Edexcel IGCSE Maths A Paper 1H Higher November 2023 question paper 4MA1/1H

Here is a Venn diagram.

List the members of the set

A

A B

A B

Factorise fully 12 pq 18p

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

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

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

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.

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.

Work out the value of x

The spinner is spun 250 times.

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

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.

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

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.

Solve the inequality 8x 4 3x 10

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

Write down the three inequalities that define the region R

Write 5 87. 10⁴ as an ordinary number.

Write 84 000 000 in standard form.

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.

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

Here is triangle ABC

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

Express as a single fraction in its simplest terms.

Here are four graphs.

Write down the letter of the graph that could have the equation y

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

Find an estimate for the median time.

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

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.

15Make n the subject of the formula x

16A curve has equation y 4x³ 8x 5 Find the x coordinates of the two points on the curve where the gradient is

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.

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.

Here are the first 4 terms in an arithmetic sequence.

3 7 11 15

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.

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

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.

[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.

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.

24The curve with equation f(x) = 5x² 9x 2 is transformed to the curve with equation

g(x) = 5 x 4² 9 x 4 8 by the translation b a

Write down the value of a and the value of b

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

find the value of p and the value of q