L1 Mathematical Reasoning
Question Bank
Solve the equation $x^2 - 2x - 15 = 0$.
Solve to find the values of $x$ for the equation $x(x-5) = 0$.
Solve to find the values of $x$ for the equation $(x+4)(x+1) = 0$.
Solve to find the values of $x$ for the equation $2x(x-4) = 0$.
Solve to find the values of $x$ for the equation $(x-4)(x-8)(x+1) = 0$.
Note that this is technically a cubic equation (not a quadratic), but the same principle for solving applies
Solve to find the values of $x$ for the equation $(x+5)(x-10)^2 = 0$.
Note that this is technically a cubic equation (not a quadratic), but the same principle for solving applies
Solve to find the value of $x$ in the equation $x(x-a) = 0$.
Solve the following equation for $x$:
$ (x - 7)^2 = 16 $
Solve the following equation for $y$:
$ (y + 1)^2 - 49 = 0 $
Solve the equation $5x^2 + 13x = 6$.
Solve the equation $(x+3)(x-1) = 12$.
Solve for x: $(x+5)(x-5) = 3x - 15$.
Solve the following equation for $x$:
$\frac{36}{x-5} = x-5$
Find the values of $x$ that solve the equation:
$x-4 = \frac{12}{x}$
Solve the equation $4x^2 + 5x - 6 = 0$.
Solve for $x$ in the equation $3x^2 - 10x - 8 = 0$.
The right-angled triangle shown has an area of 21 cm². Calculate the value of x.
The length of a rectangular garden is 4 metres longer than its width. The total area of the garden is 45 m².
By forming and solving a quadratic equation, find the dimensions of the garden.
Where would the graph of $y = 3x^2 - 5x - 2$ cut the x-axis?
The diagram below shows the graphs of a parabola, $y = 3x^2 - 4x + 1$, and a straight line, $y = x + 3$.
Use algebra to find the $x$-values of the two points where the graphs intersect.
A box is a cuboid. Its length is $(x + 3)$ cm, its width is $x$ cm and its height is 4 cm.
The volume of the box is 160 cm³.
(i) Show that $x^2 + 3x - 40 = 0$.
(ii) Solve the equation to find the length and width of the box.
Find the values of x for which $x(2x+3) = 4 - 4x$.
Solve the following equation for $y$:
$ \frac{\displaystyle 45}{\displaystyle y + 4} = y - 4 $
The right-angled triangle shown has a hypotenuse of $\sqrt{41}$ cm. Calculate this value of x.
The right-angled triangle and the square shown in the diagram have the same area. Calculate the value of x.
The diagram below shows the graphs of two parabolas, $y = 3x^2 + 10x - 1$ and $y = x^2 + 3x + 3$.
Use algebra to find the $x$-values of the two points of intersection for the graphs.
A rugby ball is kicked off a tee. Its height, $h$ metres, $t$ seconds after it is kicked is given by
$h = -5t^2 + 20t$
(i) After how many seconds does the ball hit the ground?
(ii) What is the greatest height the ball reaches?
(iii) For how many seconds is the ball higher than 15 m?
An open-top box (it has no lid) has a square base of side $x$ cm and a height of 3 cm.
The box is made from 85 cm² of card: the base plus the four sides.
(i) Form a quadratic equation in $x$.
(ii) Solve it to find $x$, and then find the volume of the box.
The parabola $y = x^2 + kx - 12$ passes through the point $(2, 0)$, where $k$ is a constant.
(i) Find the value of $k$.
(ii) Find the other $x$-intercept of the parabola.
(iii) Find the coordinates of the vertex.
Alice was exploring an ancient forest when she came across a wise, talking oak tree. Curious about its age, Alice asked how old it was.
The tree creaked and boomed in reply, "I am very old indeed! In 190 years' time, my age will be the square of my age 190 years ago!"
Determine the tree's current age.
Hint: $210 \times 171 = 35910$ and $171 + 210 = 381$.
Both a square and a rectangle each have a perimeter of 44 cm. If their combined area is 238 cm², what are the dimensions of the rectangle?
Four identical parallelograms make a pinwheel shape, as shown in the diagram. The area of the entire shape is 84 m². Find the perimeter of the shape.
The area of the right-angled trapezium shown below is 15 cm². Find the perimeter of the shape.
A right-angled triangle has side lengths which follow a linear sequence (i.e., they have a common difference). If the shortest side is 12 cm, what are the other two sides? You must use an algebraic method to find your answer.
A rectangular garden has a perimeter of 34 metres and an area of 60 m². What are the dimensions of the garden?
A closed cylinder has a height of 7 cm and a radius of $r$ cm.
Its total surface area is $88\pi$ cm².
(i) Show that $r^2 + 7r - 44 = 0$.
(ii) Find the radius, and then calculate the volume of the cylinder.