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 tecnnically 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 tecnnically 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 $3x^2 - 10x - 8 = 0$.
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.
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.
