An operation is defined by a @ b = 5 a − 3 b \sqrt{5a-3b} 5 a − 3 b <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> . State the value of 4 @ 2.

14 \sqrt{14} 1 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 a − 2 b \sqrt{4a-2b} 4 a − 2 b <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 2 \sqrt{-2} − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Binary Operations

Quiz

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-BF.A.1C, HSF.BF.B.5, HSF-BF.A.1B

+2

Standards-aligned

Candacy Lindie

Used 1K+ times

FREE Resource

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Suppose a ♠ b = 3a + 2b. Find 3 ♠ 2

12

13

5

6

Tags

CCSS.HSF-BF.A.1C

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If
$a\cdot b=a^b$ then $2\cdot5=$

10

25

32

52

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $p\Phi q$ denotes $2a^b$ then $2\Phi3=$

12

16

32

64

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $x\ \Omega\ y=\ 2x+y\ +\ 6,$ then $\left(-1\right)\ \Omega\ 2$ is

6

8

9

10

Tags

CCSS.HSF-BF.A.1C

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $a\ \cdot\ b$ denotes $\frac{ab}{a\ +\ b}$ then $2\ \cdot\ 6\ =$

$\frac{13}{4}$

$\frac{3}{2}$

$\frac{2}{3}$

$\frac{1}{3}$

Tags

CCSS.HSF-BF.A.1B

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

An operation is defined by a @ b = $\sqrt{5a-3b}$ . State the value of 4 @ 2.

$\sqrt{14}$

$\sqrt{2}$

$\sqrt{4a-2b}$

$\sqrt{-2}$

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Given that $p\nabla q$ denotes p3 - 2pq + q2. Evaluate the exact value of $3\nabla2$ .

-5

10

19

-7

8.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

An operation is defined by $p\perp q=4pq^2-q$ . Calculate the value of $2\perp\left(-3\right)$ .

69

-27

75

27

Tags

CCSS.HSA.APR.D.7

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

If $x\ \parallel\ y=x+y^2$ , what is the value of $2\ \parallel\ \left(2\ \parallel\ 3\right)$ ?

11

13

85

123

Tags

CCSS.HSF-BF.A.1C

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Binary Operations

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Suppose a ♠ b = 3a + 2b. Find 3 ♠ 2

If a⋅b=aba\cdot b=a^ba⋅b=ab then 2⋅5=2\cdot5=2⋅5=

If pΦqp\Phi qpΦq denotes 2ab2a^b2ab then 2Φ3=2\Phi3=2Φ3=

If x Ω y= 2x+y + 6,x\ \Omega\ y=\ 2x+y\ +\ 6,x Ω y= 2x+y + 6, then (−1) Ω 2\left(-1\right)\ \Omega\ 2(−1) Ω 2 is

If a ⋅ ba\ \cdot\ ba ⋅ b denotes aba + b\frac{ab}{a\ +\ b}a + bab​ then 2 ⋅ 6 =2\ \cdot\ 6\ =2 ⋅ 6 =

An operation is defined by a @ b = 5a−3b\sqrt{5a-3b}5a−3b​ . State the value of 4 @ 2.

Given that p∇qp\nabla qp∇q denotes p3 - 2pq + q2. Evaluate the exact value of 3∇23\nabla23∇2 .

An operation is defined by p⊥q=4pq2−qp\perp q=4pq^2-qp⊥q=4pq2−q . Calculate the value of 2⊥(−3)2\perp\left(-3\right)2⊥(−3) .

If m * n denotes m + 5n. Evaluate 3 * (1 * 2).

If x ∥ y=x+y2x\ \parallel\ y=x+y^2x ∥ y=x+y2 , what is the value of 2 ∥ (2 ∥ 3)2\ \parallel\ \left(2\ \parallel\ 3\right)2 ∥ (2 ∥ 3) ?

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If
$a\cdot b=a^b$ then $2\cdot5=$

If $p\Phi q$ denotes $2a^b$ then $2\Phi3=$

If $x\ \Omega\ y=\ 2x+y\ +\ 6,$ then $\left(-1\right)\ \Omega\ 2$ is

If $a\ \cdot\ b$ denotes $\frac{ab}{a\ +\ b}$ then $2\ \cdot\ 6\ =$

An operation is defined by a @ b = $\sqrt{5a-3b}$ . State the value of 4 @ 2.

Given that $p\nabla q$ denotes p3 - 2pq + q2. Evaluate the exact value of $3\nabla2$ .

An operation is defined by $p\perp q=4pq^2-q$ . Calculate the value of $2\perp\left(-3\right)$ .

If $x\ \parallel\ y=x+y^2$ , what is the value of $2\ \parallel\ \left(2\ \parallel\ 3\right)$ ?