Feb/March 2017

State the temperature difference between $-4\degree\text{C}$ and $-9\degree\text{C}$.

The four operations

Determine the highest common factor (HCF) of 36 and 63.

Types of number

The explanatory data set lists these numbers: 7, 2, 3, 5, 1, 2, 6, 9, 7, 2, 6, 4, 2, 3, 6.

Averages and measures of spread

Exchange rates displayed: the box states "1 euro = $1.09" and "$1 = 62 rupees".

Rates

A right-angled triangle ABC is drawn, and it is NOT TO SCALE. AB is vertical and measures 6.2 m, BC is horizontal and measures 13.8 m, the angle at B is a right angle, and the angle at C is marked $x\degree$.

Right-angled triangles

The bar chart displays how many students are in Classes A, B, C, D and F. The vertical axis is marked "Number of students" and goes from 0 to 30. The horizontal axis is marked "Class" and lists A, B, C, D, E and F. The bars shown are: A = 22, B = 15, C = 19, D = 24, F = 14. No bar is drawn for Class E.

Statistical charts and diagrams

Give the next term in the sequence: 19, 15, 11, 7, 3.

Sequences

Use the circle shown below, together with its centre indicated, to demonstrate this.

Geometrical constructions

Do this without a calculator.

Fractions, decimals and percentages

First expand the brackets, then simplify $4(5w + 3) - 2(w - 1)$.

Algebraic manipulation

Kaasni placed $2400$ into an investment that earned compound interest at a yearly rate of $7.5%$.

Percentages

Shade two additional squares so that this shape has rotational symmetry of order 2.

Symmetry

The pie chart illustrates the way Miranda used her time yesterday. The segments are named Playing, Eating, Sleeping, Watching TV, and Working.

Statistical charts and diagrams

Calculate $\begin{pmatrix}3\\-2\end{pmatrix} + \begin{pmatrix}1\\-1\end{pmatrix}$.

Coordinates

Solve the equation $4x = 10$.

Equations

A straight line $l$ appears on the coordinate grid.

Equations of linear graphs

Find $\sqrt{196}$.

Powers and roots

The cuboid measures 12 m by 15 m by 20 m.

Surface area and volume

The values listed are 34, 38, 10, 87, 45, 28, 19, 23.

Averages and measures of spread

Write 629 000 in standard form

Standard form

The plate is circular, and its diameter is 27 cm.

Circles, arcs and sectors

Do not use your calculator; round every number to 1 significant figure.

Estimation

Factorise $15c^2 - 5c$ fully.

Algebraic manipulation

Expand the brackets, then simplify the expression: $4(5w + 3) - 2(w - 1)$.

Algebraic manipulation

Indira purchases a television during a sale for $924. That price is 12% less than the original cost.

Percentages

A coordinate grid is displayed with the axes marked $x$ and $y$. Shape $A$ appears on the grid. $T(X)$ denotes the image of shape $X$ when it is translated by the vector $\begin{pmatrix}-1 \\ 3\end{pmatrix}$. $M(Y)$ denotes the image of shape $Y$ when it is reflected in the line $x = 2$.

Transformations

$y$ is inversely proportional to $x^2$. If $x = 5$, then $y = 16$.

Ratio and proportion

Factorise completely the expression $15c^2 - 5c$.

Algebraic manipulation

The points $A$ and $B$ are shown on the grid, and $\vec{BC} = \begin{pmatrix}-4 \\ 0\end{pmatrix}$.

Vectors in two dimensions

Find the value of $t^{24} \div t^4$.

Indices II

The speed-time graph represents the opening 60 seconds of a train journey. The vertical axis is marked Speed (m/s) up to 15, while the horizontal axis is marked Time (s) up to 60. A straight line is drawn from $(0, 0)$ to $(60, 15)$.

Graphs in practical situations

A checkpoint was used to test a total of 20 trucks. 6 trucks did not pass the brakes test ($B$). 7 trucks did not pass the lights test ($L$). 9 trucks passed both the brakes and lights tests. A Venn diagram is displayed with two overlapping circles labelled $B$ and $L$ inside a universal set.

Sets

$M = \begin{pmatrix}5 & 3 \\ 1 & -2\end{pmatrix}$ and $N = \begin{pmatrix}3 & -6 \\ 4 & 2\end{pmatrix}$.

Algebraic manipulation

A triangle $PQR$ is illustrated, NOT TO SCALE. $PQ = 2.8$ cm, $QR = 8.3$ cm, and the angle at $Q$ is $79^\circ$.

Non-right-angled triangles

Segment AB forms one side of equilateral triangle ABC.

Geometrical constructions

A straight line labelled $l$ is plotted on a set of $x$- and $y$-axes.

Equations of linear graphs

The three functions are $f(x) = \dfrac{x}{4} - 3$, $g(x) = 6x - 7$, and $h(x) = 2^x$.

Functions

Estimate the value of $\dfrac{10.3 \times 19.5}{88.9 - 43.2}$, without using your calculator, after rounding each number to 1 significant figure. Show all your working.

Estimation

The world’s population increases exponentially by 1.1% each year.

Exponential growth and decay

Use $s = ut + 16t^2$.

Introduction to algebra

Express the recurring decimal $0.\dot{1}7$ as a fraction. Show all your working.

Fractions, decimals and percentages

The rectangle has a length of 9.3 cm, accurate to 1 decimal place, and a width of 7.7 cm, also accurate to 1 decimal place.

Limits of accuracy

Without a calculator, find $3\frac{1}{3} \div 2\frac{1}{2}$. Show all your working and state your answer as a mixed number in simplest form.

Fractions, decimals and percentages

A pyramid with a square base $ABCD$ is shown in the diagram. Every sloping edge of the pyramid has length 20 cm, and $AC = 17$ cm. The figure is marked NOT TO SCALE. The sketch shows vertex $V$ at the top, the base points $A$, $B$, $C$, $D$, one sloping edge labelled 20 cm, and the diagonal $AC$ labelled 17 cm.

Pythagoras' theorem and trigonometry in 3D

State a square number that lies between 30 and 40.

Types of number

The diagram displays shapes A and B on a coordinate grid.

Transformations

Mrs Singh and Mr Patel work as teachers. They bring their two classes to the theatre to watch a play.

Ratio and proportion

Complete the sentence. For an angle to count as obtuse, it has to lie between [BLANK] degrees and [BLANK] degrees.

Scale drawings

A train leaves Green Hill, pauses for 5 minutes at Deep Valley, and then continues to Clear Lake. The timetable for the train gives the times.

Rates

Choose a marble at random from the bag, then replace it. Write down the probability that the marble is black.

Equations

Ten students work out the length and width of their rectangular school hall, and the findings are presented in the table.

Scatter diagrams

Complete parts (a)(i) and (b)(i) of this question with a straight edge and compasses only. Include every construction arc.

Geometrical constructions

Complete the table of values for $y = \frac{8}{x}$.

Graphs of functions

For a holiday in India, the Smith family paid $5635$. This total was split in the ratio travel : accommodation : entertainment = 10 : 17 : 8.

Ratio and proportion

The diagram depicts a regular hexagon $ABCDEF$ with side length 10 cm.

Trigonometric functions

On Monday, Ankuri sent this text message to two friends. "Today is Day Number 1. Tomorrow, please add 1 to the Day Number and send this text message to two friends." Every friend who gets a text message carries out the instructions.

Sequences

The coordinate grid displays the shapes P, Q, R and S.

Transformations

The table lists some values for $y = 1.5^x - 1$.

Graphs of functions

Ravi uses a biased 5-sided spinner, labelled 1 to 5. The table gives the probability for each number.

Probability of combined events

Factorise $3x^2 + 11x - 4$ into brackets.

Equations

In the diagram, $EH$ runs parallel to $FG$. The lines $EG$ and $FH$ cross at $Z$. Angle $ZFG = 27^\circ$.

Circle theorems II

The table presents data on how long it took 400 people to finish a race.

Cumulative frequency diagrams

In triangle $TXZ$, the side $TX$ measures $12.5$ cm and angle $TZX$ is $37^\circ$. Point $Y$ lies on line $XZ$ so that $TY = 9.9$ cm, angle $XTY = 23^\circ$ and angle $TYZ = 72^\circ$.

Non-right-angled triangles

Bernie is purchasing $x$ packets of seeds and $y$ plants for his garden. He intends to buy a greater number of seed packets than plants, so the inequality $x > y$ represents this. He also wants fewer than 10 packets of seeds and no fewer than 2 plants.

Inequalities