Convert the number $562\,000$ into standard form .

Standard form is expressed as $a \times 10^b$ where $1 \le a < 10$. Moving the decimal point 5 places left gives $5.62 \times 10^5$.

Expand the algebraic brackets: $(x + 4)(x - 5)$

Using the distributive law (FOIL method): $x \times x = x^2$ $x \times -5 = -5x$ $4 \times x = 4x$ $4 \times -5 = -20$ Combining terms: $x^2 - x - 20$.

Find the value of $x$ in the equation $\frac{24}{x} = 4$.

Multiply both sides by $x$ to get $24 = 4x$. Dividing both sides by 4 results in $x = 6$.

Calculate the hypotenuse of a right-angled triangle with legs of length 3 cm and 4 cm.

Using Pythagoras' Theorem $a^2 + b^2 = c^2$: $3^2 + 4^2 = c^2$ $9 + 16 = c^2$ $25 = c^2$ $c = \sqrt{25} = 5\,\text{cm}$

Solve for $x$ and $y$ using simultaneous equations : $x + 5y = 15$ and $x + 3y = 11$.

Subtract the second equation from the first: $(x + 5y) - (x + 3y) = 15 - 11$ $2y = 4 \implies y = 2$ Substitute $y = 2$ into $x + 3(2) = 11 \implies x + 6 = 11 \implies x = 5$ Solution: $x = 5, y = 2$.

If two events $A$ and $B$ are independent , what is the probability of both occurring?

The probability of both independent events occurring is the product of their individual probabilities: $P(A \text{ and } B) = P(A) \times P(B)$.

Find the inverse function of $f(x) = 4x + 1$.

Let $y = 4x + 1$. Swap $x$ and $y$ to get $x = 4y + 1$. Rearrange for $y$: $x - 1 = 4y \implies y = \frac{x - 1}{4}$. The inverse function is $f^{-1}(x) = \frac{x - 1}{4}$.

Identify the relationship between speed and time for a fixed distance.

Speed and time are inversely proportional . As speed increases, the time taken to cover a fixed distance decreases proportionally, keeping the product (distance) constant.

Estimate the value of $\sqrt{55}$ to the nearest whole number.

Identify the nearest perfect squares: $\sqrt{49} = 7$ and $\sqrt{64} = 8$. Since 55 is closer to 49 than 64, $\sqrt{55} \approx 7$.

A circle has a radius of $r = 7\,\text{cm}$. Calculate its circumference using $\pi \approx 3.14$.

The formula for circumference is $C = 2\pi r$. Substituting the values: $C = 2 \times 3.14 \times 7 = 43.96\,\text{cm}$.

What happens to the inequality sign when you multiply or divide an inequality by a negative number?

The inequality sign reverses . For example, if $x -5$.

Determine the mean of a dataset if the total sum is 150 and there are 10 data points.

The mean is calculated as the sum of all values divided by the number of values: $\frac{150}{10} = 15$.

Explain the difference between rational and irrational numbers.

Rational numbers : Can be expressed as a fraction $\frac{a}{b}$ where $a, b$ are integers. This includes recurring decimals. Irrational numbers : Cannot be expressed as a simple fraction, such as $\sqrt{2}$ or $\pi$.

Cambridge Lower Secondary Mathematics Stage 9 Core Concepts And Applications Flashcards

Browse 1 flashcard sets with 15 cards for Cambridge Lower Secondary Mathematics Stage 9 Core Concepts And Applications in Stem. Study for free or create your own with AI.

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Flashcard Sets

Cambridge Lower Secondary Mathematics Stage 9 Core Concepts and Applications

This deck provides comprehensive practice on algebraic manipulation, geometric properties, statistical data interpretation, and advanced arithmetic for Stage 9 mathematics learners.

15 cards

intermediate

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by @yasser_al_wahidi

Q: Simplify the expression using index laws: $4^2 \div 4^{-4}$

Q: Determine the sum of interior angles for a polygon with $n = 8$ sides.

Q: Convert the number $562\,000$ into <strong>standard form</strong>.

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