GCSE Maths 2027 predicted topics

$\theta$ is an acute angle.

(a) $\cos\theta = \frac{\sqrt{3}}{2}$. Write down the value of $\theta$.

(b) Work out the value of $\sin 90^\circ - \cos 0^\circ + \tan 45^\circ$.

The diagram shows triangle PQR.

(a) Find the exact length of PR.

(b) Find the exact length of QR.

A straight line has equation $y = 2x - 1$.

(a) Work out the value of $y$ when $x = -1$.

(b) Write down the gradient of the line.

(c) Write down the $y$-coordinate of the point where the line crosses the $y$-axis.

A table of values for a straight line gives y = 7, 4, 1 and −2 when x = −1, 0, 1 and 2.

(a) Write down the y-intercept of the line.

(b) Find the gradient of the line.

(c) Write down the equation of the line.

Find the coordinates of the turning point of $y = x^{2} + 10x + 17$.

$y=x^2-6x+10$.

(a) Write y in completed-square form.

(b) Find the minimum point.

The cumulative frequency graph shows information about the waiting times of 80 people.

Use the graph to find an estimate for the number of people who waited more than 25 minutes.

The cumulative frequency graph shows information about 120 processing times.

Use cumulative frequencies 30 and 90 for the lower and upper quartiles.

A new process changes every time according to $u = 1.2t + 3$.

Use the graph to estimate the interquartile range of the new times. Give your answer to 1 decimal place.

Solve the simultaneous equations 2x + y = 13 and x $-$ y = 2. Give your answer as (x, y).

Solve the simultaneous equations $3x + 2y = 16$ and $5x - 2y = 8$.

Find the values of $x$ and $y$. Give your answer as $(x, y)$. You must show your working.

Two fair six-sided dice are rolled and their scores are added.

(a) Work out the probability that the total is 7.

(b) Work out the probability that the total is more than 10.

Four cards are labelled 1, 1, 2 and 3. Two cards are chosen at random without replacement. Work out the probability that their numbers add to 4. Give a fraction in its simplest form.

Point P has coordinates ($-3$, 5). It is translated by the column vector (7, $-9$), meaning 7 units right and 9 units down. Write the coordinates of its image.

Point A is $(3,-2)$. Rotate A 90 degrees anticlockwise about the origin.

(a) Find the image coordinates.

(b) Find the image after another 90 degree anticlockwise turn.

The scatter graph shows the length and mass of 12 objects of one type. A line of best fit has been drawn.

Use the line of best fit to estimate the mass of an object of length 24 cm.

The scatter graph shows the hours of revision and the test scores of 12 students.

(a) Write down the type of correlation.

(b) Kai says, "This proves that revising more causes higher scores." Explain why Kai is wrong.

A bag contains 2 blue counters and 5 white counters. A counter is taken at random, replaced, and then another counter is taken at random. Work out the probability that both counters are blue. Give a fraction in its simplest form.

A bag contains 5 red counters and 3 blue counters. Two counters are taken at random, one after the other, without replacement.

Work out the probability that both counters are the same colour.

There are $2000$ bacteria in a dish. The number of bacteria increases by $50\%$ each day.

Work out the number of bacteria after 3 days.

£1500 is invested at 4% compound interest per year. Interest is added at the end of each year. What is the least whole number of years before the balance exceeds £1750? You must show your working.