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Algebra, STD2 EQ-Bank 3 MC

If  \(d=\sqrt{\dfrac{h}{5}}\), what is the value of \(d\), correct to one decimal place, when  \(h=28\)?

  1. 1.1
  2. 2.4
  3. 2.8
  4. 5.6
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\(B\)

Show Worked Solution

\(\text{When}\ h=28:\)

\(d\) \(=\sqrt{\dfrac{h}{5}}\)
\(d\) \(=\sqrt{\dfrac{28}{5}}\)
  \(=2.366…\)
  \(=2.4\  (\text{1 deccimal place})\)

   
\(\Rightarrow B\)

Algebra, STD2 A1 2024 HSC 1 MC

If  \(x=-2.531\), what is the value of \(x^2\) rounded to 2 decimal places?

  1. \(-6.41\)
  2. \(-6.40\)
  3. \(6.40\)
  4. \(6.41\)
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\(D\)

Show Worked Solution
  \( x^2\) \(=(-2.531)^2 \)
    \(=6.405\ldots \)
    \(=6.41\)

 
\(\Rightarrow D\)

♦♦ Mean mark 29%!
COMMENT: Brain dead calculator usage will cause issues here.

Algebra, STD2 A1 SM-Bank 23

What is the value of  `(a + b)/(ab)`  if  `a =-2.1`  and  `b =-3.6`, correct to 1 decimal place?   (2 marks)

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`-0.8`

Show Worked Solution
`(a + b)/(ab)` `= (-2.1-3.6)/(-2.1 xx -3.6)`
  `= (-5.7)/7.56`
  `= -0.753…`
  `= -0.8`

Algebra, STD2 A1 EQ-Bank 22

If  `S = V_0 (1-r)^n`, find `S` given  `V_0 = $42\ 000, r = 0.16 and n = 4`. Give your answer to the nearest cent.   (2 marks)

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`$20\ 910.60\ text{(to nearest cent)}`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 42\ 000 (1-0.16)^4`
  `= 42\ 000 (0.84)^4`
  `= $20\ 910.597…`
  `= $20\ 910.60\ \ text{(to nearest cent)}`

Algebra, STD2 A1 2017 HSC 7 MC

It is given that  `I = 3/2 MR^2`.

What is the value of  `I`  when  `M = 26.55`  and  `R = 3.07`, correct to two decimal places?

A.     `375.35`

B.     `3246.08`

C.     `9965.45`

D.     `14\ 948.18`

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`A`

Show Worked Solution

`I= 3/2 xx 26.55 xx (3.07)^2= 375.346…`

`=> A`

Algebra, STD2 A1 EQ-Bank 2

If   `A = P(1 + r)^n`, find  `A`  given  `P = $300`,  `r = 0.12`  and  `n = 3`  (give your answer to the nearest cent).   (2 marks)

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`$421.48\ \ text{(nearest cent)}`

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`A` `= P(1 + r)^n`
  `= 300(1 + 0.12)^3`
  `= 300(1.12)^3`
  `= 421.478…`
  `= $421.48\ \ text{(nearest cent)}`

Algebra, STD2 A1 EQ-Bank 21

What is the value of  `5a^2-b`, if  `a =-4`  and  `b = 3`.   (2 marks)

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`77`

Show Worked Solution
`5a^2-b` `= 5(-4)^2-3`
  `= 5 xx 16-3`
  `= 77`

Algebra, STD2 A1 2006 HSC 2 MC

If  `V = 4/3 pir^3`, what is the value of  `V`  when  `r = 2`, correct to two decimal places?

  1. `8.38`
  2. `12.57`
  3. `25.13`
  4. `33.51`
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`D`

Show Worked Solution

`V = 4/3 pir^3`

`text(When)\ \ r = 2,`

`V= 4/3 pi xx 2^3= 33.510\ …=33.51\ text{(2 dp)}`

`=>  D`

Algebra, STD2 A1 2005 HSC 2 MC

What is the value of  `(a-b)/4`, if  `a = 240`  and  `b = 56`?

  1. `4`
  2. `46`
  3. `226`
  4. `736`
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`B`

Show Worked Solution

`(a-b)/4= (240-56)/4= 46`

`=> B`

Algebra, STD2 A1 2004 HSC 3 MC

If  `K = Ft^3`,  `F = 5`  and  `t = 0.715`, what is the value of `K` correct to three significant figures?

  1. `1.82`
  2. `1.827`
  3. `1.828`
  4. `1.83`
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`D`

Show Worked Solution
`K` `= Ft^3`
  `= 5 xx (0.715)^3= 1.8276…`
  `= 1.83\ \ text{(3 sig figures)}`

 
`=> D`

Measurement, STD2 M1 2007 HSC 28b

This shape is made up of a right-angled triangle and a regular hexagon.
 

 

The area of a regular hexagon can be estimated using the formula  `A = 2.598H^2`  where `H` is the side-length.

Calculate the total area of the shape using this formula.   (3 marks)

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`22.784\ text(cm)^2`

Show Worked Solution

`text(Area) = 2.598H^2`

`text(Using Pythagoras:)`

`H^2` `= 2^2 + 2^2= 8`
`H` `= sqrt 8`

  
`text(Area of hexagon)= 2.598 xx (sqrt 8)^2= 20.784\ text(cm)^2`

`text(Area of triangle)= 1/2 bxx  h= 1/2 xx 2 xx 2= 2\ text(cm)^2`

`:.\ text(Total Area)= 20.784 + 2= 22.784\ text(cm)^2`

Algebra, STD2 A1 2008 HSC 9 MC

What is the value of  `sqrt((x+2y)/(8y))`   if  `x = 5.6`  and  `y = 3.1`, correct to 2 decimal places? 

  1. `0.69`
  2. `2.62`
  3. `2.83` 
  4. `4.77`  
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`A`

Show Worked Solution
`sqrt((x+2y)/(8y))` `=sqrt((5.6+(2 xx 3.1))/((8 xx 3.1)))`
  `=sqrt(11.8/24.8)=0.6897…`

`=>  A`

Algebra, STD2 A1 2010 HSC 7 MC

If  `M=-9`, what is the value of   `(3M^2+5M)/6`

  1. `-250.5`
  2. `-48`
  3. `\ \ \ 33`
  4. `\ \ \ 235.5`
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`C`

Show Worked Solution
 ♦♦ Only 31% of students answered correctly!
`(3M^2+5M)/6` `=(3xx(–9)^2+5xx(–9))/6`
  `=((3xx81)-45)/6`
  `=33`

`=>  C`