Cambridge IGCSE Mathematics Paper 2 Specimen B

7 cm

5 cm

5 cm

<p>$20\pi$ $cm^2$</p> Signup and view all the answers

<p>5 cm</p> Signup and view all the answers

<p>6 $cm^2$</p> Signup and view all the answers

<p>20 $cm^3$</p> Signup and view all the answers

<p>(4, -6)</p> Signup and view all the answers

<p>(7, 15)</p> Signup and view all the answers

<p>$ 4\sqrt{3}$</p> Signup and view all the answers

<p>$-2 - 2\sqrt{5}$</p> Signup and view all the answers

<p>$ \frac{\sqrt{13}}{7}$</p> Signup and view all the answers

<p>$6x^3 - 16x^2$</p> Signup and view all the answers

<p>$(x-19)(x+19)$</p> Signup and view all the answers

<p>6200</p> Signup and view all the answers

<p>800 newtons/cm^2</p> Signup and view all the answers

<p>(-6, 1)</p> Signup and view all the answers

<p>(-1, -3)</p> Signup and view all the answers

<p>(-20, 3)</p> Signup and view all the answers

<p>4.5</p> Signup and view all the answers

<p>40.5</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>2:5</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>27</p> Signup and view all the answers

<p>25</p> Signup and view all the answers

<p>22 3/4</p> Signup and view all the answers

<p>$b^2 - 4ac$</p> Signup and view all the answers

<p>$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$</p> Signup and view all the answers

<p>$a^2 = b^2 + c^2 - 2bc\cos A$</p> Signup and view all the answers

<p>$\frac{1}{2}ab\sin C$</p> Signup and view all the answers

<p>Rotation of 180 degrees about the origin.</p> Signup and view all the answers

<p>38/99</p> Signup and view all the answers

<p>18</p> Signup and view all the answers

<p>20</p> Signup and view all the answers

<p>$\begin{pmatrix} 4 \ 8 \end{pmatrix}$</p> Signup and view all the answers

<p>$4\sqrt{5}$</p> Signup and view all the answers

<p>12</p> Signup and view all the answers

<p>$150\pi$</p> Signup and view all the answers

<p>$(x-4)^2 - 6$</p> Signup and view all the answers

A mathematical formula used to calculate the area of a triangle. It states that the area (A) is equal to half the product of the base (b) and the height (h).

A mathematical formula used to calculate the area of a circle. It states that the area (A) is equal to pi (π) multiplied by the square of the radius (r).

A mathematical formula used to calculate the circumference of a circle. It states that the circumference (C) is equal to 2 times pi (π) multiplied by the radius (r).

A mathematical formula used to calculate the curved surface area of a cylinder. It states that the curved surface area (A) is equal to 2 times pi (π) multiplied by the radius (r) multiplied by the height (h).

A mathematical formula used to calculate the curved surface area of a cone. It states that the curved surface area (A) is equal to pi (π) multiplied by the radius (r) multiplied by the sloping edge (l).

A mathematical formula used to calculate the surface area of a sphere. It states that the surface area (A) is equal to 4 times pi (π) multiplied by the square of the radius (r).

A mathematical formula used to calculate the volume of a prism. It states that the volume (V) is equal to the cross-sectional area (A) multiplied by the length (l) of the prism.

The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0, where a ≠ 0. It provides the values of x that satisfy the equation.

The sine rule relates the sides and angles of a triangle. It states that the ratio of the length of a side to the sine of the angle opposite that side is constant for all sides of the triangle.

The cosine rule relates the sides and angles of a triangle. It states that the square of a side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.

The area of a triangle can be calculated by multiplying half the product of two sides by the sine of the included angle.

Simplifying a ratio means finding the simplest equivalent form by dividing both parts of the ratio by their greatest common factor.

A kite is a quadrilateral with two pairs of adjacent sides equal. It has one line of symmetry that bisects the angle between the two unequal sides.

The range of a dataset is the difference between the highest and lowest values in the dataset.

The median of a dataset is the middle value when the data items are arranged in ascending order. If the number of data items is even, the median is the average of the two middle values.

A pie chart is a graphical representation of data using sectors of a circle. The proportion of each sector represents the proportion of the corresponding data value in the whole dataset.

Expanding an expression means multiplying each term inside the parentheses by the factor outside.

Factoring an expression involves finding two or more expressions that multiply to give the original expression.

To calculate the pressure applied on a surface, you divide the force by the area of the surface.

Rounding a number to 1 significant figure means keeping only the most important digit (the leftmost non-zero digit) and setting all other digits to 0.

A reflection in the line y = x + 2 is a transformation that flips a shape over the line y = x + 2. Each point in the shape reflects to a point on the opposite side of the line, at the same distance from the line.

An enlargement by scale factor 3 with center (1, 0) is a transformation that makes a shape 3 times bigger. The center (1, 0) is a fixed point from which the shape is scaled.

The image of a shape after a reflection or enlargement is the transformed shape that results from the transformation.

A reflection is a transformation that flips a shape across a line. Each point in the shape is reflected to a point on the opposite side of the line, at the same distance from the line.

An enlargement is a transformation that makes a shape bigger or smaller. The scale factor determines how much bigger or smaller the shape becomes.

A scale factor is a number that tells you how much bigger or smaller a shape becomes after an enlargement.

The turning point of the graph is the point where the graph changes from increasing to decreasing or vice versa. The y-intercept is the point where the graph crosses the y-axis.

The gradient of a graph at a point is the slope of the tangent line at that point. The tangent line is a straight line that touches the curve at that point and has the same slope as the curve at that point.

The turning point of a parabola is the point where the gradient is zero.

To rationalise the denominator of a fraction, you multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of a binomial expression (for example, 1 - √5) is the same expression but with the opposite sign between the terms (for example, 1 + √5).

To expand and simplify an expression, you multiply out the brackets and then combine like terms. It's helpful to use the distributive property to multiply each term in one bracket with each term in another bracket.

A transformation that changes the size and/or orientation of a shape. It involves scaling and/or rotation.

To convert a decimal to a fraction, write the decimal as a fraction with the denominator being a power of 10. Then simplify the fraction to its simplest form.

A percentage is a way of expressing a part of a whole as a fraction of 100. To calculate a percentage decrease, subtract the new value from the original value, divide the difference by the original value, and multiply by 100.

The length of a line segment is the distance between its endpoints. To find the length of a line segment, use the distance formula or the Pythagorean theorem.

The area of a sector is a fraction of the area of the entire circle. To calculate the area of a sector, use the formula: Area of sector = (θ/360) * πr^2, where θ is the central angle of the sector and r is the radius of the circle.

The perimeter of a sector is the sum of the lengths of the arc and the two radii. To calculate the perimeter of a sector, use the formula: Perimeter of sector = (θ/360) * 2πr + 2r, where θ is the central angle of the sector and r is the radius of the circle.

The volume of a prism is the product of the area of its cross-section and its length. To calculate the volume of a prism, use the formula: Volume of prism = Area of cross-section * length

The total surface area of a prism is the sum of the areas of all its faces. To calculate the total surface area, calculate the areas of each of its faces and add them up.

Completing the square is a technique used to rewrite a quadratic expression in the form (x - a)^2 + b. To complete the square, take half of the coefficient of x, square it, and add and subtract it from the expression.

A quadratic expression is an expression that can be written in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. It can be graphed as a parabola.