Stage 9 Maths Paper 2

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Questions and Answers

When substituting a value for $x$ in the expression $\frac{3(x-2)^2}{5}$, which operation is performed first?

  • Square
  • Divide by 5
  • Multiply by 3
  • Subtract 2 (correct)

A book is measured to be 25 cm to the nearest centimeter. Which of the following represents the range of possible lengths for the book?

  • 24.0 cm ≤ length < 26.0 cm
  • 24.5 cm ≤ length < 25.5 cm (correct)
  • 24.5 cm < length ≤ 25.5 cm
  • 24.0 cm < length < 26.0 cm

In the diagram with two straight lines crossing a pair of parallel lines, which of the following statements are both correct regarding angle a?

  • Angle *a* is corresponding to angle *b*, and angle *a* is vertically opposite to angle *e*.
  • Angle *a* is equal to angle *d*, and angle *a* is vertically opposite to angle *e*. (correct)
  • Angle *a* is corresponding to angle *b*, and angle *a* is alternate to angle *c*.
  • Angle *a* is alternate to angle *c*, and angle *a* is equal to angle *d*.

What is the measure of each interior angle in a regular pentagon?

<p>108° (A)</p> Signup and view all the answers

A prism has a regular pentagon as its cross-section. How many planes of symmetry does this prism have?

<p>6 (A)</p> Signup and view all the answers

A cylinder has a radius of 7 cm and a height of 15 cm. What is the volume of the cylinder?

<p>2310 cm³ (A)</p> Signup and view all the answers

Given the equation $y = x^2 - 4$, what are the y-values when $x = -2$ and $x = 2$?

<p>y = 0 and y = 0 (C)</p> Signup and view all the answers

In a set of temperature data from 20 cities, the median temperature falls within a certain range. Which statement correctly describes the median temperature?

<p>The median temperature is the middle value when the temperatures are arranged in order. (A)</p> Signup and view all the answers

What is the greatest possible range of temperatures, given the intervals, $6 \le t < 8$, $8 \le t < 10$, $10 \le t < 12$, $12 \le t < 14$, and $14 \le t < 16$?

<p>10°C (D)</p> Signup and view all the answers

Two lines have equations $y = 2x + 1$ and $y = 6x + 1$. Besides both being straight lines and having a positive gradient, what other property do they share?

<p>They have the same y-intercept. (B)</p> Signup and view all the answers

Shape Q is an enlargement of shape P. What transformation fully describes this?

<p>Enlargement (B)</p> Signup and view all the answers

What information do you need to describe an enlargement fully?

<p>The scale factor and center of enlargement (B)</p> Signup and view all the answers

A semi-circle has a radius of 12.3 cm. Which calculation gives the perimeter of the semi-circle?

<p>$24.6 + \pi (12.3)$ (B)</p> Signup and view all the answers

It takes 5 workers 300 minutes to decorate some cakes. How long would it take 12 workers to decorate the same number of cakes, assuming they work at the same rate?

<p>125 minutes (B)</p> Signup and view all the answers

Laptop A costs $650 and its price increases by 12%. Laptop B costs $760 and its price decreases by 5%. After these changes, which laptop is more expensive?

<p>Laptop B (A)</p> Signup and view all the answers

The (n)th term of a sequence is (n^2 + a). If the 6th term of the sequence is 29, what is the sum of the first 4 terms?

<p>25 (C)</p> Signup and view all the answers

Make $t$ the subject of the formula: $w = \frac{2t}{5} - 1$.

<p>$t = \frac{5(w + 1)}{2}$ (B)</p> Signup and view all the answers

Rajiv sells balloons that are colored red, green, blue, or yellow. 25% are red. The probability of getting green is 0.05. The probability of blue is twice the probability of green. What is the probability of getting a yellow balloon?

<p>0.65 (B)</p> Signup and view all the answers

Bag A contains 56 counters shared between Angelique and Hassan in the ratio 3:5. Bag B contains counters shared between Angelique and Hassan in the ratio 4:3. If Angelique receives 45 counters in total, how many counters are in Bag B?

<p>21 (B)</p> Signup and view all the answers

A music teacher, Gabriella, wants to know if children in her school like music. She surveys students in the school orchestra. Why is this data likely to be biased?

<p>The sample is not random and is likely to have a higher proportion of students who enjoy music. (A)</p> Signup and view all the answers

Flashcards

What does Simplify mean?

To make something simpler or easier to understand

Order of operations in expressions.

The operation performed first is squaring (x-2)². Solve inside the parentheses first, then apply the exponent.

What is the lower limit?

The smallest possible value a measurement could be, given its level of precision.

What is the Upper Limit?

The greatest possible value a measurement could be, given its level of precision.

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What are Corresponding Angles?

Angles that occupy the same relative position at each intersection where a transversal crosses two lines.

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What are Alternate Angles?

Angles formed on opposite sides of a transversal crossing two lines, inside the two lines.

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What are Vertically Opposite Angles?

Angles that share a vertex and are opposite each other, formed by two intersecting lines.

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What is the Radius?

A line segment from the center of a circle to any point on the circle.

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What is volume?

The amount of space a 3D object occupies.

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What is a line of symmetry?

A line that divides a shape into two identical halves.

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What is a Graph?

A diagram showing the relationship between two or more sets of data.

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What is the Median?

The middle value in a set of data when ordered from least to greatest.

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What is the Range?

The difference between the largest and smallest values in a data set.

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What is gradient?

A measure of how steeply a line rises or falls.

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What is Enlargement?

A transformation that enlarges or reduces the size of a shape.

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What is work rate?

The rate at which work is done or energy is transferred.

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What is a Kite?

A quadrilateral with two pairs of adjacent sides that are equal in length.

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What is Probability?

A measure of how likely an event is to occur.

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What is the Mean?

A value that represents the 'average' of a set of numbers.

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What is Bias?

A systematic error that favors certain outcomes.

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Study Notes

  • This is a Mathematics Paper 2 for Stage 9 students, designed for use with the curriculum published in September 2020.
  • The test duration is 1 hour and the total mark for the paper is 50.
  • Students are allowed to use a calculator, geometrical instruments, and tracing paper (optional).

Question 1: Simplifying Expressions

  • Simplify x⁴ × x⁵ to x⁹ by adding the exponents.

Question 2: Order of Operations

  • Given the expression 3(x − 2)² / 5, the first operation performed when substituting a value for x is subtracting 2.

Question 3: Rounding and Limits

  • For a book length of 25 cm to the nearest centimetre, the lower limit is 24.5 cm and the upper limit is 25.5 cm.

Question 4: Angles and Parallel Lines

  • In a diagram with two straight lines crossing a pair of parallel lines:
    • Angle a is corresponding to angle b.
    • Angle a is vertically opposite to angle e.

Question 5: Regular Pentagon

  • Each interior angle in a regular pentagon measures 108°.
  • A prism with a regular pentagon cross-section has 5 planes of symmetry.

Question 6: Cylinder Volume

  • Volume of a cylinder is calculated using the formula πr²h where r is radius and h is height.
  • A cylinder with a radius of 7 cm and a height of 15 cm has a volume that is approximately 2310 cm³.

Question 7: Quadratic Equation and Graph

  • In the equation y = x² – 4:
    • When x = -3, y = 5.
    • When x = -1, y = -3.
  • A graph of y = x² – 4 (for x values between –3 and 3) is a parabola with the vertex at (0, -4).

Question 8: Frequency Polygon and Median

  • Temperature and Frequency Data
    • Shows distribution of temperatures in 20 cities
  • To complete frequency polygon plot points using midpoint of temperature range and frequency
  • Median temperature interval requires arranging frequencies to find middle position.

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