12 questions · 100 marks · ≈ 2 hours
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Charles asks each of the students in his class which flavour of ice cream they prefer. There are 30 students in his class. He uses the information he collects to draw this accurate pie chart. mint fudge vanilla strawberry chocolate Find how many of the 30 students prefer chocolate ice cream.
P Q Scale: 1 cm represents 2 metres S R The trapezium PQRS is a scale drawing of Abdul’s garden.
Construct the locus of all points inside the trapezium that are 6 metres from P
Construct the locus of all points inside the trapezium that are 12 metres from QR
Using ruler and compasses only and showing all your construction lines, construct the locus of all points inside the trapezium that are equidistant from PS and RS Abdul is going to put a fountain in his garden. The fountain must be greater than 6 metres from P greater than 12 metres from QR closer to PS than to RS
Show, by shading, the region in which Abdul can place the fountain. Label the region R
Write 34 700 000 in standard form.
Write 9.8 10 3 as an ordinary number. x 5.4 10121 y 2 10120
Calculate xy Give your answer in standard form.
Calculate x + y Give your answer in standard form.
B C Diagram NOT 5m accurately drawn 50° A 5m D Figure 1 Figure 1 shows the section of a park, ABCD, where ADB is a sector of a circle centre D AD = BD = 5 m ADB BCD CDA
Calculate the area, in m² to 3 significant figures, of the sector ADB Grass is to be grown in this section ABCD of the park. 35 g of grass seed is needed for each 1
…………… m²
Calculate, in g to the nearest g, the weight of grass seed needed to cover this section of the park. Show all your working.
A company buys blankets, cushions and towels in the ratios number of blankets : number of cushions : number of towels = 2 : 3 : 6 The company buys a total of 3850 of these items.
Calculate the number of blankets that the company buys. The company sells each cushion for £15.95 The company makes a profit of 16% on each cushion.
Calculate, in £, how much the company pays for each cushion. The company buys 1500 small towels for £7 each and 600 large towels for £11 each. In January, it sells of the small towels for £15 each and 95% of the large towels for £18 each. The remaining towels were given away for free.
Calculate the percentage profit that the company makes in January. Give your answer to one decimal place. The company buys some items from a new supplier. The company spends $9460 Using the exchange rate of £1 = $1.23
calculate the amount, in £ to the nearest £, that the company spends with this new supplier.
The Venn diagram shows information about the number of students in a school who are members of the Athletics Club (A), the Brass Band (B) and the Chess Club (C) 15 students are not members of any of these clubs. E C A B 25 10 21 x 37 There are twice as many members of the Chess Club than there are members of the Brass Band.
Find the value of x
Find the number of these students who are not members of the Chess Club.
Find the number of these students who are members of all three clubs.
Find n B C ' At the start of 2022, the Drama Club had 80 members. From the start of 2022 until the start of 2023, the number of members of the Drama Club increased by 12.5% From the start of 2023 until the start of 2024, the number of members of the Drama Club increased by 30%
Calculate the number of students who were members of the Drama Club in 2024
Bag A contains 10 red counters and 5 yellow counters. Two counters are taken at random from bag A.
Complete the tree diagram below. First counter Second counter red red yellow red yellow yellow
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.
Calculate the probability that the two counters taken are the same colour. Bag B contains 4 red counters and 3 yellow counters. The two counters that have been taken from bag A are both placed into bag B so that there are a total of 9 counters in bag B. A counter is then taken at random from bag B. Given that each of the two counters taken from bag A and the one counter taken from bag B are all the same colour …………… , ……………
calculate the probability that the three counters are all red.
y cm x cm 2x cm Figure 2 Figure 2 shows a solid cuboid with length 2x cm, width x cm and height y cm The volume of the cuboid is a cm³ , where a is a constant. The total surface area of the cuboid is S cm² 3a
Show that S 4 x 2 x Given that the minimum value of S is 400
Find, to 3 significant figures, the value of a
X M Diagram NOT F E accurately drawn A D O B C Figure 3 Figure 3 shows a solid right pyramid ABCDEFX The base ABCDEF of the pyramid is horizontal and is a regular hexagon of side 3 cm O is the midpoint of the base. The vertex X of the pyramid is vertically above point O such that OX = 5 cm M is the midpoint of XD
Find the area, in cm² to one decimal place, of the hexagonal base.
Calculate the size, in degrees to 3 significant figures, of ∠AMX Show all your working. Area of triangle = absinC Cosine rule : a b c 2bc cos A 2 2 2
f(x) x 3 3 x
Use the factor theorem to show that that x 2 is a factor of f( x)
Hence, factorise f( x) completely.
Complete the table of values for y x 3 3 x Give your values of y to one decimal place where necessary. x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 y −4 −0.9 −2 −3.4 −4 0 6.1
On the grid opposite, plot the points from your completed table and join them to form a smooth curve.
By drawing a suitable straight line on the grid, find an estimate, to one decimal place, for the solution of the equation 2 x 3 7 x 6 0 in the interval −2 ≤ x ≤ 2.5
The functions f, g and h are defined as f : x ↦ 6 − x² 0< x<3 x 1 g : x ↦ + x x + 6x + 8 x + 2 x+5 h : x ↦ x>0 2x + 3
Write g(x) as a single fraction in its simplest form. Show clear algebraic working.
Find hf(2)
Find the inverse function h–1 in the form h −1 : x ↦ ... Give your answer in its simplest form.
Solve the equation hh( x) = x Show your working clearly.
Triangle A and triangle E are drawn on the grid opposite.
Describe fully the single transformation that maps triangle A onto triangle E Triangle A is transformed to triangle B under a reflection in the y-axis.
On the grid, draw and label triangle B Triangle A is transformed to triangle C under a translation with the vector
On the grid, draw and label triangle C
On the grid, draw and label triangle D Triangle F is transformed to triangle A under the transformation with matrix N where k N Triangle F is transformed to triangle D under the transformation with matrix P Given that the determinant of P is 5
calculate the value of k.
[Determinant of matrix ]