Troy School District · Mathematics · Grade 7 · Form B
Standards Drill · 120 minutes · 100 points

Grade 7 Mathematics — Standards-Aligned Skills Examination

A calculation-focused, standards-walkthrough exam covering the CCSS-M Grade 7 standards (7.RP, 7.NS, 7.EE, 7.G, 7.SP). Each problem cites the standard(s). Form B complements Form A.

Student Name
Proctor
Score

Instructions

1. 7.NS · Operations with rational numbers 12 points
  1. Compute (signed integers):

    (i) \( -8 + 14 \)    (ii) \( -12 - 7 \)    (iii) \( -9 \cdot 6 \)    (iv) \( (-7)(-8) \)    (v) \( -42 \div 6 \)    (vi) \( \dfrac{-18}{-3} \)

  2. Compute (fractions; simplest form):

    (i) \( \dfrac{2}{3} + \dfrac{5}{6} \)    (ii) \( \dfrac{3}{4} - \dfrac{2}{5} \)    (iii) \( \dfrac{2}{3} \cdot \dfrac{9}{16} \)    (iv) \( \dfrac{5}{6} \div \dfrac{2}{3} \)    (v) \( -\dfrac{3}{4} + \dfrac{1}{2} \)    (vi) \( \dfrac{7}{8} - \left(-\dfrac{1}{4}\right) \)

  3. Compute (decimals):

    (i) \( 4.7 + (-2.85) \)    (ii) \( -6.3 - 4.7 \)    (iii) \( -3.2 \cdot 0.5 \)    (iv) \( -8.4 \div 1.2 \)

  4. Apply order of operations:

    (i) \( -2 + 3 \cdot (-4) \)    (ii) \( (-3)^2 - 4 \cdot (-2) \)    (iii) \( \dfrac{1}{2} - \dfrac{2}{3} \cdot \dfrac{3}{4} \)

2. 7.RP · Ratios, proportional relationships, percent 12 points
  1. Express each as a unit rate:

    (i) 240 miles in 4 hours    (ii) $18 for 6 lbs    (iii) 144 words in 3 minutes

  2. Solve each proportion:

    (i) \( \dfrac{x}{12} = \dfrac{5}{8} \)    (ii) \( \dfrac{4}{x} = \dfrac{14}{21} \)    (iii) \( \dfrac{x + 1}{6} = \dfrac{x - 1}{4} \)

  3. Identify the constant of proportionality \(k\) for the table; then write the equation \(y = kx\):
    \(x\)25811
    \(y\)717.52838.5
  4. Percent calculations:

    (i) Find 35% of 240.    (ii) What percent of 80 is 28?    (iii) 45 is 30% of what number?

  5. Compute each:

    (i) A $80 jacket is discounted 25%. New price?
    (ii) A $50 meal has 18% tip. Total?
    (iii) An item increased from $40 to $46. Percent increase?

3. 7.EE.A · Expressions 8 points
  1. Combine like terms:

    (i) \( 4x + 7 - 2x + 3 \)    (ii) \( 5y - 3 + 2y + 9 - 4y \)    (iii) \( 6a + 2b - 3a + 5b \)

  2. Distribute and simplify:

    (i) \( 3(2x - 5) \)    (ii) \( -2(4x + 7) \)    (iii) \( 4(x - 2) - 3(x + 1) \)    (iv) \( -(x - 5) + 3(2x + 1) \)

  3. Evaluate \( 2a^2 - 3b + 4 \) when \( a = 3, b = -2 \).
  4. Factor (find a GCF):

    (i) \( 6x + 9 \)    (ii) \( 12y - 8 \)    (iii) \( 5a + 10b - 15 \)

4. 7.EE.B · Equations and inequalities 12 points
  1. Solve each one-step equation:

    (i) \( x + 17 = 25 \)    (ii) \( y - 8 = -3 \)    (iii) \( -4z = 28 \)    (iv) \( \dfrac{m}{6} = -2 \)

  2. Solve each two-step equation:

    (i) \( 3x + 5 = 17 \)    (ii) \( -2y + 4 = 18 \)    (iii) \( \dfrac{x}{4} - 3 = 5 \)

  3. Solve each multi-step equation:

    (i) \( 2(x - 3) = 14 \)    (ii) \( 4x + 7 = 2x - 9 \)    (iii) \( 5(2x - 1) = 3(x + 4) + 5 \)

  4. Solve each inequality and graph the solution on a number line:

    (i) \( 3x - 5 > 7 \)    (ii) \( -2x + 1 \le 9 \)    (iii) \( 4(x - 1) \ge 12 \)

5. 7.G.A · Scale drawings & geometric figures 8 points
  1. On a map drawn at scale 1 in : 25 mi, two cities are 6.4 inches apart. Find the actual distance.
  2. A scale drawing of a room uses 1 cm = 2 m. The drawing shows the room as 8 cm by 5 cm. Find the actual area in square meters.
  3. Determine whether each set of three side lengths can form a triangle:

    (i) 4, 7, 10    (ii) 3, 5, 9    (iii) 6, 6, 12    (iv) 8, 11, 14

  4. Determine whether a unique triangle, multiple triangles, or no triangle exists:

    (i) three angles 40°, 70°, 70°    (ii) three sides 5, 5, 5    (iii) three sides 3, 4, 8

6. 7.G.B · Angles, area, circumference 12 points
  1. Find the missing angle. Justify the relationship used (vertical, supplementary, complementary, triangle-sum):

    (i) Two angles form a linear pair; one is 47°. Find the other.
    (ii) Two angles are vertical; one is 132°. Find the other.
    (iii) Two angles are complementary; one is \( (3x + 7)° \), the other \( (2x - 12)° \). Find each.

  2. Find the area of each polygon:

    (i) parallelogram, base 10, height 7    (ii) triangle, base 12, height 5    (iii) trapezoid, parallel sides 6 and 14, height 8

  3. For a circle of radius 6 (express exactly in terms of \(\pi\), and decimally to 0.01):

    (i) circumference    (ii) area    (iii) length of a 90° arc    (iv) area of a 90° sector

  4. The area of a circle is \(64\pi\) cm\(^2\). Find its radius and circumference.
7. 7.G.B · Volume and surface area 10 points
  1. Compute the volume:

    (i) rectangular prism, 4 × 5 × 8    (ii) triangular prism, triangular base with legs 3 and 4 (right triangle), depth 10    (iii) cube, edge 6    (iv) rectangular pyramid: not in 7.G — use \(\tfrac{1}{3} \times \text{base} \times \text{height}\) for: square base 6 × 6, height 9

  2. Compute the surface area:

    (i) rectangular prism, 4 × 5 × 8    (ii) cube, edge 6    (iii) triangular prism in (a)(ii)

  3. A swimming pool is 25 m × 12 m × 2 m. Find the volume in cubic meters and the volume in liters (1 m\(^3\) = 1000 L).
8. 7.SP.A · Random sampling and inferences 6 points
  1. A school has 800 students. A simple random sample of 50 students is asked their preferred lunch option. Out of the sample, 18 said pizza. Estimate the number of students in the whole school who would choose pizza.
  2. A box of 1{,}000 jellybeans is sampled. Out of 80 sampled, 30 are red. Estimate the total number of red jellybeans in the box.
  3. A polling firm wants to estimate the proportion of voters who support a candidate. They survey 100 randomly selected adults at a downtown shopping mall on Tuesday morning. Identify two reasons this is not a simple random sample of all voters in the area, in one or two sentences.
9. 7.SP.B · Comparing populations 8 points

Two random samples of 30 students each were drawn from two schools and asked their daily exercise time (minutes).

MeanMedianIQR
School A54.05220
School B41.04018
  1. Which school's typical exercise time is greater?
  2. State the difference of the medians: \(|52 - 40|\).
  3. State the difference of the means: \(|54.0 - 41.0|\).
  4. The IQRs are about 20 and 18 minutes, both noticeably larger than the gap between the two medians. In one or two sentences, comment informally on whether the schools' exercise times differ meaningfully relative to the spread within each school.
10. 7.SP.C · Probability models 12 points
  1. A fair six-sided die is rolled. Find:

    (i) \(P(\text{rolling a 4})\)    (ii) \(P(\text{rolling an even number})\)    (iii) \(P(\text{rolling at least 5})\)

  2. A bag has 5 red, 3 blue, and 2 green marbles. One marble is drawn. Find:

    (i) \(P(\text{red})\)    (ii) \(P(\text{not red})\)    (iii) \(P(\text{red or blue})\)

  3. From the same bag, two marbles are drawn with replacement. Find \(P(\text{both red})\). Show the independence multiplication.
  4. Two marbles are drawn without replacement. Find \(P(\text{both red})\). Show the dependence (different denominators).
  5. A coin is flipped 4 times. Find \(P(\text{exactly 2 heads})\) using a tree diagram or by counting outcomes from the sample space.
  6. An experiment: flip a thumbtack 200 times. It lands point-up 124 times. Estimate the probability \(P(\text{point-up})\). Predict the number of point-up landings in 1000 future flips.
  7. A spinner has 4 equal sectors labeled 1, 2, 3, 4. The spinner is spun twice. List all 16 outcomes in the sample space (as ordered pairs). Then find \(P(\text{sum} = 5)\).