Westminster Math Difficult One - Best Buys - Conversion Graphs - LCM/HCF - Compound Interest - Reverse Percentages

Aug 25, 2026

Uploaded by Aurelia

Set of challenging Westminster-style math questions covering multiple topics across algebra, number theory, and problem solving. Tasks include converting between currencies using conversion graphs, calculating LCM/HCF, modelling decay with compound interest percentages, reversing percentage loss to find an original amount, and counting problems using product rule constraints. The sheet also includes bracket expansion, factorising quadratics, sequence nth-term calculations, rearranging formulas, inequalities and regions, line geometry, iteration, tangent equation, curve area and graph sketching, and an algebraic proof task.

LanguageEnglish

CategoryExam

FormatPDF

Pages21

Reading Time53 min

AccessFree to download

Best Buys

Conversion Graphs

LCM/HCF

Compound Interest

Reverse Percentages

Product Rule for Counting

Expanding Two/Three Brackets

Factorising Quadratics

nth Term-Linear

Quadratic nth Term

Changing the Subject

Inequalities-Regions

Quadratic Inequalities

Parallel/Perpendicular Lines

Iteration

Equation of a Tangent

Area Under a Curve

Quadratic Graphs

Algebraic Proof

1. BEST BUYS Two shops sell the same type of perfume. A 100ml bottle of perfume normally costs £40. 3. CONVERSION GRAPHS (a) Change £30 into Euros. ......................... Euros (2) (b) Change 200 Euros into Pounds (£) +998944905775 @westminstermath £......................... (2) 4. LCM/HCF Find the lowest common multiple (LCM) of 28 and 63. +998944905775 @westminstermath (2) 5. COMPOUND INTEREST A radioactive substance decays over time. Every year its mass decreases by 14% . How many years will it take for 500kg of the substance to decay to a mass less than 200kg? .........................years (3) 6. REVERSE PERCENTAGES A ﬁsh tank sprung a leak and loses 45% of its water. There is now 363 litres of water in the ﬁsh tank. How much water was in the ﬁsh tank before the leak? .........................l 7. PRODUCT RULE FOR COUNTING Jim picks a ﬁve digit even number. The second digit is less than 5. The fourth digit is a cube number. The ﬁrst digit is a prime number. How many different numbers could he pick? +998944905775 @westminstermath (3) 8. EXPANDING TWO/THREE BRACKETS (a) Expand and simplify (x + 9)(x − 4) (2) (b) Expand and simplify (x + 1)(x + 2)(x − 3) ............................. (2) 9. FACTORISING QUADRATICS (a) Factorise x² − x − 30 (2) (b) Factorise 3y² + 10y − 8 10. NTH TERM-LINEAR The ﬁrst 5 terms in a number sequence are 2 2.5 3 3.5 4 (a) Work out the nth term of the sequence. (2) (b) Work out the 20th term of the sequence. (2) 11. QUADRATIC NTH TERM Here are the ﬁrst 5 terms of a quadratic sequence 4 10 18 28 40 Find an expression, in terms of n, for the nth term of this quadratic sequence. +998944905775 @westminstermath 12. CHANGING THE SUBJECT Rearrange y + 3 = x(y + 2) to make y the subject of the formula. y = ......................... (4) 13. INEQUALITIES-REGIONS The region labelled R satisﬁes three inequalities. State the three inequalities 14. QUADRATIC INEQUALITIES Solve the inequality 2x² + 9x + 10 > 0 (4) 15. PARALLEL/PERPENDICULAR LINES The straight line K has equation y = 2x − 5 The straight line J is perpendicular to line K and passes through the point (−4, 8) . Find the equation of line J (3) 16. ITERATION (a) Show that the equation 3x − x³ = −11 can be rearranged to give +998944905775 @westminstermath +998944905775 @westminstermath (3) 17. EQUATION OF A TANGENT Here is a circle, centre O, and the tangent to the circle at the point (2, −4) . Find the equation of the tangent at the point P. 18. AREA UNDER A CURVE Harry and Jack ran a 300 metre race. Here is a graph for the ﬁrst 4 seconds of Harry’s race. Harry completed the race at a constant speed of 6 m/s Jack completed the race in 51 seconds. Did Harry ﬁnish before Jack? You must show your working. …………………………………………………………………………………………… …………………………………………………………………………………………… (3) +998944905775 @westminstermath 19. QUADRATIC GRAPHS On the grid, draw the graph of y = x² + x + 2 for the values of x from-3 to 3. (2) 20. ALGEBRAIC PROOF Prove the sum of four consecutive odd numbers is always a multiple of 8 98944905775westminstermath (4)

FAQs

What topics are included in this Westminster math worksheet?

It includes currency conversion, LCM/HCF, compound interest and reverse percentages, counting by product rule, algebraic expansion and factorising, sequence nth terms, inequalities, line equations, iteration, tangents, graphing, and algebraic proof.

How do the compound interest and reverse percentages questions work?

The compound interest question models percentage decay over years to reach a target mass. The reverse percentages question finds the original amount by using the given percentage loss and the current quantity.

What kinds of graph and geometry tasks appear on the sheet?

There are tasks such as drawing quadratic graphs for given x-values and finding the equation of a tangent line to a circle at a specified point, plus a question comparing race completion times using a graph.

Aug 25, 2026

Uploaded by Aurelia