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Algebraic Techniques, SM-Bank 030 MC

If \(\large x\) is a negative number, which of the following is true?

  1. \(x+2\)  is always negative.
  2. \(x\times -1\)  is always negative.
  3. \(2-x\)  is always negative.
  4. \(x-2\)  is always negative.
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\(D\)

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\(\text{Considering the options}\)

\(\text{Option 1: If}\ x\ge -2\ \text{then}\ x+2\ge 0, \therefore \text{not always negative}\)

\(\text{Option 2:}\ x\ \text{is negative }\therefore x\times -1\ \text{is always positive}\)

\(\text{Option 3:}\ x\ \text{is negative }\therefore 2-x\ \text{is always positive}\)

\(\text{Option 4:}\ x\ \text{is negative }\therefore x-2\ \text{is always negative}\)

\(\Rightarrow D\)

Algebraic Techniques, SM-Bank 029

A triangle has a base of length \(3\) metres and a perpendicular height of  \(h\) metres.

Write an expression for the area of the triangle.  (2 marks)

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\(\dfrac{3h}{2}\ \text{m}^2\)

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\(\text{Area}\)

\(=\dfrac{1}{2}\times \text{base}\times\text{perpendicular height}\)

\(=\dfrac{1}{2}\times 3\times h\)

\(=\dfrac{1}{2}\times 3h\)

\(=\dfrac{3h}{2}\ \text{m}^2\)

Algebraic Techniques, SM-Bank 028

A rectangle has sides of  \(b\) metres and  \(c\) metres in length.

  1. Write an expression for the perimeter of the rectangle.  (1 mark)

  2. Write an expression for the area of the rectangle.  (2 marks)

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a.    \((2b+2c)\ \text{m}\)

b.    \(bc\ \text{m}^2\)

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a.    \(\text{Perimeter}\)

\(=b+c+b+c\)

\(=(2b+2c)\ \text{m}\)

b.    \(\text{Area}\)

\(=\text{length}\times\text{width}\)

\(=b\times c\)

\(=bc\ \text{m}^2\)

Algebraic Techniques, SM-Bank 027

A square has sides \(x\) centimetres in length.

  1. Write an expression for the perimeter of the square.  (1 mark)

  2. Write an expression for the area of the square.  (2 marks)

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a.    \(4x\ \text{cm}\)

b.    \(x^2\ \text{cm}^2\)

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a.    \(\text{Perimeter}\)

\(=4\times x\)

\(=4x\ \text{cm}\)

b.    \(\text{Area}\)

\(=\text{side}^2\)

\(=x^2\ \text{cm}^2\)

Algebraic Techniques, SM-Bank 025

Juan bought 8 identical Christmas presents online for his relatives.

  1. Write an expression for the total price in dollars, if the cost of each present is \($y\).  (1 mark)

  2. When he goes to the checkout Juan discovers that all the presents were reduced in price by $10 each.
     
    i.    Write an expression for the reduced price of one present.  (1 mark)

    ii.   Write an expression for the total reduced price of all 8 presents.  (2 marks)

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a.    \(8y\)

b.    i.   \(y-10\)

ii.   \(8(y-10)\)

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a.    \(\text{Price}=8\times y=8y\)

b.    i.   \(\text{Reduced Price per present}=y-10\)

ii.   \(\text{Total Reduced Price}=8\times (y-10)=8(y-10)\)