No questions found
(a) Write 0.047996 correct to 4 decimal places. .................................................. [1]
(b) Write 60449 correct to 3 significant figures. .................................................. [1]
512
535
553
Work out $4\frac{1}{4} - 1\frac{5}{6}$.
Give your answer as a mixed number in its simplest form.
577
530
597
(a) Write down the mathematical name of the quadrilateral that has rotational symmetry of order 2 but no lines of symmetry.
................................. [1]
(b) Write down the mathematical name of the quadrilateral that has exactly one line of symmetry.
................................. [1]
518
554
576
A biased four-sided spinner is spun 150 times. The number of times that the spinner lands on each number is shown in the table.
[Table_1]
Number on spinner | 1 | 2 | 3 | 4
Frequency | 34 | 63 | 27 | 26
(a) Write down the relative frequency of the spinner landing on 2. ......................................................... [1]
(b) Explain why it is reasonable to use your answer to part (a) as the probability of this spinner landing on 2. ............................................................................................................................................................. [1]
(c) The spinner is spun 3000 times.
Find the expected number of times that the spinner lands on 2. ......................................................... [2]
522
600
581
Divide 96 cm in the ratio 5:3.
................. cm , ............. cm [2]
591
539
587
A is the point $(-2, 4)$ and B is the point $(7, 1)$.
Find the length of $AB$ giving your answer in its simplest surd form.
518
567
569
A, B, C \text{ and } D \text{ are points on the circle. } PBQ \text{ is a straight line. }
(a) \text{ Find angle } DCB, \text{ giving a reason for your answer.}
\text{Angle } DCB = \text{..................... because (reason) ...................}
\text{[2 marks]}
(b) \text{ Is } PBQ \text{ a tangent to the circle? Give a reason for your answer.}
\text{.................... because .........................}
\text{[1 mark]}
504
574
503
Solve the simultaneous equations.
$2x + 3y = 5$
$y = 3x + 9$
$x = \text{................................................}$
$y = \text{...............................................................}$
549
516
512
The table shows some trigonometric ratios, each correct to 3 decimal places.
[Table_1]
\begin{array}{|c|c|c|c|} \hline & \text{Sine} & \text{Cosine} & \text{Tangent} \\ \hline 40^\circ & 0.643 & 0.766 & 0.839 \\ \hline 70^\circ & 0.940 & 0.342 & 2.747 \\ \hline \end{array}
Use this information to find
(a) \sin 110^\circ, ........................................................ [1]
(b) \tan 320^\circ. ........................................................ [1]
541
553
584
Factorise completely.
(a) \(4x^2y - 6xy^2\) ................................. [2]
(b) \(9x^2 - 1\) ................................. [1]
550
524
597
Solve.
(a) $\log_{x} 9 = 2$
$x = \text{..................................................}$ \[1\]
(b) $2 \log x - \log 4 = \log 9$
$x = \text{..................................................}$ \[2\]
524
542
500
y varies inversely as the square root of x. When $x = 25$, $y = 6$.
Find $y$ in terms of $x$.
$y = \text{.................................................}$ [2]
559
586
573
(a) On the Venn Diagram, shade the set $A \cap B \cap C'$.
[1]
(b) Use set notation to describe the shaded region.
......................................................... [1]
567
515
589
