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India
Class IX

Modelling non-linear Relationships

Interactive practice questions

A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40xx2, where $x$x is the length of one side of the rectangle.

a

Using the equation, state the area of the rectangle if one side is $12$12 metres long.

b

The graph below displays all the possible areas that can be obtained using this amount of wire. From the graph, determine the nearest value for the longer side of a rectangle that has an area of $256$256 square metres.

Loading Graph...

A Cartesian plane featuring an horizontal axis labeled "x," ranging from 0 to $40$40, marked at intervals of $4$4. The vertical axis labeled "A," extends from 0 to $400$400, marked at intervals of $100$100 with minor tick marks every $20$20 units. A parabola is graphed on this plane, with its vertex positioned at ($20$20, $400$400) opening downward and passes through the origin and ($40$40, 0). Its coordinates of the vertex and y-intercept are not explicitly labeled or given.

$33$33 m

A

$9$9 m

B

$8$8 m

C

$32$32 m

D
c

Using the graph, what is the greatest possible area of a rectangle that has a perimeter of $80$80 m?

d

Using the graph, state the dimensions of the rectangle with the maximum area.

Length $=$=$\editable{}$ m

Width $=$=$\editable{}$ m

Easy
5min

The height $h$h, in metres, reached by a ball thrown in the air after $t$t seconds is given by the equation $h=10t-t^2$h=10tt2.

Easy
6min

The formula for the surface area of a sphere is $S=4\pi r^2$S=4πr2, where $r$r is the radius in centimetres.

Easy
6min

The volume of a sphere has the formula $V=\frac{4}{3}\pi r^3$V=43πr3. The graph relating $r$r and $V$V is shown.

Easy
6min
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9.A.P.1

Definition of a polynomial in one variable, its coefficients, with examples and counterexamples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation.

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