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

The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.

Frame size (Scm)	Frequency
30 S 36	4
36 S 42	14
42 S 48	18
48 S 54	19
54 S 60	5

Write down the modal class.

Work out an estimate for the mean frame size.

The diagram shows a solid triangular prism.

Work out the total surface area of the triangular prism. Give your answer correct to 3 significant figures.

Here is a list of six numbers written in order of size.

x 5 y z 10 12

qhe=numbers=h~$ve= a range of 9 a median of 8 a mode of 10

Find the value of x, the value of y and the value of z

Divya and Yuan each pay for a holiday at a special offer price.

The amount that Divya pays is the same as the amount that Yuan pays.

Work out the value of k

C grams of chocolate is shared in the ratios 2: 5: 8 The difference between the largest share and the smallest share is 390 grams.

Work out the value of C

Solve the simultaneous equations

x + 2 y = 15 4 x – 6 y = 4

Show clear algebraic working.

Write 9.3210^–5as an ordinary number.

Work out 310⁵ – 610⁴ Give your answer in standard form.

Work out (310⁵⁵) (610⁶⁵) Give your answer in standard form.

Factorise fully 18c³d² – 21c²

Factorise y² – 3y – 18

Hence, solve y² – 3y – 18 = 0

The diagram shows an isosceles triangle ABC

AB = 7 cm AC = BC = ycm

The area of the triangle is 42 cm²

Work out the value of y

R and T are points on a circle, centre O

RT = 12 cm M is the midpoint of RT Angle ROM = 52

Work out the area of the circle. Give your answer correct to 3 significant figures.

The table shows information about the times, in minutes, that 80 patients had to wait to see a doctor.

Time (W minutes)	Frequency
0 W 10	7
10 W 20	10
20 W 30	15
30 W 40	32
40 W 50	16

Complete the cumulative frequency table below.

On the grid opposite, draw a cumulative frequency graph for your table.

Use your graph to find an estimate for the median.

Use your graph to find an estimate for the interquartile range.

12Solve 2^–4x = 32

p = 0.51 correct to 2 significant figures. r = 6.3 correct to 2 significant figures.

Work out the upper bound for the value of T Show your working clearly.

Complete the table of values for y = x³ – 3x + 2

On the grid, draw the graph of y = x³ – 3x + 2 for values of x from –2 to 2

By drawing a suitable straight line on the grid, use your graph to find an estimate for the solution of

Give your answer correct to one decimal place.

The function f is such that

Find f^–1(x)

The function g is such that

Express g(x) in the form a(x – b)² + c

AB = 4.6 cm BC = 8.3 cm angle ABC is acute

The area of triangle ABC is 12 cm²

Work out the perimeter of triangle ABC Give your answer correct to 3 significant figures.

P is inversely proportional to y² When y = 4, P = a

Find a formula for P in terms of y and a

find a formula for P in terms of x and a

20Here is a sketch of the curvey = acos(x + b) for 0 ≤ x ≤ 360

Given that 0 < b < 180

find the value of a and the value of b

The diagram shows a triangular prism, ABCDEF, with a rectangular base ABCD

AB = 6 cm DE = 2.2 cm angle DAE = 18 angle ADE = 90

Work out the angle that BE makes with the plane ABCD Give your answer correct to one decimal place.

The diagram shows triangle OAB with OA extended to E

OA = a OB = b

M is the point on OB such that OM:MB = 4: 1 N is the point on AB such that AN: NB = 3: 2 OA: AE = 5: 3

Find an expression for ON →in terms of a and b Give your answer in its simplest form.

ON → =_........

Use a vector method to show that MNE is a straight line.

G is the point on the curve with equation y = 8x² – 14x – 6 where the gradient is 10 The straight line Q passes through the point G and is perpendicular to the tangent at G

Find an equation for Q Give your answer in the form ax + by + c = 0 where a, b and c are integers.

An arithmetic sequence has first term 8 and common difference 11 The sequence has k terms, where k 21

The sum of the last 20 terms of the sequence is 10 170

Find the value of k Show clear algebraic working.