Summary
Highlights
This section tackles questions involving fractions and percentages from past papers. It covers evaluating expressions with fractions, converting mixed numbers to improper fractions, and solving problems involving discounts and percentage increases/decreases, including examples with late payment charges and annual profit appreciation.
Learn to evaluate and perform calculations in standard form and scientific notation. Examples include calculating the weight of a pollen grain, determining the number of platelets in blood, and finding the volume of Earth given Venus's volume as a percentage.
This part focuses on calculating the volume of spheres, such as Earth, and comparing it to other celestial bodies like the Moon. It also delves into simplifying surds and rationalizing denominators in fractional expressions involving square roots.
Explore the laws of indices, including negative and fractional powers. The section then transitions into expanding and simplifying complex algebraic expressions, including those with multiple brackets and binomials.
Master techniques for factorizing quadratic expressions, including the difference of two squares and trinomials. This knowledge is then applied to simplifying algebraic fractions, including those involving division and subtraction.
Learn to solve quadratic equations by factorizing, identifying common factors, and using double brackets. This section also covers simplifying algebraic fractions further by cancelling common terms after factorization.
This part introduces functions, focusing on evaluating functions for given values and solving for unknown variables when the function's output is provided. It also touches on rationalizing denominators involving surds within functions.
Understand how to find the equation of a straight line given two points, and how to rearrange equations to identify the gradient and y-intercept. The concepts are extended to real-world scenarios like a line of best fit for fuel consumption and determining where a line crosses the x or y-axis.
This section covers solving linear equations, including those with fractions, by finding the lowest common multiple. It then moves to solving linear inequalities, emphasizing how to handle negative coefficients and the implications for the inequality sign.
Master solving systems of simultaneous linear equations by finding common coefficients and adding or subtracting equations. Examples include finding the intersection point of two lines and solving real-world problems like the cost of mangoes and apples.
Learn various techniques for changing the subject of a formula, including cases with fractions, brackets, squares, and square roots. The focus is on isolating the desired variable by applying inverse operations systematically.
This part explains completing the square to express quadratic equations in vertex form, which helps in identifying turning points and the axis of symmetry for parabolas. It also covers sketching quadratic graphs, showing roots, y-intercepts, and turning points.
Apply the quadratic formula to solve complex quadratic equations, including those where factorization is not straightforward or non-calculator settings. This section features real-world problems like a ball kicked from a cliff and calculating dimensions of a rectangular card.
Understand how to use the discriminant (B squared minus 4AC) to determine the nature of the roots of a quadratic equation. This includes identifying if there are no real roots, two equal real roots, or two distinct real roots.
Learn to find the gradient of a line joining two points, even when the coordinates involve algebraic expressions. This involves using the standard gradient formula and then simplifying the resulting algebraic fraction by factorizing.
This section covers calculating arc length and area of a sector. It includes examples for both calculator and non-calculator papers, emphasizing how to simplify fractions and use formulas effectively. Specific problems involve attraction rides and parts of circles.
Master calculating volumes of composite shapes, specifically those involving cones and spheres where a smaller shape is removed from a larger one. Examples include finding the volume of a carton and a chocolate-covered sweet, requiring careful consideration of radii and heights.
Learn to calculate the height of a pyramid given its volume and base dimensions by inverting the volume formula. This section also revisits cone volume calculations, stressing the importance of using given values for Pi and handling non-calculator scenarios.
Explore applications of Pythagoras' theorem in 3D, including calculating the height of a tunnel from its cross-section and determining if an umbrella fits in a locker by finding the space diagonal of a cuboid. The importance of identifying relevant lengths and using correct formulas is highlighted.
This part delves into calculating angles within regular polygons (like a decagon) and circles. It covers properties of isosceles triangles, angles on a straight line, and angles formed by tangents and radii. Examples include complex angle calculations in geometrical figures.
Learn to calculate the area of a triangle using the formula: Area = 0.5 * a * b * sin(C). This section includes applications in both calculator and non-calculator contexts, emphasizing the requirement for the angle to be between the two known sides.
Master the sine rule (a/sinA = b/sinB = c/sinC) to find unknown sides or angles in triangles. Examples include calculating angles in step ladders and determining the height of a hot air balloon by breaking down complex problems into smaller triangles.
Learn to use the cosine rule (a² = b² + c² - 2bc cosA) to find an unknown side when two sides and the included angle are known, or to find an unknown angle when all three sides are known. Real-world applications include fence lengths and bearings in navigation problems.
This section covers interpreting trigonometric graphs (sine and cosine), identifying amplitude and period (value of B). It also teaches solving trigonometric equations, including those involving shifts and vertical transformations, and finding all possible solutions within a given range using the CAST diagram.
Simplify trigonometric expressions using identities such as sin(x)/cos(x) = tan(x) and sin²(x) + cos²(x) = 1. Examples include simplifying complex fractions and expanding squared trigonometric expressions.
Learn to calculate the mean and standard deviation of a data set. This includes setting up tables for calculations and interpreting the results to make valid comparisons about average performance and consistency between different groups.
Understand how to calculate the median, lower quartile, upper quartile, and semi-interquartile range for a given data set. This involves ordering the data and finding central values. It also includes making comparative statements about data sets based on these statistical measures.
Revisit finding the equation of a line of best fit from a scatter graph, interpreting it in terms of real-world variables like fuel consumption, and using the equation to make predictions. This section also covers setting up cost functions for services like taxis based on distance.