Flashcards · 10 cards

Variation

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Rule
" $y$ varies directly as $x$ ." Write it as an equation.
Answer
$y = kx$ , where $k$ is a constant.
Direct: y = kxA straight line through the origin
From the lesson: Direct, inverse and joint variation
Rule
" $y$ varies as the square of $x$ ." Write it as an equation.
Answer
$y = kx^2$ . Doubling $x$ makes $y$ four times as big.
Square: y = kx²Doubling x makes y 4 times as big
From the lesson: Direct, inverse and joint variation
Rule
" $y$ varies as the square root of $x$ ." Write it as an equation.
Answer
$y = k\sqrt x$ .
Square root: y = k√xGrows ever more slowly
From the lesson: Direct, inverse and joint variation
Rule
" $y$ varies inversely as $x$ ." Write it as an equation.
Answer
$y = \dfrac kx$ . Doubling $x$ halves $y$ .
Inverse: y = k/xDoubling x halves y
From the lesson: Direct, inverse and joint variation
Rule
" $y$ varies inversely as the square of $x$ ." Write it as an equation.
Answer
$y = \dfrac{k}{x^2}$ . Doubling $x$ divides $y$ by 4.
Inverse square: y = k/x²Doubling x divides y by 4
From the lesson: Direct, inverse and joint variation
Know it
" $t$ varies directly as $V$ and inversely as $P$ ." Write it as an equation.
Answer
$t = \dfrac{kV}{P}$ : direct goes on top, inverse underneath.
From the lesson: Direct, inverse and joint variation
Know it
The method for any variation question?
Answer
Write the equation with $k$ . Put in the given values to find $k$ . Write the equation again with that $k$ , then use it.
From the lesson: Direct, inverse and joint variation
Know it
$y$ varies as $x^2$ , and $y = 36$ when $x = 3$ . Find $k$ .
Answer
$36 = k \times 3^2 = 9k$ , so $k = 4$ . Divide by $x^2$ , not by $x$ .
From the lesson: Direct, inverse and joint variation
Rule
"Partly constant and partly varies as $n$ ." Write it as an equation.
Answer
$C = a + bn$ . There are two constants, so you need two pairs of values and two equations.
Partial: y = a + bxA straight line that crosses the y-axis at the constant a
From the lesson: Partial variation and proportion problems
Which method?
WAEC 2019 · Paper 2 · Q5 (a)
The cost of dinner for a group of tourists is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.
What equation do you start from?
Answer
Partly constant and partly varying: $C = a + bn$ . The two groups give $a + 20b = 740$ and $a + 30b = 960$ : solve them together.
From the lesson: Partial variation and proportion problems Try the question