Exam Instructions and Setup

Your GCSE maths paper covers the essential basics you need to know before diving into the questions. This non-calculator paper means you'll need to rely on your mental maths and written methods - no shortcuts allowed!

You've got 90 minutes to tackle 80 marks, so that's roughly just over a minute per mark. The paper includes everything from basic multiplication to complex algebraic problems, so pacing yourself is crucial.

Top Tip: The marks in brackets tell you exactly how much time and effort to spend on each question - use them as your guide!

Remember to bring your geometric tools (ruler, protractor, compasses) as you'll need them for construction questions. Always show your working clearly, even when the answer seems obvious to you.

Basic Multiplication Without Calculator

Question 1 asks you to work out 6.3 × 2.4 using only pen and paper - no calculator allowed! This tests your ability to handle decimal multiplication manually.

The key is breaking it down systematically. You can use the traditional long multiplication method or split it into parts: (6 + 0.3) × (2 + 0.4). Either way works as long as you show every step clearly.

Remember: In non-calculator papers, the arithmetic is designed to work out neatly - trust the process!

This 3-mark question might seem straightforward, but those marks are often lost through careless errors. Double-check your decimal point placement and addition of partial products.

Powers and Indices Rules

Question 2 tests your understanding of index laws - those crucial rules about powers that trip up loads of students. You need to know that any number to the power of 0 equals 1, so 5⁰ = 1.

For negative indices like 5⁻², remember this means 1 divided by 5², which gives you 1/25 or 0.04. It's the reciprocal of the positive power.

The algebraic part asks you to simplify 2⁵ × 2⁴ ÷ 2³ using index laws. When multiplying powers with the same base, you add the indices. When dividing, you subtract them.

Quick Check: 2⁵⁺⁴⁻³ = 2⁶ - always combine the operations step by step to avoid mistakes!

Prime Factors and HCF

Question 3 focuses on prime factorisation - breaking numbers down into their basic building blocks. To write 156 as a product of prime factors, you'll need to divide repeatedly by prime numbers (2, 3, 5, 7, 11...).

Start with the smallest primes: 156 ÷ 2 = 78, then 78 ÷ 2 = 39, then 39 ÷ 3 = 13. Since 13 is prime, you're done! So 156 = 2² × 3 × 13.

Finding the highest common factor (HCF) of 156 and 130 means identifying the largest number that divides both. You'll need to find 130's prime factors too, then pick out the common ones.

Pro Tip: Drawing factor trees can help you visualise the process and avoid missing any prime factors!

Mean and Statistics Problems

Question 4 is all about mean calculations and how changing data affects your results. If 5 sticks have a mean length of 4.2 cm, their total length must be 5 × 4.2 = 21 cm.

When you know one stick is 7 cm, the other four must total 21 - 7 = 14 cm. So their mean is 14 ÷ 4 = 3.5 cm.

The twist comes when that 7 cm stick is actually 17 cm. This adds an extra 10 cm to the total, so the mean of the other four sticks increases by 10 ÷ 4 = 2.5 cm.

Key Insight: When one value changes in a data set, you can work out the effect on the mean without recalculating everything!

Geometric Construction

Question 5 tests your compass and ruler skills - no protractor allowed for this one! You need to construct a perfect 90° angle at point P using only traditional geometric methods.

The standard method involves drawing arcs from P to intersect line AB at two points. Then, from these intersection points, draw arcs of the same radius that cross each other above and below the line.

Join these crossing points to P, and you've got your perpendicular line! The key is keeping your compass radius consistent and making clear, accurate arcs.

Construction Tip: Don't rub out your construction lines - the examiners need to see them to award full marks!

Angle Properties in Triangles

Question 6 combines isosceles triangles with angle relationships. Since triangle ABD is isosceles with BA = BD, the base angles are equal - this is fundamental to solving the problem.

The ratio x:y = 2:1 gives you a relationship between two of the angles. You'll need to use the fact that angles on a straight line sum to 180°, and angles in a triangle also sum to 180°.

Setting up equations using these angle properties will lead you to the value of w. Remember that isosceles triangles have two equal angles opposite the equal sides.

Angle Alert: Keep track of which angles are equal and which add up to 180° - draw clear labels on your diagram!

Algebraic Word Problems

Question 7 is a classic algebra problem disguised as a real-world scenario about books on shelves. You need to set up an equation using the given expressions: x + $3x + 1$ + $2x - 5$ = 44.

Simplifying gives you 6x - 4 = 44, so 6x = 48, which means x = 8. This tells you there are 8 books on shelf A and 3(8) + 1 = 25 books on shelf B.

Since shelf B's 25 books weigh 7500g total, each book weighs 300g. Therefore, shelf A's 8 books weigh 8 × 300 = 2400g.

Word Problem Strategy: Always define what your variable represents clearly, then translate the words into mathematical expressions!

Percentage Problems and Reverse Calculations

Question 8 is a reverse percentage problem - you know the sale price and need to find the original price. If the mattress is reduced by 40%, the sale price represents 60% of the original.

So £660 = 60% of the original price. To find 100%, you can set up the proportion: if £660 is 60%, then the original price is £660 ÷ 0.6 = £1100.

Alternatively, think of it as £660 ÷ 60 × 100 = £1100. Both methods work - choose the one that makes most sense to you.

Percentage Hack: When working backwards from a percentage, always identify what percentage the given amount represents first!

Ratio and Linear Graphs

Question 9 connects ratios with coordinate geometry. The ratio 4:5 for rice to water means for every 4 cups of rice, you need 5 cups of water - this creates a straight line through the origin.

Your graph should show points like (4,5), (8,10), etc. The gradient of this line is 5/4 or 1.25, which you calculate using rise over run.

This gradient has real meaning - it represents how many cups of water you need per cup of rice. It's the constant multiplier that converts rice quantities into water quantities.

Graph Connection: The gradient in ratio problems always represents the rate of change between the two quantities!