Peter Symonds College - Maths Department Preparation for A Level Mathematics - Pre-Enrolment Task

Sep 5, 2026

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Pre-enrolment task for Peter Symonds College Maths Department to prepare students for A Level Mathematics by consolidating core GCSE algebra skills. The pack includes instructions to complete a series of worksheets independently, show full working, mark using provided solutions, and transfer the scores to a front sheet out of 120. It covers basic algebra, equations, quadratic equations, surds, fractions and indices, simultaneous equations, straight lines and gradients, and forming equations from worded questions.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Instructions

Question sheet 1 - Basic algebra

Expand and simplify

Factorising

Multiply out and simplify

Simplify to lowest terms

Express as a single fraction

Question sheet 2 - Equations

Solve equations

Make a variable the subject of the formula

Question sheet 3 - Quadratic equations

Expand and simplify

Factorise

Solve by factorising

Solve using the quadratic formula

Question sheet 4 - Surds, Fractional & Negative Indices

Simplify surds

Expand and simplify products

Write fractional powers in index form

Question sheet 5 - Simultaneous equations

Solve by elimination

PETER SYMONDS COLLEGE Maths Department Preparation for A Level Mathematics You will need to make sure that you are confident with some core algebraic GCSE skills in preparation for the start of your A Level Mathematics course. INSTRUCTIONS 1. USING YOUR OWN PAPER complete all the questions on the following worksheets. 2. MARK YOUR WORK using the answers at the back of the booklet. 3. Transfer your marks to the table below, GIVING YOURSELF A MARK out of 120. 4. Please write any comments in the NOTES boxes if you need to explain your marks. 5. Attach your written work to this front sheet & BRING IT TO YOUR FIRST MATHS LESSON. | QUESTION SHEETS | Mark | Notes | | --- | --- | --- | | 1 Basic Algebra | ⁄24 | | | 2 Equations | ⁄18 | | | 3 Quadratic equations | ⁄22 | | | 4 Surds, Fractional & Negative Indices | ⁄18 | | | 5 Simultaneous equations | ⁄8 | | | 6 Straight Lines & Gradients | ⁄12 | | | 7 Forming equations from worded questions | ⁄18 | | | TOTAL | ⁄120 | | PETER SYMONDS COLLEGE Maths Department Preparation for A Level Mathematics Pre-Enrolment Task A Level Maths assumes knowledge and competence in the algebraic skills and techniques included in this booklet. Making sure you are confident in these GCSE skills will give you practice and help you prepare for early lessons, ensuring a good start on your A level course. Complete all of the following worksheets, using your own file paper and showing working out. DO NOT WRITE INSIDE THE BOOKLET There are some hints and examples. You could use your GCSE revision guides and/or internet resources if necessary. Answers to the last 3 questions will be given and discussed during one of your first three lessons. Please mark your work using the solutions on page 6 and transfer your marks to the front sheet , making any notes that you need to where you might have found a topic difficult or to inform your teacher areas you will need help with. PLEASE MARK YOUR WORK AND BRING IT TO YOUR FIRST LESSON. Question sheet 1 Basic algebra 1. Expand, and then simplify as far as possible, each of the following expressions. i. 3 􀀋x 􀀎 2 􀀌􀀎 5 􀀋x 􀀐1􀀌 ii. 4 􀀋5a 􀀎 3 􀀌􀀐 3 􀀋2a 􀀐 5 􀀌 iii. t 􀀋2 p 􀀎1􀀌􀀎 p 􀀋3t 􀀐 2 􀀌 iv. 2 􀀋 p 􀀎 q􀀌􀀎 3q 􀀋 p 􀀐 3 􀀌􀀐 p 􀀋3q 􀀎1􀀌 2. Factorising – putting brackets in by taking out highest common factors, even if the factors look a bit different! HCF is 5(􀝔 + 1) Example: Factorise 5 (􀝔 + 1) + 10􀝔(􀝔 + 1) = 5 (􀝔 + 1) × 1 + 5(􀝔 + 1) × 2􀝔 = 5 (􀝔 + 1)(1 + 2􀝔) Factorise the following expressions. i. iii. v. 9a2 􀀎 3abc 2􀝔3 − 􀝔 2 + 4􀝔 2 (􀝔 − 1) + 􀝔(􀝔 − 1) ii. 3􀝔 + 6􀝔2 iv. 10􀝕2 − 5􀝕 vi. 7􀝔(􀝔 + 2)2 − 􀝔(􀝔 + 2) 3. In each of the following questions, multiply the terms or expand the brackets. i. 3x􀁵 4xy ii. 5a2b􀁵 2ab 2 iii. 3 (􀝔5􀝕 2 ) 7 iv. (2􀝔2􀝕 3 )4 4. Simplify each of the following as far as possible. x 3y 2 6a3b4 i. ~~ ~~ ii. ~~ ~~ xy 3b iii. 4x 􀁵 9~~ ~~y22~~ ~~ iv. 10 p 􀁵 3q2 􀁵 4q3 3y 2x 3q2 2 p2 5 p 5. Express each of the following as a single fraction. Same rules as for numeric fractions. Example: 25􀯫 + 7􀯫42 LCD is 4􀝔 so 2 + 7􀯫4􀯫 = 7􀯫3410 i. iii. v. x x ~~ ~~􀀎~~ ~~ 3 4 2 3 􀀎 p q x􀀎 2 x 􀀎 3 4 ii. iv. vi. 3x 2x 􀀐 5 3 3 x 􀀎 x 2 3x􀀐1 2x􀀎1 􀀎 3 2 TOTAL 24 MARKS Question sheet 2 Equations 1. Solve the following equations. Example: Solve 47 + 52 = 6 (X through by LCD to get rid of fractions) 47 × 20 + 52 × 20 = 6 × 20 ⇒ 4(4􀝔 + 7) + 5(5􀝔 + 2) = 120 then expand brackets, collect like terms and solve in usual way. . . 16􀝔 + 28 + 25􀝔 + 10 = 120 ⇒ 41􀝔 = 82 ∴ 􀝔 = 2 i. 7 y 􀀎 40 􀀠 5 ii. 5 􀀋x 􀀎 3 􀀌 􀀠 3 􀀋3x 􀀐1􀀌 iii. 5􀝔2 = 180 iv. ~~ ~~54 (2􀜿 − 1) = 3􀜿 − 2 v. ~~ ~~8~~ ~~2􀯫 + 24 = 12 vi. q􀀐 3 􀀠 q4 􀀎 3 vii. 16􀝔2 − 5 = 4 viii. 3 􀀋5 􀀐 2x􀀌 􀀠 2x3 ix. 􀯫82 = 3236 x. ~~ ~~43 + 􀝔 = 5􀯫+441 2. For each of the following, make the indicated letter the subject of the formula. i. 􀝕 = 10 − 4􀝔 (􀝔) ii. 􀜸 = 􀟨􀝎2 ℎ (ℎ) iii. 􀝏 = 12 (􀝑 + 􀝒)􀝐 (􀝐) iv. 􀝏 = 12 􀝃􀝐 2

FAQs

What should students do before their first A Level Maths lesson?

Complete all provided worksheets using your own paper and show full working, then mark your work using the solutions provided and bring the completed front sheet with transferred marks to the first lesson.

How are marks recorded?

Students transfer their marks from the worksheets to the front sheet and give themselves a total out of 120, adding notes if they need to explain any marks or indicate where help may be needed.

Which math topics are covered in the worksheets?

The task covers basic algebra, equations, quadratic equations, surds/fractional/negative indices, simultaneous equations, straight lines & gradients, and forming equations from worded questions.

Sep 5, 2026

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