ≥ 100
3. C. 40w + 6 ≤ 100
4. D. 6 + 40w ≥ 100
A salesperson earns a 6% commission on a $3,500 sale. How much commission does she earn?
1. A. $210
2. B. $2,100
3. C. $21
4. D. $3,710
What is 15% of 80?
1. A. 1.2
2. B. 15
3. C. 12
4. D. 68
A plant grew from 50 cm to 65 cm tall. What is the percent increase?
1. A. 15%
2. B. 77%
3. C. 30%
4. D. 23%
A shirt costs $40 and is on sale for 25% off. What is the sale price?
1. A. $10
2. B. $35
3. C. $15
4. D. $30
18 is 30% of what number?
1. A. 5.4
2. B. 60
3. C. 48
4. D. 54
What is the circumference of a circle with a radius of 5 cm?
1. A. 5π cm
2. B. 25π cm
3. C. 20π cm
4. D. 10π cm
Two angles are supplementary. One angle measures 118°. What is the measure of the other angle?
1. A. 72°
2. B. 242°
3. C. 62°
4. D. 28°
Two lines intersect. One of the four angles formed measures 47°. What is the measure of the angle vertical to it?
1. A. 133°
2. B. 43°
3. C. 94°
4. D. 47°
A triangle has a base of 12 cm and a height of 7 cm. What is its area?
1. A. 84 square cm
2. B. 19 square cm
3. C. 38 square cm
4. D. 42 square cm
What is the surface area of a cube with edges 3 inches long?
1. A. 54 square inches
2. B. 27 square inches
3. C. 18 square inches
4. D. 36 square inches
What is the median of 3, 9, 4, 12, 7, and 5?
1. A. 6
2. B. 7
3. C. 8
4. D. 5
You flip a coin and roll a number cube. How many outcomes are in the sample space?
1. A. 8
2. B. 6
3. C. 36
4. D. 12
A spinner landed on red 18 times in 60 spins. Based on this, how many times would you predict red in 200 spins?
1. A. 36
2. B. 18
3. C. 60
4. D. 120
In a random sample of 50 students, 20 prefer basketball. The school has 600 students. About how many students prefer basketball?
1. A. 120
2. B. 20
3. C. 300
4. D. 240
A bag has 3 red, 5 blue, and 2 green marbles. One marble is picked at random. What is P(blue)?
1. A. 3/10
2. B. 1/2
3. C. 5/8
4. D. 1/5

Part 2: Written Response

The perimeter of a rectangle is 64 cm. Its length is 2 cm more than twice its width. Write and solve an equation to find the width and the length. Show your work.
Two fair number cubes are rolled and the numbers are added. (a) What is the probability the sum is 7? (b) If the cubes are rolled 120 times, how many times would you expect a sum of 7? Show your work.

Answer Key — Math 7 (Grade 7) Midterm — Full-Course Review

D — 87.5 miles 3.5 × 25 = 87.5 miles.
C — y = 4x Only y = kx form is proportional; y = 4x has k = 4 and no added constant.
D — A straight line that passes through the origin Proportional relationships graph as straight lines through (0, 0).
D — 2 (1/2) ÷ (1/4) = 2 miles per hour.
C — 7 In y = kx, k is the constant of proportionality, so k = 7.
B — -25 feet -30 + 12 - 7 = -25 feet.
A — -1/4 Rewrite 1/2 as 2/4: -3/4 + 2/4 = -1/4.
A — -3/2 Multiply by the reciprocal: (-2/3)(9/4) = -18/12 = -3/2.
D — 14 Subtracting a negative is adding: 5 + 9 = 14.
D — 0.375 Divide 3 by 8 to get 0.375.
D — 8a + 5b Combine like terms: 5a + 3a = 8a and -2b + 7b = 5b.
A — x < -4 Divide by -3 and reverse the inequality sign: x < -4.
A — 7 months 25 + 15m = 130, so 15m = 105 and m = 7.
A — x = 7 Add 7 to get 4x = 28, then divide by 4: x = 7.
B — 40 + 6w ≥ 100 Start at 40, add 6 per week, and "at least" means ≥ 100.
A — $210 0.06 × 3,500 = $210.
C — 12 0.15 × 80 = 12.
C — 30% Increase of 15 divided by original 50 is 0.30, or 30%.
D — $30 The discount is 0.25 × 40 = $10, so the price is $40 - $10 = $30.
B — 60 18 ÷ 0.30 = 60.
D — 10π cm C = 2πr = 2π(5) = 10π cm.
C — 62° Supplementary angles sum to 180°: 180 - 118 = 62.
D — 47° Vertical angles are congruent, so it also measures 47°.
D — 42 square cm A = (1/2)bh = (1/2)(12)(7) = 42.
A — 54 square inches Six faces of 3 × 3 = 9 each: 6 × 9 = 54.
A — 6 Order: 3, 4, 5, 7, 9, 12. Middle values 5 and 7 average to 6.
D — 12 2 coin outcomes × 6 cube outcomes = 12.
C — 60 Experimental probability 18/60 = 0.3; 0.3 × 200 = 60.
D — 240 20/50 = 40%; 0.40 × 600 = 240.
B — 1/2 5 blue out of 10 marbles is 5/10 = 1/2.

Written Response — Look-Fors

Width w, length 2w + 2; 2(w + 2w + 2) = 64; 6w + 4 = 64; w = 10. Final answer: width 10 cm, length 22 cm; check 2(10 + 22) = 64.
36 equally likely outcomes; 6 give a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1); P = 6/36 = 1/6; 120 × 1/6. Final answers: 1/6 and 20 times.

Math 7 (Grade 7) Midterm — Full-Course Review

Part 1: Multiple Choice

Part 2: Written Response

Written Response — Look-Fors

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