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this maths homework will boost your grades, Exercises of Mathematics

Mathematics

this maths homework will boost your grades

Typology: Exercises

2025/2026

Uploaded on 12/04/2025

takeda-shingen 🇬🇧

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Name:

HIGHER HOLIDAY HOMEWORK

Section 1 - Non-Calculator - 80 marks available - 1 hour 30 minutes Time Limit

Answer all NINETEEN questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

(a) Simplify e÷e2

(b) Expand and simplify (x-3)(x + 1)

Find the value of p, given that

78×72

(1)

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Name: HIGHER HOLIDAY HOMEWORK Section 1 - Non-Calculator - 80 marks available - 1 hour 30 minutes Time Limit Answer all NINETEEN questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1

(a) Simplify e÷e

(b ) Expand and simplify (x- 3 )(x + 1) 2 Find the value of p, given that 78 × 72 7P = 76 ( 1 )

(Total for Question 1 is 3 marks) p = (Total for Question 2 is 2 marks)

3 ( a ) Simplify (3x2y)°

(b ) (i) Factorise x2 - 5x- 36

(ii) Hence solve x2-5x- (1)

cm (Total for Question 4 is 4 marks) 2 5

The table gives information about the times taken by 90 runners to complete a 10 km race.

Time ( t minutes) Frequency 25 <t < 35 12 35 <t < 45 24 45 <t < 55 28 55 <t < 12 65 < t < 75 10 75 <t < 4

( a ) Complete the cumulative frequency table.

Time (t minutes) 25 < t < 25 < t < 45

Cumulative frequency 12 25 < t < 55 25 < t < 25 <t< 75 25 < t < 85

(b ) On the grid below, draw a cumulative frequency graph for your table.

90- 80- 70 60 Cumulative frequency 50 40 30 20 10 0 25 35 45 55 65 75 85 Time (t minutes)

48 ° C B B, D, E and F are points on a circle, centre O. ABC is a tangent to the circle. ODC is a straight line. BOE is a diameter of the circle. Angle BCD = 48° Find the size of angle DFE. Diagram NOT accurately drawn

O (Total for Question 6 is 3 marks) 7

(a) Simplify

(c) Expand and simplify 4x( x - 5 )( 2x + 3 )

Show your working clearly.

(Total for Question 7 is 7 marks) 8 ABCDEF and GHIJKL are regular hexagons each with centre O. G H

(iii) LD (2)

The triangle OAB has an area of 5 cm

(b ) Calculate the area of the shaded region. cm ( 3 ) (Total for Question 8 is 8 marks ) 9 The functions f and g are such that

(b ) Find gf(x)

Simplify your answer.

f(x)=2x- 3

X g(x)= 3x + 1 gf(x)= =

E M 3 2 F E (a ) Use all the given information about the results of students who passed the test in Maths to find the value of x. x=

(b) Use your value of x to complete the Venn diagram to show the number of students in

each subset. E M 3 2 E

A student who passed the test in Maths is chosen at random.

(c) Find the probability that this student failed the test in French.

(Total for Question 11 is 5 marks)

(Total for Question 12 is 8 marks) 13 Express 8 √5-

in the form √a+b where a and b are integers.

Show each stage of your working clearly.

(Total for Question 13 is 3 marks) 14 0.4x is a recurring decimal. x is a whole number such that 1 ≤ x ≤