No questions found
Round these numbers to 3 significant figures.
(a) 0.00060483
Answer(a) ........................................................... [1]
(b) 6998800
Answer(b) .......................................................... [1]
584
543
595
By rounding each number to 1 significant figure, estimate the value of $$\frac{0.583 \times 311.6}{1.82 + 10.43}$$.
Show your working.
587
525
590
Given: $a = 2^3 \times 3 \times 5^2$ and $b = 2^2 \times 3^2 \times 7^6$.
(a) Find, giving each answer as the product of prime factors,
(i) the highest common factor (HCF) of $a$ and $b$, Answer(a)(i) ............................................................... [1]
(ii) $\sqrt{b}$. Answer(a)(ii) ............................................................... [1]
(b) $ap$ is a cube number.
Find the smallest integer value of $p$. Answer(b) ............................................................... [1]
531
529
572
The diagram shows a rectangle, two semicircles and two right-angled triangles.
(a) Find the total area of the shape. Give your answer in the form $a + b\pi$.
Answer(a) ..........................................................cm$^2$ [3]
(b) Describe fully the symmetry of the shape.
Answer(b) .................................................................................................................... .................................................................................................................... [2]
600
552
509
Solve.
$$5(x + 2) < 2(4x - 7)$$
Answer .................................................. [3]
546
537
554
François and George each ask a sample of students at their college how they travel to college.
These are their results.
[Table_1]
\begin{array}{|c|c|c|c|c|c|c|} \hline & \text{Walk} & \text{Cycle} & \text{Bus} & \text{Train} & \text{Car} & \text{Total number of students} \\ \hline \text{François} & 7 & 3 & 4 & 1 & 5 & 20 \\ \hline \text{George} & 46 & 24 & 44 & 11 & 25 & 150 \\ \hline \end{array}
(a) Explain why George’s results will give the better estimates of the probabilities of the different types of travel.
\text{Answer(a)} \text{............................ [1]}
(b) A student is selected at random.
(i) Use George’s results to estimate the probability that the student cycles to college.
\text{Answer(b)(i)} \text{............................ [1]}
(ii) There are 3000 students at the college.
Use George’s results to estimate the number of students who cycle to college.
\text{Answer(b)(ii)} \text{............................ [1]}
556
593
560
The diagram shows the lines $x = -2$, $y = \frac{1}{2}x + 1$ and $3x + 4y = 20$.
(a) Use simultaneous equations to find the co-ordinates of the point $A$.
(b) (i) $P$ is a point in the region such that $x < -2$, $y > \frac{1}{2}x + 1$ and $3x + 4y < 20$.
On the diagram, mark and label a possible position of $P$.
(ii) $Q$ is a point in the region such that $x > -2$, $y = \frac{1}{2}x + 1$ and $3x + 4y < 20$.
On the diagram, mark and label a possible position of $Q$.
Answer(a) $\text{( .................. , .................. )}$ [3] [1] [1]
569
502
530
In the diagram, $A, B, C, D$ and $E$ are points on the circle. $AD$ is a diameter and angle $CAD = 35^\circ$.
Find
(a) angle $ACD$, Answer(a) ............................. [1]
(b) angle $CBD$, Answer(b) ............................. [1]
(c) angle $AEC$. Answer(c) ................................................. [2]
566
525
549
The sets $P$, $Q$ and $R$ are subsets of the universal set $U$.
• $P \cap R \neq \emptyset$
• $Q$ is a subset of $R$
• $Q \cap P = \emptyset$
Complete the Venn diagram to show the sets $P$, $Q$, and $R$.
515
513
578
(a) Factorise $x^2 - 3x - 10$.
Answer(a) .......................................................... [2]
(b) Make $x$ the subject of $y = \frac{\sqrt[3]{x}}{a}$.
Answer(b) $x = $ .................................................. [2]
592
561
522
(a) Find $\log_{5}\frac{1}{25}$.
Answer(a)............................................................... [1]
(b) Find $x$ when
(i) $\log x - \log 2 = \log 6$,
Answer(b)(i)............................................................... [1]
(ii) $\log_{x} 4 = \frac{1}{2}$.
Answer(b)(ii)............................................................... [1]
540
572
564
The diagram shows a sketch of the graph of $y = ax^2 + bx + c$.
The graph goes through the points $(-3, 0)$, $(0, -12)$ and $(2, 0)$.
Find the values $a$, $b$ and $c$.
578
566
575
