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iGCSE (2021 Edition)

17.07 Direct and inverse variation (Extended)

Interactive practice questions

Suppose the constant of variation $k$k is positive.

a

If $y$y varies directly as $x$x, which of the following is true?

When $x$x increases, $y$y increases. When $x$x decreases, $y$y decreases.

A

When $x$x increases, $y$y decreases. When $x$x decreases, $y$y decreases.

B

When $x$x increases, $y$y increases. When $x$x decreases, $y$y increases.

C

When $x$x increases, $y$y decreases. When $x$x decreases, $y$y increases.

D
b

If $y$y varies inversely as $x$x, which of the following is true?

When $x$x increases, $y$y decreases. When $x$x decreases, $y$y increases.

A

When $x$x increases, $y$y increases. When $x$x decreases, $y$y decreases.

B

When $x$x increases, $y$y decreases. When $x$x decreases, $y$y decreases.

C

When $x$x increases, $y$y increases. When $x$x decreases, $y$y increases.

D
Easy
1min

Does the equation $y=5x$y=5x represent direct or inverse variation?

Easy
< 1min

Does the equation $y=\frac{5}{x}$y=5x represent direct or inverse variation?

Easy
< 1min

The period of a pendulum varies directly with the square root of its length.

If the length is quadrupled, what happens to the period?

Easy
< 1min
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Outcomes

0607E2.13

Direct variation (proportion) and inverse variation. Best variation model for given data.

0607C3.5

Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes.

0607C3.6

Use of a graphic display calculator to: sketch the graph of a function, produce a table of values, find zeros, local maxima or minima, find the intersection of the graphs of functions.

0607E3.2D

Recognition of reciprocal, f(x) = a/x, function types from the shape of their graphs.

0607E3.3

Determination of the value of at most two of a, b, c or d in simple linear, quadratic, cubic, reciprocal, exponential, absolute value and trignometric functions.

0607E3.5

Understanding of the concept of asymptotes and graphical identification of simple examples parallel to the axes.

0607E3.6

Use of a graphic display calculator to: sketch the graph of a function produce a table of values, find zeros, local maxima or minima, find the intersection of the graphs of functions.

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