4MB1/02 — January 2022 (Edexcel IGCSE Maths): Past Paper

Write 248 000 000 in standard form.

Write 2.56 × 10–4 as an ordinary number.

Calculate, giving your answer in standard form 2.5 × 1060 − 1.3 × 1059 1.5 × 10 − 48

The ages, in years, of 7 friends are 9 8 7 6 10 a 7 The mean age of the 7 friends is 8 years.

Work out the value of a

Find the median age of the 7 friends. There are 34 passengers on a bus. The mean age of these passengers is 49 years. 11 of these passengers are pensioners. The mean age of these pensioners is 72 years.

Calculate the mean age, in years, of the passengers on the bus who are not pensioners.

Triangles A and D are drawn on the grid below. Triangle B is the image of triangle A under a reflection in the line with equation y = –x

On the grid below, draw and label triangle B. ⎛ −9⎞ Triangle A is transformed to triangle C under the translation −2⎠

On the grid, draw and label triangle C.

Describe fully the single transformation that maps triangle A onto triangle D.

A curve C has equation x 2 + y 2 = 64 A straight line l has equation 4y + 3x = 40 Show that the line l intersects the curve C only once. Show clear algebraic working.

A B E Diagram NOT accurately drawn C D O Figure 1 Figure 1 shows triangle OAB → → Given that OA = a and OB = b →

find AB in terms of a and b The point C lies on OA such that OC : OA = 1 : 3 → 2→ The point D lies on OB such that OD = OB Given that the point E is such that ABE and CDE are straight lines, →

find and simplify an expression, in terms of a and b, for AE

6 ⎛ −2 −3⎞ ⎛ 4 x −14⎞ A= 2 4 BA = x −1 Given that the determinant of B is 10 find B Show your working clearly. ⎡ ⎛ a b⎞ ⎤ ⎢ Determinant of matrix = ad − bc ⎥ ⎢ ⎝ c d⎠ ⎥ ⎢ ⎛ a b⎞ 1 ⎛ d − b⎞ ⎥ ⎢Inverse of matrix c d ad − bc −c a = ⎢⎣ ⎥⎦

B C F 86° Diagram NOT accurately drawn O 38° D A G E Figure 2 In Figure 2, ABCDG is a circle, centre O EDF is the tangent to the circle at the point D ∠ABC = 86° ∠CDF = 38° The length of the arc AGD is 0.8π cm.

Giving reasons, show that the radius of the circle is 1.5 cm.

Calculate the area, in cm² to 2 decimal places, of the circle ABCDG

All 66 students in a drama group take part in at least one of the four activities given below. acting (A) dancing (D) singing (S) stage management (M) Of these 66 students 11 take part in acting, dancing and singing 17 take part in acting and singing 14 take part in dancing and singing 16 take part in acting and dancing 33 take part in singing 37 take part in acting 29 take part in dancing Any student who takes part in stage management does not take part in acting, dancing or singing.

Show all this information on the Venn diagram, giving the number of students in each subset. E A D S

n([A ∩ D¢] ∪ S)

n([A ∩ D ∩ S¢]¢) One of the students in the drama group is selected at random. Given that this student takes part in dancing …………… , ……………

stage management …………… , ……………

singing.

Figure 3 Figure 3 shows three points A, B and C on horizontal ground. A vertical mast BT of height 30 m is at point B. The angle of elevation of T from A is 32° The angle of elevation of T from C is 25° The bearing of A from B is 195° The bearing of C from B is 280° Calculate the bearing, in degrees to the nearest degree, of C from A. ⎛ Sine rule: a b c ⎞ = = ⎜ sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 − 2bc cos A ⎠

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: T, C, B, A · Figure values: 30.

The production costs of building a Kimo boat are $L for labour $M for materials $H for overheads In 2020, the total of the production costs for a Kimo boat was $120 000 where L:M:H = 5:3:2

Calculate the value of H in 2020 The production costs were different in 2021 from what they were in 2020 The labour costs had increased by 10% The cost of materials had increased by 5% The overheads had decreased by 4%

Calculate the percentage increase, from 2020 to 2021, in the total of the production costs of building a Kimo boat. Gordon bought a Kimo boat and sold it a year later for $360 000, making a loss of 25% on the price for which he bought the boat.

Calculate the price for which Gordon bought the boat. Gordon sold the boat to a friend living in Hungary. Gordon’s friend paid Gordon the $360 000 in Hungarian forints. Using exchange rates of £1 = $1.35 £1 = 388.50 Hungarian forints

change $360 000 to Hungarian forints.

4y – 3x = 6 –3 ≤ x ≤ 4

3y + 2x = 15 –3 ≤ x ≤ 4

Using your straight lines, find an estimate, to one decimal place, of the solution of the simultaneous equations 4y – 3x = 6 3y + 2x = 15 6 + 3 x 15 − 2 x

Hence, or otherwise, solve the inequality < 4 3

Complete the table of values for $y = x^2 - 2x - 1$

On the same grid on the opposite page, plot the points from your completed table and join them to form a smooth curve.

Using part (a) and part (e), find an estimate, to one decimal place, for the range of values of x for which 11 5 x² − x− <0 4 2 Show your working clearly.

The function g is defined for all values of x by g : x ↦ 5 – x²

Find g(–4)

Write down the range of the function g The function f is defined as 4 11 f:x ↦ x≠ 2 x − 11 2

Find fg(2)

Express the inverse function f –1 in the form f –1 : x ↦ ...

State the value of x that must be excluded from any domain of f –1

Express ff(x) in terms of x giving your answer as a single fraction in its simplest form. The function h is defined for all values of x by h : x ↦ x(x + 1) The function m is defined for all values of x by m : x ↦ ax + b where a and b are constants such that a > 0 and b > 0 Given that hm(x) = 3(x + 1)(3x + 2) for all values of x

find the value of a and the value of b