In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The sizes of angles a and b in the triangle shown below are in the ratio 2: 3.
Diagram not drawn to scale
Calculate the size of each of the angles a and b. You must show all your working. [3 + 2 OCW]
[5]
Find the Lowest Common Multiple (LCM) of 60 and 72.
LCM of 60 and 72 is…………........ ……….
[2]
Express 882 as a product of its prime factors.
Give your answer in index form.
[3]
Complete the table below.
Draw the graph of y = 7 − x2 for values of x between −2 and 4.
Use the graph paper below.
| x | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
| y = 7 − x2 | 3 | 7 | 6 | 3 | −9 |
[4]
Rearrange the following formula to make k the subject.
p = 3k + 2
[2]
Does the midpoint of the straight line joining points (3, 15) and (7, 19) lie on the line y = 3x + 2?
You must show all your working.
[3]
A group of people have put their names forward to carry the Welsh flag at a sporting event.
Each person lives in North Wales, Mid Wales or South Wales.
One person from the group is chosen at random. The probability of choosing a person who lives in North Wales is 0·3. The probability of choosing a person who lives in Mid Wales is 0·25.
The probability of choosing a person who is under 18 years old is 0·2.
The people’s ages are independent of where they live.
What is the probability of choosing a person who lives in South Wales and is under
18 years old?
[2]
The diagram below shows an isosceles triangle and a square.
Perimeter of triangle = 19 cm
Diagram not drawn to scale
Use an algebraic method (not trial and improvement) to find the value of x and the value of y.
You must show all your working.
[5]
Describe fully the single transformation that transforms shape A onto shape B.
[3]
Two similar solids are shown below.
Solid A has a height of 5 cm. Solid B has a height of 7 cm.
Mari claims that the surface area of solid B is more than double the surface area of solid A. Is Mari correct?
You must justify your answer.
[2]
Rearrange the following formula to make w the subject.
xw + 4 = 3y – 8w
[3]
Solve the equation
You must use an algebraic method and show all your working.
[3]
A solid object is made out of a hemisphere and a cylinder.
The radius of the common circular surface is 3 cm. The volume of the whole object is 63
cm3.
Calculate the total height of the object.
[5]
The following diagram shows a sketch of y = sin x for values of x from 0° to 360°.
Given that sin 38° = 0·6157, correct to 4 decimal places, write down all the solutions of the equation
sin x = – 0·6157
for values of x from 0° to 360°.
[2]
Three of the seven cards shown above are selected at random, without being replaced.
Find the probability that the first card selected is a 3, the second is a 4 and the third is
a 5.
[2]
Find the probability that the sum of the numbers selected is greater than 9.
[3]
The paper as printed
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