Pearson Edexcel GCSE Mathematics May 2019
Foundation Tier – Paper 1 (Non-Calculator)

What are we being asked to find?

We need to convert a time value from minutes to hours. To do this, we need to know how many minutes are in one hour.

Why we do this:

There are 60 minutes in 1 hour. To find the number of hours, we divide the total minutes by 60.

What are we being asked to find?

We need to express the decimal number 0.73 as a percentage.

Why we do this:

“Percent” means “out of 100”. To convert a decimal to a percentage, we multiply by 100.

What are we being asked to find?

We need to solve an arithmetic expression using the correct order of operations.

Why we do this:

We use BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction). We must always calculate the content inside the Brackets first.

What are we being asked to find?

We need to find a number between 20 and 30 that has exactly two factors: 1 and itself.

Why we do this:

Let’s check the numbers between 20 and 30:

• 21: \(3 \times 7\) (Not prime)
• 22: Even (Not prime)
• 23: Prime
• 24: Even (Not prime)
• 25: \(5 \times 5\) (Not prime)
• 26: Even (Not prime)
• 27: \(3 \times 9\) (Not prime)
• 28: Even (Not prime)
• 29: Prime

What are we being asked to find?

We need the average (mean) of the two numbers.

Why we do this:

To find the halfway point, we add the two numbers together and divide by 2.

What are we being asked to find?

We need to find the total bill for one person first. The travel and spending money are fixed, but the hotel cost depends on the number of days (7).

Why we do this:

Now that we know one person costs £750, we multiply this by 4 to get the grand total for the whole group.

What this tells us:

The total budget Harry needs to plan for the entire holiday group is £3000.

Why we do this:

We know the total is 30. If we subtract all the flowers we know about (Red, White, and Yellow), the leftover must be the Blue ones.

What this tells us:

The “mode” is the value that appears most often. In a bar chart, it is the tallest bar.

Why we do this:

It is difficult to compare fractions with different denominators. We find a number that 3, 4, 12, and 2 all go into. The Lowest Common Multiple is 12.

What this tells us:

Now we order the fractions by looking at the top numbers (3, 4, 6, 7, 9) and then write back the original fractions.

How we find this:

Distance = Speed × Time. First, we find the duration of her walk from 9 am to 10:30 am.

Why we do this:

We add the duration of her stay and the duration of her walk home to her arrival time at the library.

To find \( x \), we perform the opposite of subtracting 2, which is adding 2 to both sides.

First, isolate the term with \( w \) by subtracting 2. Then, divide by 6.

What are we being asked to find?

We need to find the product of two 2-digit numbers. Since this is a non-calculator paper, we must show a clear arithmetic method like long multiplication or the grid method.

What this tells us:

By breaking the multiplication into smaller parts (\( 8 \times 74 \) and \( 50 \times 74 \)) and adding them, we find that the total is 4292.

Why we do this:

The term “perpendicular” means the total angle between the lines is \( 90^\circ \). The three smaller angles must add up to this total.

How we know:

On parallel lines, specific pairs of angles are equal due to geometric properties. We are looking for an angle that matches the \( 125^\circ \) provided.

What this tells us:

A full circle of angles around a single point adds up to \( 360^\circ \). The angles \( a, b, c \) and the given \( 125^\circ \) together form a complete turn.

Why we do this:

There are 10 millimetres (mm) in 1 centimetre (cm). To change from cm to mm, we must multiply by 10.

To find one fifth, we divide the total by 5.

Why we do this:

When you divide a number by a value smaller than 1 (like \( \frac{1}{2} \)), the answer gets larger. Fiona correctly identifies there are 2 halves in every 1, but she then divided 48 by 2 instead of multiplying 48 by 2.

We need a number that, when multiplied by itself, equals 64.

A “cube” means multiplying the number by itself, then by itself again (three times total).

Why we do this:

To “expand” means to multiply the term outside the bracket by every term inside the bracket.

How we find this:

Factorising is the opposite of expanding. we look for the Highest Common Factor of \( 3n \) and \( 12 \), which is 3, and place it outside the bracket.

Why we do this:

In probability, the more times an experiment is carried out (the larger the sample size), the more reliable the estimate becomes. This reduces the effect of random luck.

How we find this:

To get the best possible estimate, we combine all the data from both people to find the total number of Tails relative to the total number of throws.

Why we do this:

We need to figure out how many 30cm stones fit along the length and the width of the path.

How we find this:

We multiply the 80 stones by the cost of each stone (£2.50).

What this tells us:

We compare the total cost to Wasim’s budget of £220.

Why we do this:

To subtract fractions, we must have a common denominator. The Lowest Common Multiple of 3 and 5 is 15.

How we find this:

Multiplying is simpler: multiply the top numbers (numerators) together and multiply the bottom numbers (denominators) together. Then simplify.

How we find this:

Let’s use simple numbers to represent the sides. If Square B has a side length of 2, then Square A (at 50%) has a side length of 1.

Why we do this:

The shaded part of Square A is exactly half of its area (\( 0.5 \text{ units}^2 \)). We need to find what percentage this is of Square B’s area (4).

What are we being asked to find?

We need the total number of walkers (boys + girls). We already know 9 girls walk, so we need to find how many boys walk.

Why we do this:

We have enough information to find how boys travel. If we know the total boys and how many bus and cycle, the remainder must walk.

What this tells us:

Finally, we combine the walking girls and walking boys to answer the question.

Why we do this:

The sum of all probabilities in a mutually exclusive set must equal 1. Since Red and Yellow cubes are equal in number, their probabilities must also be equal.

How we find this:

Probability is defined as \( \frac{\text{Quantity}}{\text{Total}} \). We know 12 cubes represent a probability of 0.2.

How we find this:

First, we find the amount of flour for 15 biscuits. Then, we find the “scale factor” to get from 15 biscuits to 60 biscuits.

Why we do this:

We need to find the total grams of butter needed and then see how many 250g packs are required. We must round up to the nearest whole pack.

Why we do this:

The HCF is the largest number that divides exactly into both 72 and 90. We can list the factors of each and pick the largest one they share.

How we find this:

We look at the three views. A “Plan” (view from the top) that is a circle, combined with “Elevations” (views from the side/front) that are rectangles, identifies the shape as a cylinder.

Why we do this:

We need to perform the first part of the transformation to see where the intermediate shape lands. Reflection in the \( x \)-axis flips the shape vertically, changing the sign of the \( y \)-coordinates.

How we find this:

We compare a corresponding vertex of our reflected shape to shape B. Let’s look at the “right-angle” vertex.

What this tells us:

The vector \( \binom{-6}{-1} \) tells us to move the shape 6 units left and 1 unit down.

Why we do this:

The 212 total is for individual pens, but the ratio is for packs. We need to multiply each part of the ratio by the number of pens in that pack.

How we find this:

We add the parts of the pen ratio and divide the total number of pens (212) by this sum.

What this tells us:

Multiply the “Green” part of the pen ratio (24) by the value per part (4).

Why we do this:

We know the area and one side (\( QR = 10 \)) of \( PQRS \). We can find the other side length, \( PQ \).

How we find this:

The question states \( BC = PQ \). So we now know the height of the first rectangle.

What this tells us:

Perimeter is the sum of all four sides. For a rectangle, it is \( 2 \times (\text{Length} + \text{Width}) \).

What are we being asked to find?

The turning point is the vertex of the parabola—the exact point where the curve stops going down and starts going up (the minimum point).

How we find this:

The “roots” of the equation are the values of \( x \) where the graph crosses the \( x \)-axis (where \( y = 0 \)).