4MA1 Mathematics A: Oct/Nov 2023 Paper 1HHigher Tier Paper 1

Here is a Venn diagram.

List the members of the set

(a)A

[1]

(b)A ∩ B

[1]

(c) A  B

[1]

(a)Factorise fully 12 pq −18 p

[2]

There are 56 metal bars in a box. Each metal bar is gold or silver or zinc.

y metal bars are gold. (3y + 7) metal bars are silver. (2y − 5) metal bars are zinc.

(b)Work out the number of metal bars that are zinc. Show clear algebraic working.

[4]

Joshua buys a car for $12 500

He sells the car to Nina.

Nina pays

• a deposit of $1500 • followed by 36 monthly payments of $450

Work out Joshua’s percentage profit.

%[4]

A biased spinner has three sections each of a different colour.

The table shows the probability that, when the spinner is spun once, it will land on blue or on orange or on white.

(a)Work out the value of x

x = [2]

The spinner is spun 250 times.

(b)Work out an estimate for the number of times the spinner will land on blue.

[2]

The diagram shows a shaded shape made from three identical semicircles, X, Y and Z

ABCDE is a straight line.

AC is the diameter of semicircle X and B is the centre of semicircle X BD is the diameter of semicircle Y and C is the centre of semicircle Y CE is the diameter of semicircle Z and D is the centre of semicircle Z

AC = BD = CE = 20 cm

Work out the perimeter of the shaded shape. Give your answer correct to the nearest whole number.

cm[3]

Juan wants to buy a ticket to fly from Madrid to Berlin.

He finds two different types of ticket he can buy in a sale, ticket A and ticket B

The sale price of ticket A is 140 euros. The sale price of ticket B is 136 euros.

Work out the difference between the normal price of ticket A and the normal price of ticket B

euros[4]

A  5³  7³ 11⁶ and B  5⁶  7² 11⁴

Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.

[2]

(a)Solve the inequality 8x − 4  3x −10

[2]

The region R, shown shaded in the diagram, is bounded by three straight lines.

(b)Write down the three inequalities that define the region R

[3]

(a)Write 5. 87 10⁴ as an ordinary number.

[1]

(b)Write 84 000 000 in standard form.

[1]

The number of neurons in a human brain is 8.5×10¹⁰ The number of neurons in a monkey brain is 1. 47 ×10⁹

The number of neurons in a human brain is K × the number of neurons in a monkey brain.

(c)Work out the value of K Give your answer correct to one decimal place.

K = [2]

Here is triangle ABC

Work out the value of x Give your answer correct to one decimal place. Show your working clearly.

x = [5]

Express 34  5  x6x as a single fraction in its simplest terms.

[3]

(a)Complete the table of values for y = x³ − 3x + 1

[2]

(b)On the grid, draw the graph of y = x³ − 3x + 1 for values of x from − 2 to 2

[2]

Here are four graphs.

(c)Write down the letter of the graph that could have the equation y   1x₂

[1]

The cumulative frequency graph gives information about the times, in seconds, that 80 adults took to log in to an online bank.

(a)Find an estimate for the median time.

seconds[1]

(b)Work out the percentage of these adults that took longer than 50 seconds to log in. Show your working clearly.

%[3]

A, B and C are points on a circle, centre O

Angle OAC = 52°

Find the size of angle ABC Give reasons for your working.

[3]

Make n the subject of the formula x  3 p  n3n  4

[3]

A curve has equation y  4x³  8x  5

Find the x coordinates of the two points on the curve where the gradient is 13

[4]

The histogram gives information about the weights, in grams, of some oranges in a box.

24 of these oranges weigh less than 20 grams.

Medium oranges weigh between 35 grams and 55 grams.

Work out an estimate for the number of medium oranges in the box.

[3]

The diagram shows the positions of three villages, A, B and C

The bearing of B from A is 054° The bearing of C from B is 132°

Melur walks from A to B She then walks from B to C and from C to A

Melur walks at an average speed of 6 km/h

Work out the total time Melur takes. Give your answer in hours and minutes.

hours minutes[5]

Here are the first 4 terms in an arithmetic sequence.

The last term of the sequence is x The sum of the terms of the sequence is 7260

Find the value of x Show clear algebraic working.

x = [6]

A bag contains only 10 cent coins and 20 cent coins.

Josip takes at random a coin from the bag, records its value and replaces it in the bag. He then takes at random a second coin from the bag, records its value and replaces it in the bag.

Josip finds the mean value of the two coins.

The probability that the two coins have a mean value of 10 cents is 49121

Work out the probability that the two coins have a mean value of 15 cents.

[4]

Here is a triangular prism ABCDEF

AD = 53 cm DF = 28 cm Angle FDE = 30°

Work out the volume of the triangular prism. Give your answer correct to the nearest whole number.

cm³[5]

[In this question 1 cm = 1 unit on the x-axis and 1 cm = 1 unit on the y-axis]

P is a point on a circle with centre (0, 0) The coordinates of P are (8, −10)

The line L is the tangent to the circle at the point P L crosses the x-axis at the point Q and crosses the y-axis at the point R

Work out the length of RQ Give your answer correct to 3 significant figures.

cm[6]

Solid A is similar to solid B

Here is some information about solid A and solid B

Work out the height of solid B Give your answer as a decimal.

cm[5]

The curve with equation f(x) = 5x² + 9x + 2 is transformed to the curve with equation

g(x) = 5 x  4  9 x  4  8 by the translation  a b    

(a)Write down the value of a and the value of b

a =

b = [2]

The graph of y  p cos x  q for 0  x  360 is drawn on the grid below.

Given that p > 0 and 0 < q < 360

(b)find the value of p and the value of q

p =

q = [2]