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10th grade Add, subtract and scale vectors worksheet

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Add, subtract and scale vectors

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. Three ropes pull Ari's sled with u = ⟨12, 0⟩, v = ⟨0, 5⟩ and w = ⟨-6, 3⟩ newtons. How hard do they pull in total, the length of u + v + w?

    • 17 N
    • About 18.1 N
    • 10 N
    • About 23.7 N

  2. Their directions are not given. Esme rides two legs of 7 km and 4 km, in any directions. Which statement describes how far from the start the finish can be?

    • Exactly 11 km, because 7 + 4 = 11
    • Anywhere from 0 km to 11 km
    • Anywhere from 3 km to 11 km
    • Exactly 3 km, because 7 − 4 = 3

  3. Jun's boat aims straight across a 2 km wide river at ⟨0, 8⟩ km/h. The current is ⟨3, 0⟩ km/h. How far downstream does the boat land?

    • 0.75 km
    • 6 km
    • 3 km
    • 12 km

  4. Luz's drone A flies from A(1, -2) to B(7, 6). A second drone leaves C(-4, 3) and flies twice that slide. Where does the second drone stop?

    • (2, 11)
    • (8, 11)
    • (8, 19)
    • (-16, -13)

  5. Pia's robot map is a parallelogram ABCD with A(1, 1), B(5, 2) and C(8, 6) in order around it. Where is corner D?

    • (4, 5)
    • (9, 7)
    • (-2, -3)
    • (12, 7)

  6. Ren places a beacon halfway between sensors P(-2, 6) and Q(10, -4). Which position is right, and how is it found?

    • (22, -14), from P + 2(Q − P)
    • (6, -5), from ½(Q − P)
    • (4, 1), from P + ½(Q − P)
    • (8, 2), from P + Q

  7. The lists give |u|, |v| and |u + v|. Vectors u and v have lengths 5 and 9. Tala lists possible lengths for u, v and u + v. Which list cannot happen?

    • 5, 9 and 10
    • 5, 9 and 15
    • 5, 9 and 4
    • 5, 9 and 14

  8. Zee's scooter makes slide A = 3⟨2, -1⟩ and slide B = ⟨8, -4⟩. How do A and B compare?

    • B points the same way as A and is 2 units longer in the run
    • B points opposite to A, since its parts are 8 and -4
    • B points the same way as A and is 4 times as long
    • B points the same way as A and is 4/3 as long

  9. Kira swims at 5 km/h in still water. The current pushes ⟨3, 0⟩ km/h. Kira wants the total velocity to point straight north. Which swim vector works?

    • ⟨-3, 5⟩
    • ⟨0, 5⟩
    • ⟨-3, 4⟩
    • ⟨3, 4⟩

  10. Esme's rug border is a loop of four slides: u = ⟨4, 3⟩, v = ⟨-1, 5⟩, w, and x = ⟨-6, -2⟩. The loop ends where it began. What is w?

    • ⟨-3, 6⟩
    • ⟨-9, -10⟩
    • ⟨3, 6⟩
    • ⟨3, -6⟩
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10th grade Add, subtract and scale vectors worksheet – printable
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About this worksheet

Add, subtract and scale vectors. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can add and subtract vectors as one slide after another.
  • I can multiply a vector by a number and say how its length and direction change.
  • I can use vectors to find a missing slide, a multiplier or a diagonal.

Standard: N-VM.B.4 (+), N-VM.B.5 (+)

Words to know

tip to tail: Start the second arrow where the first arrow ends.

sum, u + v: The single slide that does u and then v.

−v: The same arrow as v, pointing the opposite way.

scalar: A plain number that stretches, shrinks or flips a vector.

resultant: The total slide or velocity after combining vectors.

Common mistakes

Added the lengths of two vectors as if the total slide were the sum of the lengths. That only works when both point the same way. Draw the two slides tip to tail together.

Reversed something: the order of a subtraction, the direction of a slide, or stretching and shrinking. Ask together where the arrow starts and where it ends.

Changed only one part: one component, one vector or one condition. A slide has a run and a rise, and both must follow the rule.

Questions parents ask

What is the most common mistake with add, subtract and scale vectors?

Added the lengths of two vectors as if the total slide were the sum of the lengths. That only works when both point the same way. Draw the two slides tip to tail together.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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