L1 Mathematical Reasoning
Question Bank
The perimeter of a rectangle is 44 cm. Its width is $(x+5)$ cm and its length is $(3x+1)$ cm. Form an equation and solve it to find the value of x.
The cost of a taxi ride, $C$ dollars, can be calculated from the distance travelled, $d$ km, using the formula $C = 2.5d + 4$. Use the formula to find the distance of a ride, $d$, if the total cost, $C$, was $31.50.
The total monthly cost for a phone plan, $C$ dollars, is calculated based on the extra data used, $G$ gigabytes, with the formula $C = 5G + 40$. If a monthly bill was $57.50, how much extra data was used?
The temperature in degrees Fahrenheit, $F$, can be found from the temperature in degrees Celsius, $C$, using the formula $F = 1.8C + 32$. If the temperature is 68°F, what is the temperature in degrees Celsius?
The total cost, $T$ dollars, for a group booking at an event is given by the formula $T = 22p + 15$, where $p$ is the number of people. If the total cost for a group was $213, how many people were in the group?
Five consecutive houses on one side of a street have numbers that sum to 350.
On this street, consecutive house numbers increase by 2 (e.g., 2, 4, 6...).
By forming and solving an equation, find the number of the last house.
The formula for kinetic energy is $E = \frac{1}{2}mv^2$. Give the equation for $v$ in terms of $E$ and $m$.
The period of a pendulum is given by $T = 2\pi\sqrt{L}$. Give the equation for the length $L$ in terms of $T$.
The formula to convert from Fahrenheit to Celsius is $C = \frac{5}{9}(F - 32)$. Give the equation for $F$ in terms of $C$.
The surface area of a sphere is $A = 4\pi r^2$. Give the equation for the radius $r$ in terms of $A$.
Find the value of the expression $4x^3 - 5x^2 + x$ when $x=-2$.
What is the value of the expression $5a^2 - 2ab + 3b$ when $a=3$ and $b=-4$?
The volume of a grain silo is given by the formula $V = \pi r^2(h + \frac{k}{3})$. Find the volume, $V$, if the radius $r=5$ m, the cylinder height $h=10$ m, and the cone height $k=6$ m.
Find the value of the expression $3x^3 + 2x^2 - 5x + 1$ when $x=-3$.
What is the value of the expression $4a^2 - 3ab + b^3$ when $a=2$ and $b=-1$?
The surface area of a cylinder is given by the formula $A = 2\pi r^2 + 2\pi rh$. Find the surface area, $A$, if the radius $r=3$ cm and the height $h=10$ cm. Give your answer in terms of $\pi$.
Expand and simplify the expression:
$ (4y^3 - 3)(y + 2) $
Expand and simplify the expression:
$ 3p(p - 4) - (2p - 7) $
Expand and simplify the expression:
$ (m^2 - 2n)(m + 5n) $
Simplify the following expression:
$ \frac{\displaystyle (x^3)^2 \times x^{4}}{\displaystyle x^{2}} $
The area of a sector is given by the formula $A = \frac{\theta}{360}\pi r^2$. Give the equation for the radius $r$ in terms of $A$ and $\theta$.
The formula for the force of gravity between two objects is $F = G\frac{m_1m_2}{r^2}$. Give the equation for the distance $r$, in terms of $F, G, m_1,$ and $m_2$.
The formula for impedance in a circuit is $Z = \sqrt{R^2 + X^2}$. Give the equation for the reactance $X$, in terms of $Z$ and $R$.
The velocity of an orbiting satellite is given by the formula $v = \sqrt{\frac{GM}{r}}$. Give the equation for the mass of the planet, $M$, in terms of $v, G,$ and $r$.
What same number must be added to the top (numerator) and bottom (denominator) of the fraction $\frac{81}{148}$ to make it equal to $\frac{2}{3}$?
You must form an equation to represent this situation and then solve your equation.
If $k = 5\sqrt[3]{\frac{x^2+a}{b}}$, give the equation for $x$ in terms of $a, b,$ and $k$.
The surface area of a cone is given by $A = \pi r(r + \sqrt{h^2+r^2})$. Give the equation for the height $h$, in terms of $A, r,$ and $\pi$.
If $m - k = \frac{\sqrt{a(n^2+b)}}{c}$, give the equation for $n$ in terms of $a, b, c, k,$ and $m$.
If $a(x-b) = c(x+d)$, give the equation for $x$ in terms of $a, b, c,$ and $d$.
The equation $my^2 + 2n^2 = 5p^2 - 3qy^2$ relates five variables. Give the equation for $y$ in terms of $m, n, p,$ and $q$.