May/June 2024

Using this word, write down the letters that have

Symmetry

The picture displays the car’s fuel gauge. This car has $40$ litres of fuel in the tank.

Rates

Tom’s pet consumes $\frac{3}{5}$ of a tin of food each day. Tom must supply food for his pet for $12$ days.

Fractions, decimals and percentages

Solve this.

Equations

The pie chart gives the fractions of junior members and senior members in a gym. There are $120$ more senior members than junior members.

Statistical charts and diagrams

Solve the simultaneous equations, showing all your working.

Equations

Using each number correct to one significant figure, estimate the value of $\dfrac{2.87 \times \sqrt{396.5}}{1.92^2}$.

Estimation

$A$, $B$, $C$ and $D$ lie on the circumference of a circle with centre $O$. Angle $BCD = 58^\circ$ and angle $DBC = 72^\circ$.

Circle theorems I

This table gives the length of time that each of $60$ children spends in the play area.

Cumulative frequency diagrams

In this table, $p$ varies directly with $q^2$.

Ratio and proportion

The function is given by $f(x) = 2x - 5$.

Functions

At the beginning of the day, the mass of a bird is $4.628\,\text{kg}$. By later in the day, the mass of the same bird is $4.693\,\text{kg}$.

Units of measure

The matrix $N$ obeys the equation $3N = N + 5\begin{pmatrix}4 & 0\\6 & -2\end{pmatrix}$.

Algebraic manipulation

Prism $A$ is mathematically similar to prism $B$. In the diagram, the shaded regions show the cross-sections of the prisms. The volume of prism $A$ is $5000\,\text{cm}^3$. The length of prism $A$ is $50\,\text{cm}$. The area of the cross-section of prism $B$ is $16\,\text{cm}^2$.

Similarity

$a = \dfrac{5b + 2x}{x - 3}$. Rewrite the formula so that $x$ is the subject.

Algebraic manipulation

$AB$ refers to the line segment connecting $A(-2,5)$ with $B(1,3)$.

Length and midpoint

In quadrilateral $ABCD$, $H$, $K$, $L$ and $M$ mark the midpoints of $AB$, $BC$, $CD$ and $AD$ respectively. $\vec{AB} = 2a$, $\vec{BC} = 2b$ and $\vec{AD} = 2d$.

Vectors in two dimensions

Calculate.

Fractions, decimals and percentages

$ABC$ forms a triangle with $AC = 5\,\text{cm}$ and $BC = 10\,\text{cm}$. With a ruler and compasses only, construct triangle $ABC$. $AB$ has already been drawn for you.

Geometrical constructions

The table gives details for a class of 28 students and the distances from school that they live.

Relative and expected frequencies

Simplify the expression $6r + 7s - r + 3s$.

Algebraic manipulation

A square and a regular pentagon are attached along a single shared edge, as the diagram indicates.

Angles

Ahmed places $\$4000$ into an account paying simple interest at $1.5\%$ each year.

Percentages

The diagram gives the cyclist’s distance-time graph for the opening two stages of a race, $AB$ and $BC$.

Graphs in practical situations

These are five temperatures in ^{\circ}C: $4$, $1$, $-6$, $0$, $-2$.

Ordering

The scale diagram depicts a section of field $ABCD$. The drawing scale is $1\text{ cm}$ representing $50\text{ m}$.

Geometrical constructions

Estimate the value of $\dfrac{5.32 + 3.97}{\sqrt{878}}$ by first rewriting each number correct to $1$ significant figure.

Estimation

$a = 5b + 7$. Find the value of $a$ for $b = -2$.

Algebraic manipulation

Kamal keeps a daily count of the phone calls he gets at work over $20$ days. The table shows the results.

Relative and expected frequencies

Write $42\,000\,000$ in standard form.

Standard form

Triangles $ABC$ and $CBD$ are mathematically similar. $AB = 5\text{ cm}$, $AC = 7\text{ cm}$ and $BC = 8\text{ cm}$.

Similarity

The set $R$ is described by the inequalities $y \geq 2x$, $x + y \leq 4$, and $x \geq 0$.

Drawing linear graphs

$A$, $B$, $C$ and $D$ lie on a circle with centre $O$. Angle $BAD = 120^{\circ}$ and angle $OBC = 20^{\circ}$.

Circle theorems I

Evaluate the value of $125^{\tfrac{1}{3}}$.

Powers and roots

The mass of a bag of almonds is $125\text{ g}$ when rounded to the nearest gram. Write down the lower bound for the mass of the bag of almonds.

Limits of accuracy

Shade one additional small square so that the diagram has a single line of symmetry.

Symmetry

The function is given by $f(x) = \dfrac{2 - 4x}{5}$.

Functions

This table lists the heights of $180$ sunflowers.

Statistical charts and diagrams

The diagram depicts the graph of $y = \dfrac{1}{x} + \dfrac{x}{2}$.

Graphs of functions

The matrix is given by $A = \begin{pmatrix} 3 & -1 \\ 2 & 0 \end{pmatrix}$.

Algebraic manipulation

Solve $\dfrac{x}{x-1} - \dfrac{5}{x-3} = 1$.

Algebraic fractions

$OCB$ forms a triangle. Point $A$ lies on $OC$ such that $OA : AC = 1 : 3$. $X$ is the midpoint of $BC$. $\vec{OA} = \mathbf{a}$ and $\vec{OB} = \mathbf{b}$.

Vector geometry

Olga puts down five numbers. The median of these numbers is $12$. Their mode is $11$. Their range is $10$. The total of the numbers is $75$.

Averages and measures of spread

Change $4$ kilograms into grams.

Units of measure

For this question, every dimension is measured in centimetres.

Area and perimeter

Jack uses number cards to form a $2$-digit number. Fill in the missing card so that the result is a $2$-digit number that is not prime.

Types of number

Work out $\frac{2}{7}\div\frac{1}{3}$.

Fractions, decimals and percentages

A train departs station $A$ at $07\,43$. It reaches station $B$ at $10\,27$. Calculate the length of time the train spends travelling from station $A$ to station $B$.

Rates

A box contains red pens, blue pens and black pens. There are $x$ red pens. The number of blue pens is $5$ greater than the number of red pens. The number of black pens is $2$ times the number of blue pens.

Equations

A basketball match ticket costs $67.60$.

Percentages

$r = \frac{4p + 3t}{2}$. Determine $p$ when $r = 10$ and $t = -2$.

Algebraic fractions

January contains $31$ days. Find how many January days you would expect to have a temperature above $14^\circ\text{C}$.

Probability of combined events

The temperature at midday was measured at ten separate mountain heights. The results are presented in the table.

Scatter diagrams

Triangle $PQR$ is isosceles because $PQ = QR$. The exterior angle at $R$ is $142^\circ$. Calculate angle $PQR$.

Similarity

Among the factors of $50$, two are square numbers. One is $1$. Determine the other square number that divides $50$.

Types of number

Company $A$ charges $\$0.50$ per box, together with a fixed charge of $\$125$. Company $B$ charges only a fixed amount of $\$350$. Find how many boxes are moved when Company $A$ and Company $B$ charge the same.

Equations

Triangle $A$ is moved onto triangle $P$ by the translation of $\begin{pmatrix}1 \\ -3\end{pmatrix}$. Draw triangle $P$.

Transformations

A cuboid measures $5\,\text{cm}$ by $12\,\text{cm}$ by $h\,\text{cm}$. Its volume is $480\,\text{cm}^3$. Calculate $h$.

Surface area and volume

Fill in the table for $y = \frac{2^x}{5}$.

Exponential growth and decay

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

Non-right-angled triangles

Oranges are sold at $\$1.45$ per kilogram. Asher purchases $1.2$ kg of oranges. Work out the change he gets from $\$10$.

Ratio and proportion

The diagram depicts a pentagon.

Non-right-angled triangles

$Q$ has coordinates $(n,-4)$, $R$ has coordinates $(-1,8)$ and $S$ has coordinates $(3,2)$.

Length and midpoint

A fair spinner numbered from $1$ to $5$ is shown in the diagram. The score is whichever number the spinner stops on.

Introduction to probability

The dollar exchange rate is $\$1 = 4.19$ MYR, while for Pakistani Rupees it is $\$1 = 179.12$ PKR. Determine the exchange rate from Malaysian Ringgits to Pakistani Rupees.

Percentages

The diagrams illustrate the first four arrangements in the sequence.

Sequences

Describe in full the single transformation that carries shape $A$ onto shape $B$.

Transformations

In the Venn diagram, shade the part that represents $P \cup Q$.

Sets

Solve $\frac{x}{3}=7$.

Algebraic manipulation

A cone is placed on top of a hemisphere to make a solid. The cone and the hemisphere each have radius $r$ cm. The total height of the solid is $10$ cm. The curved surface area of the hemisphere is $145\text{ cm}^2$.

Surface area and volume

A shop offers two varieties of apple tree.

Averages and measures of spread