O Level Mathematics 4024 Paper 12, May/June 2023

3.25 - 1.73

1.2^2

At midday the temperature is 8°C. At midnight the temperature is 12°C lower. Find the temperature at midnight.

Shazia records the temperature, in °C, at 6 am every day for one week. 5 2 -1 -7 -2 5 -5 Find the median.

Find the range.

Find the actual distance $AB$.

Find the bearing of $B$ from $A$.

A plane flies so that it is always equidistant from $A$ and $B$. Using a straight edge and compasses only, construct the path of the plane.

Write down the type of correlation that the scatter diagram shows.

Draw a line of best fit.

Use your line of best fit to estimate the time Ben takes for a 5 km walk.

Write down the number of planes of symmetry of the prism.

Work out the volume of the prism.

Describe fully the single transformation that maps shape $A$ onto shape $B$.

Draw the image of shape $A$ after a rotation of 180° about (0, 0) .

These are the first four terms of a sequence. 1 3 9 27 Find the next term of the sequence.

These are the first five terms of a different sequence. 35 31 27 23 19 Find an expression, in terms of $n$, for the $n$th term of this sequence.

Write 325 as a product of its prime factors.

$P=x^n{y}^2$ and $Q=x^{n-1}{y}^4$, where $x$ and $y$ are prime. Find the highest common factor (HCF) of $P$ and $Q$. Give your answer in terms of $x$, $y$ and $n$.

Find the three inequalities that define the shaded region.

Another region, $R$, is defined by these three inequalities. $x+y⩽5$ $y⩾2x-1$ $x⩾1$ Find the area of region $R$.

Find ${\mathrm{f}}^{-1}(x)$.

Solve $\mathrm{f}(x+5)=3\mathrm{g}(x)$.

Find how many more candles are in a large gift bag than in a small gift bag.

The mass of a soap is 120 g and the mass of a candle is 60 g. Matrix $\mathbf{M}$ represents this information. $$\mathbf{M}=\left(\begin{array}{c}120\\ 60\end{array}\right)$$ $\mathbf{N}=\mathbf{C}\mathbf{M}$ Find matrix $\mathbf{N}$.

Explain what each element in matrix $\mathbf{N}$ represents.

In the Venn diagram, shade the region represented by $(A\cap B^{\mathrm{\prime }})\cup (B\cap C^{\mathrm{\prime }})$.

One morning 50 people visit a library. • 35 of them borrow a book. • 12 of them use a computer. • 8 of them do not borrow a book and do not use a computer. Using a Venn diagram, or otherwise, find the number of people who use a computer but do not borrow a book.

Expand and simplify. (4x - y)(2x + 5y)

Simplify. ${\left(\frac{x^{12}}{8}\right)}^{\frac{2}{3}}$

Ken takes a card at random from the set, notes the colour and replaces it. He then takes a second card at random from the set, notes the colour and replaces it. Find the probability that both cards show a green shape.

Irina takes two cards at random from the set of 10 without replacement. Find the probability that both cards show the same shape.