Algebraic Representation & Manipulation Quiz Remedial

Algebraic Representation & Manipulation
Quiz Remedial Semester II 24/25

Grade 7 Narada Junior High School

Used to remove brackets so that you can manipulate the expression further by combining like terms or as needed.

Be careful on identifying which term is being multiplied with the bracket.

Expanding Brackets

Multiple Choice

5(6 + cd)

• 30 + 5cd
• 5 + c 
• 11 + 5c 

Multiple Choice

Expand -5(4v + 3)

• 20v - 15
• -54v - 53
• -20v + 15
• -20v - 15

Multiple Choice

6(3x + 5) + 2(x - 4) 

• 11x + 22
• 20x + 22
• 20x + 1
• 18x + 26

Multiple Choice

$$-4\left(8-2x+y\right)$$  

• $$32-8x+4y$$  

• $$-32+2x-y$$  

• $$-32+8x-4y$$  

• $$-32+8x+4y$$  

Multiple Choice

(3x+2)(2x +3)

• 6x² + 6x + 6
• 5x² + 11x + 6
• 6x² + 13x + 6
• 6x² + 13x + 5

Multiple Choice

3(2x + 1) + 6(x + 3)

• 12x + 21

• 12x + 6

• 11x + 21

• 11x + 6

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Factorising

• ​Simple factorising: when all terms have a common factor and you factorise it to a single bracket.

• Factorising by grouping: when there is no common factor but you can group at least two terms with common factor.

• Factorising quadratic expressions:

  • Common quadratic expression

  • Difference of two squares

Multiple Choice

5x+225

• 5(x+45)

• x(5x+45)

• 5(x+50)

• 10(x+22.5)

Multiple Choice

Factor the following expression:

$$9b\ -\ 3$$  

• $$9\left(b\ -\ 1\right)$$  

• $$3\left(3b\ -1\right)$$  

• $$9\left(3b\ -\ 3\right)$$  

• $$3\left(3b\ +\ 1\right)$$  

Multiple Choice

Factor by grouping:
4p³+8p²+3p+6

• (2p²+3)(p+2)
• (2p²+6)(p+4)
• (4p²+3)(p+2)
• (4p²+8p)(3p+6)

Multiple Choice

Factor Completely.

x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

Multiple Choice

Factor:

x² + 11x + 24

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

Replace the variables with its given values then solve the equation.

Remember to always apply PEMDAS!

Substitution

Multiple Choice

If $$a=3$$ , find  $$7-a$$  

• 2

• 3

• 4

• 5

Multiple Choice

If $$b=10$$ , find  $$\frac{40}{b}$$  .

• 10

• 2

• 30

• 4

Multiple Choice

If $$k=5$$ , find  $$\frac{k+3}{4}$$  

• $$\frac{53}{4}$$  

• $$2$$  

• $$4$$  

• $$8$$  

Multiple Choice

If y=7,find the value of 2(y+4)

• 11
• 22
• 20

Isolate the subject needed by moving other terms to the other side.

Rearranging Formulae

Multiple Choice

Make a the subject of
a + b = c

• a = c - b
• a = b - c
• a = b + c
• a = bc

Multiple Choice

Make x the subject of y = mx + 1

• x = (y - 1)/m
• x = y - 1/m
• x = y/m - 1
• x = my - 1

Multiple Choice

Make x the subject:
N = (180 + x)/2

• x = 2N -180
• x = N - 180
• x = N/2 -180
• x = N -180/2

Multiple Choice

Make r the subject:
C = 2πr

• r = C/2π
• r = C - 2π
• r = 2πC
• r = Cπ/2

Multiple Choice

Rearrange the following equation to make $$r$$ the subject

$$p=3r-5$$  

• $$r=\frac{p+5}{3}$$  

• $$r=p+5\div3$$  

• $$r=\frac{p-5}{3}$$  

• $$r=p-5\div3$$  

• Complex: apply the basic fractional operations or you might also need to factorize to cancel

Algebraic Fractions

• ​Adding and subtracting: Make sure the denominators are the same

• Multiplying: directly multiply numerator with numerator, denominator with denominator

• Dividing: Keep, change, flip

Multiple Choice

• 2a/0
• 2a/5
• 2a/10
• 2a

Multiple Choice

Combine over a common denominator:

$$\frac{2x}{3}-\frac{x}{4}$$  

• $$\frac{5x}{12}$$  

• $$\frac{x}{7}$$  

• $$\frac{x}{12}$$  

• $$\frac{11x}{12}$$  

Multiple Choice

Simplify the algebraic fraction.

• -m
• -1/m
• m/n
• 1/mn

Multiple Choice

Divide and simplify

• A.

• B.

• C.

• D.

Multiple Choice

Simplify:

• 4(x-3)/(x-7)
• 4(x+3)/(x+7)
• 4(x+3)(x-7)
• 4(x-3)/(x+7)

Multiple Choice

• 6/5x

• 6/5

• (x+3)/(x+2)

• (x+3)/(x-4)